<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" ><generator uri="https://jekyllrb.com/" version="3.10.0">Jekyll</generator><link href="https://www.ajayrangarajan.com/feed.xml" rel="self" type="application/atom+xml" /><link href="https://www.ajayrangarajan.com/" rel="alternate" type="text/html" /><updated>2026-01-03T17:39:08+01:00</updated><id>https://www.ajayrangarajan.com/feed.xml</id><title type="html">Ajay Rangarajan</title><subtitle>R&amp;D Senior Software Engineer at Ansys</subtitle><author><name>Ajay Mandyam Rangarajan</name></author><entry><title type="html">The introvert’s guide to visiting every country</title><link href="https://www.ajayrangarajan.com/posts/2025/06/introvert_travel/" rel="alternate" type="text/html" title="The introvert’s guide to visiting every country" /><published>2025-06-05T00:00:00+02:00</published><updated>2025-06-05T00:00:00+02:00</updated><id>https://www.ajayrangarajan.com/posts/2025/06/introverts_travel</id><content type="html" xml:base="https://www.ajayrangarajan.com/posts/2025/06/introvert_travel/"><![CDATA[<html lang="en">
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<section>
<p>
Hey everyone! Gather around, another one of my random thought experiment + vibe coding + optimization + plotting blogs is here!
</p>

<p>
The idea for this started many months ago when I was playing around with the map from <a href="https://patrickstotz.github.io/Travel-Score/">Patrick Stolz</a>. I wrote about it previously <a href="https://www.ajayrangarajan.com/posts/2024/07/travel/">here</a> where I visualized all the places I’ve visited so far and calculated a “Travel Score.” What fascinated me about the original dataset was this beautiful mapping: Population distribution &hArr; Geographic coordinates &hArr; Countries. I mean, come on, if that doesn’t scream “turn me into an optimization problem,” are you even a nerd?
</p>
<p>
Anyway, the idea that popped into my head was this: what if I were an introvert (I’m not) who still wanted to travel the world (which I do)? And I wanted to visit all 197 countries (as listed in the dataset) while meeting the <strong>least possible number of people</strong>. Now <em>that’s</em> a fun project I can get behind!
</p>
<p>
With that idea, it was time to sit down with the data and preprocess it into an easier format. The original data had a much more complicated structure than I liked. The first thing I did was to write the data in a way my simple human brain could understand — a CSV file with grid ID, percentage of population, percentage of land area covered by this grid, and the list of countries this grid maps to. I vibe-coded this from all the complicated files in the original dataset. This one file should be sufficient to start with the optimization algorithm, but as you will see soon, I needed a second file — one where I could connect the grid ID to the geographical coordinates (think of a polygon with each vertex given by its latitude and longitude). These are the grids we see in the <a href="https://patrickstotz.github.io/Travel-Score/">original map</a>. This second mapping would come in handy for extending the optimization to a more “realistic” scenario.
</p>

 <p>
After I started thinking more about this, I realized this is not one optimization but can be expanded into multiple ones based on the assumptions I had made. Here are a few thoughts I can explain before jumping into the algorithms and results (which I know all of you are eager to find out! /s :D). So, the first thing to know is, each grid ID might map to more than one country. Second, for every grid ID we only know the percentage of the population of the world (according to some dataset in some unknown-to-me year), but we do not have country-wise distribution. Now, this introduces our first challenge — assuming we have an optimization algorithm and it picks a grid ID, do we assume we have visited all the countries that correspond to this grid ID or only one country? If only one country, how do we select which country?
</p>

<p>
As it often turns out, one assumption makes your algorithm trivially easy, and removing that assumption makes the algorithm wildly difficult. This turned out to be such an assumption. Let’s look at the two cases below.
</p>
</section>
<section>

<h3>Case 1: All Grids, All Countries Per Grid (Simple Greedy)</h3>
<p>
This is a baby in the world of optimization problems — I pick the lowest population grid per country. If a grid belongs to multiple countries — great! One stop, many stamps. Ok, this is pretty easy (even for me, let alone my Claude-4-powered Cursor) to implement. One prompt, booooom! Implemented, done, time for coffee now. (I did not verify that this is indeed the theoretical minimum though. You will see with the results that they seem reasonable to me.)
</p>

<img src="/assets/pictures/case_1.png" width="300" style="margin-bottom: 20px;"/>
</section>
<section>

<h3>Case 2: All Grids, One Country Per Grid (Hungarian Algorithm)</h3>
<p>
Ok, this was a tough nut to crack. I don’t even know how to start — maybe Cursor does?
</p>

<img src="/assets/pictures/cursor_thinking.png" alt="Lot of the 'thinking' for this was done by Claude-4" style="margin-bottom: 20px;"/>

<p>
Wow, “THOUGHT FOR 15 seconds”!!! This one drove me down a rabbit hole — I ended up reading (and not really understanding) the <a href="https://en.wikipedia.org/wiki/Assignment_problem">assignment problem</a> and apparently something called the <a href="https://en.wikipedia.org/wiki/Hungarian_algorithm">Hungarian algorithm</a>. (Turns out this algorithm was developed by Harold Kuhn, the person who represents the second 'K' in the famous KKT condition in optimization.) Had never heard of that before. These random pursuits do teach me some new concepts! Anyway, back to our problem — this turned out to be much harder to understand and also to get working with the vibe code. It’s still amazing to see how these LLMs can help in actual scientific computing. They can not only do text and simple boilerplate code but actual realistic scientific computing. The caveat, as always, is: if this were to be a real scientific research or engineering product, I would need to ENSURE that the produced code is correct. However, this is just my random curiosity code, so I can live with some tolerance for issues in the code. One thing I had to account for, though, is that there were a few cases (two cases to be exact) where there were two or more countries in exactly one single grid and nowhere else (think of two tiny island nations next to each other — they would share the grid ID and would only be in this one single grid ID. If I assign this grid ID to one, then I can never visit the other unless I reassign the same grid ID).
</p>

<p>
Now, this is where I started comparing the optimum values (which were in the range of 1–3% of the world population) with my own travel map. As of this writing, I have visited 46 countries, but my population encountered was a whopping 25%!!! Unrealistic as it might be that I have “met” 2 billion people, this got me wondering how it is that the algorithm chooses these amazing (for an introvert) locations. Then it hit me — of course, I fly to many of the places (I know, I am guilty of my CO2 emissions — I have written about it earlier <a href="https://www.ajayrangarajan.com/posts/2024/11/travel/">here</a>), and flying is often to big cities which would have high population percentages. (And of course, the fact that I am from India accounts for a lot of the “population encountered”!)
</p>

<p>
The previous optimization would pick grids and assume that an introvert traveller would just teleport between these grids somehow. That is, of course, unrealistic (at least more unrealistic than the premise of this blog), and as anyone already down this path would normally do, I went around looking for a dataset with all airports and landing strips in the world. And surprise, surprise — it exists and is easily available in a simple CSV file. Now the next logical step was to incorporate this into my optimization. This is where the second file I had mentioned before comes in. The airport data comes with the latitude and longitude of each airport. I reverse-mapped this to grid IDs — meaning, for each airport I mapped which grid it was in. To save this reverse mapping, I needed the polygonal data of each of the grids. Ok, now we fly!
</p>

<img src="/assets/pictures/case_2.png" width="300" style="margin-bottom: 20px;"/>

</section>
<section>

<h3>Case 3: Airports, Shared Country Grids (Greedy + TSP)</h3>
<p>
The next case was to use only the grids which have airports as options for us to visit. We can reuse the greedy cover set as before. However, we still have the case that a selected grid (with an airport) could be associated with multiple countries. Now, this is like saying the traveller flew into a specific airport in one country and visited the nearby countries (that are in the same grid) by land, sea, <a href="https://www.limitezero.com/en/">zipline</a>, <a href="https://en.wikipedia.org/wiki/Boquillas_Port_of_Entry">burro</a>, or whatever. This is quite realistic, of course. Running this algorithm was quite easy, but it quickly turned out that the airports chosen are super unknown — like Random-city-landing-strip-03. Anyway, I was able to pick the full set of airports. Now, given that this worked out, I thought why not throw in my CO2 calculation for such a trip? I had the code lying around, and with one prompt, Claude-4 just integrated it into my code here. I went one step further — after integrating the CO2 calculation between all selected airports to all other selected airports, I ran the TSP algorithm to optimize my route. Now I can travel the world, avoid people, and also feel slightly less guilty about flying in an unoptimized way. Again, the TSP was included just because I had the code lying around from yet another earlier <a href="https://www.ajayrangarajan.com/posts/2025/02/aachen-grand-tour/">blog project</a> (I know! Shameless plug to my own previous blog!). To mitigate this random one-landing-strip-to-random-other-landing-strip flight, I would need to find more realistic commercial flight data and maybe use that. I can keep this for another day though. This version introduced “real-world” logistics and a CO2 tracker to account for emissions.
</p>
<img src="/assets/pictures/case_3.png" width="300" style="margin-bottom: 20px;"/>
</section>
<section>

<h3>Case 4: Airports, Host Country Only (Hardcore Realism)</h3>
<p>
Finally, coming to the strictest and cleanest version, where you only strictly fly. You can only count a country if you fly into an airport grid hosted by that country — no border-hopping. This was a bit more challenging than I had anticipated, basically because some countries either do not have airports or the airport database does not assign them correctly. The code processes this first by assigning the airports to host countries. (A side challenge was to ensure that the names of countries in the airport database match the population dataset. I did this by mapping everything into ISO names with some extra mappings just for guarantees.) After assigning host countries, we process countries without airports by checking if there are other airports in the same grid but in a different country. If yes (and it is a yes in EVERY case we consider), we assign the same airport to both countries. Anyway, after this, we throw in the CO2 and the TSP as before. This is probably not as realistic as the previous case, but I thought it would be incomplete without this version. Finally, for fun, below is a CO2-emission-optimized travel map visiting every country in the world by flying. (Note: The dashed red lines represent crossing the date line and due to plotting limitations, they seem like we are zipping across the world in an "unoptimized" way.)
</p>

<img src="/assets/pictures/case_4.png" width="300" style="margin-bottom: 20px;"/>

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      <h3 style="margin-top: 0; color: #2c3e50;">🌍 Introvert Travel Route</h3>
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          <span class="stat-label">Flights:</span> 
          <span class="stat-value" id="flight-count">-</span>
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          <span class="stat-label">Total CO2:</span> 
          <span class="stat-value" id="total-co2">-</span> tons
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<section>
  <h3>Results</h3>
  <p>
    Finally, what everyone (anyone?) has been waiting for!!! How do each of these algorithms stack up against each other? Well, my intuition said the first should be the best (or worst, depending on how you swing) in terms of people encountered, and the fourth being the worst. However, I was not sure of the ordering between 2 and 3. Turns out, limiting ourselves to airport-only grids is almost as good as the free-to-choose-any-grid option. This reinforces the idea that we have a lot of unheard of landing strips and airports in that dataset. Maybe I really need to find that flight connections data after all! The table below summarizes the percent of global population “met” during the journey for each case:
  </p>
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<th style="text-align: center;">Case</th>
<th style="text-align: center;">Travel Mode</th>
<th style="text-align: center;">Grid Constraint</th>
<th style="text-align: center;">Country Constraint</th>
<th style="text-align: center;">Population % Encountered</th>
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        <td>1</td>
        <td>Teleport</td>
        <td>Any</td>
        <td>Shared countries OK</td>
        <td>1.15%</td>
      </tr>
      <tr>
        <td>2</td>
        <td>Teleport</td>
        <td>Any</td>
        <td>Unique per country</td>
        <td>1.58%</td>
      </tr>
      <tr>
        <td>3</td>
        <td>Flights</td>
        <td>Airports only</td>
        <td>Shared countries OK</td>
        <td>1.22%</td>
      </tr>
      <tr>
        <td>4</td>
        <td>Flights</td>
        <td>Airports only</td>
        <td>Unique per country (Host country)</td>
        <td>3.70%</td>
      </tr>
    </tbody>
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</div>
  <p>
    Looking at the table, it was an interesting exercise for me to learn that by flying into remote locations, one can visit all 197 countries and practically encounter &lt;4% of the world (well obviously, we won’t meet everyone in that grid, but it is fair to assume that the number of people we encounter is proportional to the population percentage in that grid). For the people (aka weirdos) who want to play with the code, I will upload it on GitHub.
  </p>
  <p>
PS: I also wanted to try character consistency in the 4o model in just single step like the viral videos were showing. So the images were generated just for fun and to keep the blog more visually appealing. 
</p>
  
</section>
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</html>]]></content><author><name>Ajay Mandyam Rangarajan</name></author><category term="optimization" /><category term="travel" /><category term="maps" /><category term="folium" /><summary type="html"><![CDATA[]]></summary></entry><entry><title type="html">Fashionably Late for Pi Day</title><link href="https://www.ajayrangarajan.com/posts/2025/03/pi_day/" rel="alternate" type="text/html" title="Fashionably Late for Pi Day" /><published>2025-03-22T00:00:00+01:00</published><updated>2025-03-22T00:00:00+01:00</updated><id>https://www.ajayrangarajan.com/posts/2025/03/pi_day_indian_scripts</id><content type="html" xml:base="https://www.ajayrangarajan.com/posts/2025/03/pi_day/"><![CDATA[<html lang="en">
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        .script-Latin { font-family: 'Noto Sans', sans-serif; }
        .script-Devanagari { font-family: 'Noto Sans Devanagari', sans-serif; }
        .script-Bengali, .script-Assamese { font-family: 'Noto Sans Bengali', sans-serif; }
        .script-Gujarati { font-family: 'Noto Sans Gujarati', sans-serif; }
        .script-Gurmukhi { font-family: 'Noto Sans Gurmukhi', sans-serif; }
        .script-Kannada { font-family: 'Noto Sans Kannada', sans-serif; }
        .script-Malayalam { font-family: 'Noto Sans Malayalam', sans-serif; }
        .script-Tamil { font-family: 'Noto Sans Tamil', sans-serif; }
        .script-Telugu { font-family: 'Noto Sans Telugu', sans-serif; }
        .script-Odia { font-family: 'Noto Sans Oriya', sans-serif; }
        .script-Urdu, .script-Kashmiri, .script-Sindhi { font-family: 'Noto Sans Arabic', sans-serif; }
        .script-Manipuri { font-family: 'Noto Sans Meetei Mayek', sans-serif; }
        .script-Ol-Chiki { font-family: 'Noto Sans', sans-serif; } /* Fallback as Noto Sans Ol Chiki might not be available via Google Fonts */
        
        @media (max-width: 768px) {
            .container {
                flex-direction: column;
            }
            
            .preview, .controls {
                min-width: 100%;
            }
            
            .pi-cell {
                font-size: 1rem;
            }
        }
        
        /* Dynamic font sizes based on digit count */
        .small-grid .pi-cell { font-size: 1.5rem; }
        .medium-grid .pi-cell { font-size: 1.2rem; }
        .large-grid .pi-cell { font-size: 0.9rem; }
        .extra-large-grid .pi-cell { font-size: 0.7rem; }
    </style>
</head>
<body>
     <section>
  <p>Yeah, I know, Pi Day already passed. I am fashionably late to the party—by a mere few days—but hey, the circumference of my enthusiasm is irrational, right?</p>

  <p>A couple of weeks back, while spiraling down another rabbit hole (read: procrastinating) for a completely unrelated blog post, I stumbled upon the absolutely brilliant work of Martin Krzywinski whose <a href="https://mk.bcgsc.ca/pi/piday2019/" target="_blank">website</a> I have cited before. For Pi Day 2019, he created an incredible poster featuring Pi represented through characters from scripts across the globe. Mind-blowing concept—I instantly wanted my own.</p>

  <p>Of course, instead of doing the sensible thing (using his ready-made masterpiece), I decided to create my own spin on it: What if everyone could have their own unique Pi poster? Uniqueness powered by—what else—large language models (LLMs).</p>

  <p>Enter Sonnet 3.7, Cursor AI’s shiny new agent mode that my friend couldn’t stop raving about. Perfect timing! With one ambitious prompt (and probably too much optimism), I asked Agent-S to craft Pi posters using all official Indian scripts (scheduled languages with their scripts) listed neatly on <a href="https://en.wikipedia.org/wiki/Languages_with_legal_status_in_India" target="_blank">Wikipedia</a>, in addition to Latin script to accommodate english. Amazingly, Sonnet 3.7 churned out a working Python version in about ten minutes flat—talk about instant gratification!</p>

  <p>But then came the twist: converting everything from Python to JavaScript to embed it neatly into my Jekyll-based website. Let's just say things quickly turned as chaotic as the decimals of Pi itself. My pristine code became an LLM playground. Sonnet randomly rewrote entire sections, turned Jinja templates into spaghetti, and generally made me regret not committing changes frequently enough to GitHub. Lesson learned: commit early, commit often, and never fully trust an overly enthusiastic LLM.</p>

  <p>After several frustrating rounds of 'fix-it-myself' debugging, I waved the white flag and went old-school: copy-pasting code snippets between ChatGPT and my editor, circa 2022. Vintage, but effective. Finally, a functional version emerged—after some JavaScript-induced headaches and website quirks.</p>

  <p>So here is what you can do now:</p>

  <p>Below this ramble, you will find my shiny creation: input your own random seed number, choose your grid size, and voilà! A unique Pi, beautifully represented using the rich tapestry of Indian scripts. Hit "Generate," and you can even download your very own LaTeX file, ready to compile into an A4 poster to adorn your walls. A quick heads-up: you will first need to download and install the NotoSans fonts for the scripts you select—tedious, I know, but think of it as character-building (pun absolutely intended).</p>

  <p>Expanding this to include scripts worldwide is definitely doable (I just did not find an easy way to find the entire database from Noto Sans and also I could not find a way to identify all the various scripts available there!). For anyone brave enough, I have linked my <a href="https://github.com/armandyam/pi_day_indian_scripts" target="_blank">GitHub repository</a>—take it, remix it, and let me know how it goes!</p>

  <p>Happy belated Pi Day! Better late (and nerdy) than never, right?</p>

  <p>
P.S.: I don't personally know the exact digits of Pi (beyond the obvious 3.14...), nor can I verify the accuracy of numbers represented in various scripts. If you spot any mistakes—especially speakers of these languages—please let me know so I can correct them!</p>
</section>


    <div class="container">
        <div class="controls">
            <h2>Settings</h2>
            <div class="form-group">
                <label for="num-digits">Number of Digits:</label>
                <div class="slider-container">
                    <input type="range" id="num-digits" min="10" max="430" value="200" step="10">
                    <div class="slider-value" id="digits-value">200 digits</div>
                    <div class="dimensions-info" id="dimensions-info">(Optimal grid: calculating...)</div>
                </div>
            </div>
            
            <div class="form-group">
                <label for="seed">Random Seed (leave empty for random):</label>
                <input type="number" id="seed" placeholder="e.g. 42">
            </div>
            
            <div class="pi-controls">
                <button id="generate-btn">Generate New Visualization</button>
                <button id="download-latex-btn">Download LaTeX</button>
            </div>
            
        </div>
        
        <div class="preview">
            <h2>Preview</h2>
            <div id="pi-grid-container">
                <div id="pi-grid" class="pi-grid"></div>
            </div>
            
            <div class="stats">
                <h3>Statistics</h3>
                <p id="stats-text">Loading...</p>
                
                <h3>Scripts Used</h3>
                <div id="script-list" class="script-list">
                    <div class="loading">Loading scripts...</div>
                </div>
            </div>
        </div>
    </div>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/seedrandom/3.0.5/seedrandom.min.js"></script>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/decimal.js/10.4.3/decimal.min.js"></script>
    <script src="/assets/pi_functions.js"></script>
    <script>

        let piData = null;
        
        const numDigitsInput = document.getElementById('num-digits');
        const digitsValueDisplay = document.getElementById('digits-value');
        const dimensionsInfo = document.getElementById('dimensions-info');
        const seedInput = document.getElementById('seed');
        const generateBtn = document.getElementById('generate-btn');
        const downloadLatexBtn = document.getElementById('download-latex-btn');
        const piGridContainer = document.getElementById('pi-grid-container');
        const piGrid = document.getElementById('pi-grid');
        const statsText = document.getElementById('stats-text');
        const scriptList = document.getElementById('script-list');
        
        numDigitsInput.addEventListener('input', updateDigitsDisplay);
        generateBtn.addEventListener('click', generateVisualization);
        downloadLatexBtn.addEventListener('click', downloadLatex);
        
        updateDigitsDisplay();
        generateVisualization();

        function updateDigitsDisplay() {
            const numDigits = parseInt(numDigitsInput.value);
            digitsValueDisplay.textContent = `${numDigits} digits`;
            
            const ratio = 1.414; 
            const { rows, cols } = calculateGridDimensions(numDigits);
            
            dimensionsInfo.textContent = `(Optimal grid: ${rows} × ${cols})`;
        }
        
        async function generateVisualization() {
            console.log("🚀 generateVisualization started");

            showLoading();
            
            const numDigits = parseInt(numDigitsInput.value);
            let seed = seedInput.value.trim();
            seed = seed ? parseInt(seed) : null;

            if (seed !== null) {
                seedInput.value = seed;
            }
            if (!seed) {
                seed = Math.floor(Math.random() * 1000000);
                seedInput.value = seed;
            }

            
            try {
                piData = JSON.parse(generateJsonData(numDigits, seed));

                
                renderGrid(piData);
                updateStats(piData);
                
                if (piData.seed && !seedInput.value) {
                    seedInput.value = piData.seed;
                }
                
            } catch (error) {
                console.error('Error generating visualization:', error);
                
            }
        }
        
        function renderGrid(data) {
            piGrid.innerHTML = '';
            piGrid.style.gridTemplateColumns = `repeat(${data.cols}, 1fr)`;
            
            piGridContainer.className = '';
            if (data.rows * data.cols <= 50) {
                piGridContainer.classList.add('small-grid');
            } else if (data.rows * data.cols <= 200) {
                piGridContainer.classList.add('medium-grid');
            } else if (data.rows * data.cols <= 500) {
                piGridContainer.classList.add('large-grid');
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                piGridContainer.classList.add('extra-large-grid');
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            for (let row = 0; row < data.rows; row++) {
                for (let col = 0; col < data.cols; col++) {
                    const cell = data.grid[row][col];
                    const cellElement = document.createElement('div');
                    
                    let scriptClass = `script-${cell.script}`;
                    if (cell.script === "Ol Chiki") {
                        scriptClass = "script-Ol-Chiki";
                    }
                    
                    cellElement.className = `pi-cell ${scriptClass}`;
                    
                    if (cell.highlight) {
                        cellElement.classList.add('highlight');
                    }
                    
                    cellElement.textContent = cell.digit;
                    cellElement.dataset.script = `${cell.digit} ${cell.script} (${convertToLatin(cell.digit, cell.script)})`;
                    
                    piGrid.appendChild(cellElement);
                }
            }
        }
        
        function updateStats(data) {
            statsText.textContent = `Using ${data.total_scripts_used} different Indian scripts to display ${data.rows * data.cols} digits of π in a ${data.rows}×${data.cols} grid. Seed: ${data.seed}`;
            
            scriptList.innerHTML = '';
            
            const sortedScripts = Object.entries(data.script_usage)
                .sort((a, b) => b[1] - a[1])
                .map(([script, count]) => ({ script, count }));
            
            sortedScripts.forEach(item => {
                const scriptTag = document.createElement('div');
                
                let scriptClass = `script-${item.script}`;
                if (item.script === "Ol Chiki") {
                    scriptClass = "script-Ol-Chiki";
                }
                
                scriptTag.className = `script-tag ${scriptClass}`;
                scriptTag.textContent = `${item.script} (${item.count})`;
                scriptList.appendChild(scriptTag);
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        }
        
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            piGrid.innerHTML = '<div class="loading">Generating visualization...</div>';
            scriptList.innerHTML = '<div class="loading">Loading scripts...</div>';
            statsText.textContent = 'Loading...';
        }
        
        async function downloadLatex() {
            if (!piData) {
                alert('Please generate a visualization first');
                return;
            }
            
            try {
                const title = "π in Indian Scripts"; 


                const latex = generateLatex(piData.grid.map(row => row.map(cell => cell.digit)), 
                                            piData.grid.map(row => row.map(cell => cell.script)), 
                                            piData.rows, 
                                            piData.cols, 
                                            "π in Indian Scripts", 
                                            piData.pi_mask);

                                
                downloadFile('pi_visualization.tex', latex);
                
            } catch (error) {
                console.error('Error generating LaTeX:', error);
                alert('Failed to generate LaTeX. Please try again.');
            }
        }
        
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            a.href = url;
            a.download = filename;
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</body>
</html>]]></content><author><name>Ajay Mandyam Rangarajan</name></author><category term="random" /><category term="latex" /><category term="python" /><summary type="html"><![CDATA[:root { --primary-color: #3498db; --secondary-color: #2980b9; --accent-color: #e74c3c; --text-color: #333; --light-gray: #f5f5f5; --border-color: #ddd; } *, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }]]></summary></entry><entry><title type="html">Darmstadt in a day capturing time in one image</title><link href="https://www.ajayrangarajan.com/posts/2025/02/hdtr_darmstadt/" rel="alternate" type="text/html" title="Darmstadt in a day capturing time in one image" /><published>2025-02-20T00:00:00+01:00</published><updated>2025-02-20T00:00:00+01:00</updated><id>https://www.ajayrangarajan.com/posts/2025/02/high_dynamic_time_ranging_darmstadt</id><content type="html" xml:base="https://www.ajayrangarajan.com/posts/2025/02/hdtr_darmstadt/"><![CDATA[<html lang="en">
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    <p>Many years ago, like countless others before me, I had the idea of capturing a scene over time and merging the images into a single composition. There are two obvious ways to do this: a straightforward time-lapse or a single image where slices come from different points in time. As with many of my grand ideas, this one remained just that—until now. Thanks to LLMs making my procrastination harder to justify, I finally decided to give this idea a shot.</p>
    
    <p>When I revisited this idea, I found that there’s actually a term for it: <strong>High Dynamic Time Ranging (HDTR)</strong>. My original inspiration came from <a href="https://www.eirikso.com/2011/01/04/one-year-in-one-image/" target="_blank">Eirik Solheim’s project</a>, where he merged an entire year’s worth of photos into one seamless image. His results were stunning, but unfortunately, I don’t live in a place with breathtaking Norwegian forests in my backyard. My first attempt, using my GoPro on my apartment balcony, was... let’s just say, less inspiring.</p>

    <p>While searching for more examples, I stumbled upon Martin Krzywinski’s <a href="https://mk.bcgsc.ca/fun/hdtr/?home" target="_blank">incredible blog</a> (I got to know the term "HDTR" from his blog as well). He’s taken this to another level, and in fact, most of the code for this project was based on his work. (He has an excellent website with so many fun projects. His blogs have become one of my "always-open" tabs on by browser and I strongly recommend checking it out) However, I needed better images, and I found a fantastic resource: <a href="https://www.foto-webcam.eu/" target="_blank">this website</a>, which offers real-time and historical images from several cameras all over Europe, including three locations in Darmstadt. They archive images every 10 minutes over several years, which was exactly what I needed.</p>
    
    <p>I chose to process images from the spring equinox, downloading images for a 24 hour window (starting at March 21 6AM to March 22 5:50 AM). The approach was simple: sort the images chronologically, slice each one into strips of width w/N (where w is the image width and N is the number of images), and place each strip in the corresponding position of the final composition. The first results had visible bands where slices joined, as seen below:</p>
    
    <p><img src="/assets/pictures/darmstadt_west_left_to_right.jpeg" alt="Banded HDTR Image"></p>
    
    <p>To reduce the abrupt transitions, I applied a simple spatial averaging technique. This blends neighboring slices, softening some of the visual jumps but they are still dominant.</p>
    
    <p><img src="/assets/pictures/darmstadt_west_left_to_right_spatial.jpeg" alt="Spatial Averaging"></p>
    
    <p>Next, I incorporated temporal blending by averaging overlapping time slices with weighted contributions from adjacent images. This further smooths the transitions, making the image appear more continuous. To this, a few things like the time data is added. </p>
    
    <p><img src="/assets/pictures/darmstadt_west_left_to_right_temporal.jpeg" alt="Final Processed HDTR Image"></p>
    
    <p>Since the composition can be arranged in multiple ways: left-to-right, right-to-left, top-to-bottom, and bottom-to-top - I generated all four versions for each of the three location in Darmstadt. You can view all these images below. Personally to me the classic left-to-right and then top-to-bottom images seem to look best. The other two combinations produce awkward photos in my opinion. </p>

    <div class="dropdown-container">
        <label for="location-select">Select a Location:</label>
        <select id="location-select" onchange="updateGallery()">
            <option value="luisenplatz">Luisenplatz</option>
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            <option value="darmstadt-east">Darmstadt East</option>
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    <p>Encouraged by the results, I decided to take it a step further and create an HDTR image for the entire year of 2024. I selected 6 PM as the reference time (this time was recommended by the o1 model after two minutes of thinking based on sun set times and the location info, which I sort of agreed with) and collected one image per day. Just like the earlier approach, I first generated a simple banded version before applying blending techniques. Given the high-resolution images (6000x4150 pixels), processing 365 of them took quite some time. Unfortunately, the final output was not as good as expected. It goes to show that for such a year-long image blending, one needs to have very clearly defined seasons. Sigh!</p>
    
    <p><img src="/assets/pictures/darmstadt_east_left_to_right_temporal_year.jpeg" alt="Yearly HDTR Image"></p>
    
    <p>You can find a detailed tutorial and the math behind this on <a href="https://mk.bcgsc.ca/fun/hdtr/?method" target="_blank">Martin Krzywinski's blog</a>. For those who’d like to experiment with this technique, I’ve made my code available on <a href="https://github.com/armandyam/hdtr_photo_creation" target="_blank">GitHub</a>. I considered exploring more sophisticated blending techniques, perhaps even some edge-detection-based optimization, but for now, I’m moving on to my next project. I’ll come back to refine this later! </p>
    </section>

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</html>]]></content><author><name>Ajay Mandyam Rangarajan</name></author><category term="interests" /><category term="darmstadt" /><category term="photography" /><category term="python" /><summary type="html"><![CDATA[]]></summary></entry><entry><title type="html">The grand tour of Aachen</title><link href="https://www.ajayrangarajan.com/posts/2025/02/aachen-grand-tour/" rel="alternate" type="text/html" title="The grand tour of Aachen" /><published>2025-02-04T00:00:00+01:00</published><updated>2025-02-04T00:00:00+01:00</updated><id>https://www.ajayrangarajan.com/posts/2025/02/aachen_grand_tour</id><content type="html" xml:base="https://www.ajayrangarajan.com/posts/2025/02/aachen-grand-tour/"><![CDATA[<html lang="en">
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    <p>Some experiments start small. A simple question, a little curiosity—just a modest goal of optimizing a walk between fountains. But then, the dataset gets bigger. The scope expands. And suddenly, you’re looking at a 101 km optimized walking tour of Aachen, covering every fountain, sculpture, garden, and Denkmal (monument) the city has to offer.</p>

    <p>This was not the original plan.</p>

    <p>It all started with my first <a href="https://armandyam.github.io/posts/2024/11/aachen-fountains/" target="_blank">fountain-optimizing blog post</a>, where I used the Traveling Salesman Problem (TSP) to find the best route between Aachen’s fountains. But then I stumbled upon a much larger dataset from <a href="https://de.wikipedia.org/wiki/Liste_der_Denkm%C3%A4ler,_Brunnen_und_Skulpturen_in_Aachen" target="_blank">Wikipedia</a>—one that included not just fountains, but sculptures, monuments, and gardens too. At this point, it was clear: I had to go all in.</p>

    <p>Turns out, optimizing a 101 km route with hundreds of stops is no joke. Running the simulated annealing algorithm on my 2015 MacBook Pro took nearly a full day. Watching my laptop churn through permutations at a pace best described as <b>leisurely</b> made me question some of my life choices. But, in the end, it worked!</p>

    <p>As before, I fed the location data into a TSP solver using simulated annealing, letting the algorithm work its magic. The result? A path that covers all major artistic and historical landmarks in Aachen in just over 100 km. It’s still a long walk, but hey, at least it’s optimized.</p>

    <p>Let’s be honest: walking this entire route in one go is completely out of the question, at least based on my current fitness levels. Running it? Absolutely not. But biking—biking might still be an idea. A very bad idea, but an idea nonetheless.</p>

    <p>That said, it’s probably best not to make this an actual goal. I need to remind myself that just because something is computationally interesting doesn’t mean I have to physically suffer for it. Probably.</p>

    <p>If the original fountain walk was a fun side quest, this is the full-scale main mission. If anyone out there feels like attempting the <b>Grand Tour of Aachen</b> next summer, let me know—I might need company (no seriously).</p>

    <p>You can download the <a href="/assets/optimized_aachen_grand_tour.kml" download="optimized_aachen_grand_tour.kml">larger KML file</a> to import into Google Maps for your own adventure.</p>

    <p>Who knew a simple walk could turn into an optimization problem? Well, probably everyone who knows me.</p>

    </section>


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</html>]]></content><author><name>Ajay Mandyam Rangarajan</name></author><category term="interests" /><category term="aachen" /><summary type="html"><![CDATA[]]></summary></entry><entry><title type="html">A (near-)optimal tour of Aachen</title><link href="https://www.ajayrangarajan.com/posts/2024/11/aachen-fountains/" rel="alternate" type="text/html" title="A (near-)optimal tour of Aachen" /><published>2024-11-28T00:00:00+01:00</published><updated>2024-11-28T00:00:00+01:00</updated><id>https://www.ajayrangarajan.com/posts/2024/11/aachen_fountain</id><content type="html" xml:base="https://www.ajayrangarajan.com/posts/2024/11/aachen-fountains/"><![CDATA[<html lang="en">
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        <p>
            When I lived in Aachen—a city brimming with history, charm, and yes, <a href="https://aachen.de/en/ts/PDFs/City-of-fountains-and-monuments.pdf" target="_blank">fountains</a>—my friend and I made an ambitious summer plan: visit every fountain in town. A quintessential “summer” goal. But summer after summer, we let that plan evaporate. Now, years later, I’m finally solving this puzzle. Not just solving it—I’m turning it into a nice small computational adventure.
        </p>
        <p>
            Aachen is famous for its fountains, each telling its own story. From the playful <a href="https://de.wikipedia.org/wiki/Puppenbrunnen" target="_blank">Puppenbrunnen</a> to the iconic <a href="https://de.wikipedia.org/wiki/Elisenbrunnen" target="_blank">Elisenbrunnen</a>, these waterworks are scattered throughout the city. They’re not just decorative but an integral part of the city’s identity. So, when I decided to “finally do this,” I thought, why not make it fun and nerdy as always? I’m not just someone who strolls from fountain to fountain—I have some computational science skills and coding expertise! Naturally, I devised a (near-)optimal solution to the <em><a href="https://en.wikipedia.org/wiki/Travelling_salesman_problem" target="_blank">Traveling Salesman Problem</a></em> (TSP) to plan the route, even if I might never actually walk it!
        </p>
        <p>
            As many of you might already know the TSP is a classic optimization problem where a "salesman" must visit \( N \) cities (or fountains, in our case), minimizing the total distance traveled and returning to the starting point. Formally, given a set of locations \( \{1, 2, \dots, N\} \) with distances \( d(i, j) \) between them, the goal is to minimize:
        </p>
        <p>
            \[
            \text{Total Distance} = \sum d(i, i+1)
            \]
        </p>
        <p>
            Of course, the TSP is NP-complete and for larger \( N \) (which in our case is around 32), finding the exact solution via brute force is computationally infeasible (\( O(N!) \)). Instead, we settle for approximate solutions using heuristics like <em>simulated annealing</em>.
        </p>
        <p>
            Now, to get the location of the fountains themselves, I fould a helpful list from <a href="https://commons.wikimedia.org/wiki/Fountains_in_Aachen" target="_blank">Wiki Commons</a>, where each fountain has its coordinates, name, and a photo. After some <a href="https://pypi.org/project/beautifulsoup4/" target="_blank">beautifulsoup</a> parsing and cleaning (and nudging overlapping fountains by 10&nbsp;m to make them unique), I fed the data into my code. (The overlapping fountains had to be moved to make sure the optimizer does not fail with zero distances between points). This is where I tried two types of distances the first being "as the crow flies" and the second the walking distance between these (to make sure such a tour is feasiable within a days effort). Now for each of these, I had to calculate the distance matrix between every pair of points, \( d(i, j) \). For this, I used the following methods:
        </p>
       <section>
        <h3>Case 1: As the Crow Flies</h3>
        <p>
            This was the easy case and I used the <a href="https://en.wikipedia.org/wiki/Haversine_formula" target="_blank">Haversine formula</a>:
        </p>
\[
d(i, j) = 2r \cdot \arcsin\left(\sqrt{\sin^2\left(\frac{\phi_j - \phi_i}{2}\right) + \cos(\phi_i) \cos(\phi_j) \sin^2\left(\frac{\lambda_j - \lambda_i}{2}\right)}\right)
\]
        <p>
        where <em>r</em> is the Earth's radius, <em>&phi;</em> is latitude, and <em>&lambda;</em> is longitude. This gives the “straight-line” distance between fountains.
        </p>
        <h3>Case 2: Walking Paths</h3>
        <p>
            This case is of course, much harder to calculate and I ended using the <a href="https://openrouteservice.org/" target="_blank">OpenRouteService API</a> to compute the actual walking distances. The API returned a distance between two latitude longitude pairs and also a list of coordinates for the walking path. This makes the solution more realistic for those of us without wings. The idea and parts of the code for using the route service came from this blog <a href="ttps://towardsdatascience.com/solving-geographic-travelling-salesman-problems-using-python-e57284b14cd7" target="_blank">here</a> where a different optimizer is used for the same problem. 
        </p>
           </section>
        <p>
            Both distance matrices were fed into a simulated annealing algorithm (thanks, <a href="https://pypi.org/project/frigidum/" target="_blank">Frigidum</a>!). The algorithm mimics the cooling process of metals, finding a near-optimal route by progressively "cooling" the search space. I did battle with the original optimizer - <a href="https://www.math.uwaterloo.ca/tsp/concorde.html" target="_blank">concorde</a>  as in the blog but failed to get it to run successfully on my laptop so I had to resigned to using simulated annealing as mentioned in this <a href="https://stackoverflow.com/questions/71196078/scalable-implementation-of-the-travelling-salesman-problem-in-python" target="_blank">Stack Overflow answer</a>. 
        </p>

        <p>
        Coming to the actual results, you can explore it below with a dropdown menu allowing you to change from "As the Crow Flies" to "Walking Distance". You can hover over the markers to display some basic info about the fountins with an image from Wiki Commons. How did I choose the starting point I hear you asking? Well the starting fountain is chosen based on proximity to the geographic mean of all points—a little cherry on top. Now this solution of course, is great, its under 20&nbsp;km so a days worth of walking would be enough to cover all of them within a day. (Also note that as we have are doing a round trip the total distance travelled does not depend on the starting point choosen!)
    </p>

        <p>
            After solving this computationally, it’s time for the fun part: visiting Aachen again and walking the optimized route. All my friends (and frenemies! :D), if you’re reading this, pack your walking shoes. We’ve got an Aachen trip coming up next summer.
        </p>
        <p>
        If any of you want to use this for your own geeky walking trips, then head over to my <a href="https://github.com/armandyam/aachen-fountain-visualizer" target="_blank">semi documented code</a> on github, signup for your own OpenRouteService API and put this into your environment variable and setup a CSV file of your favourite places to visit. For those of you wanting to do this specific Aachen fountain trip, you can download the <a href="/assets/optimized_aachen_fountain_route.kml" download="optimized_aachen_fountain_route.kml">KML file</a> which you can import into your google maps. 
        </p>

        <p>To view this route on Google My Maps:</p>
        <ol>
            <li>Download the file using the link above.</li>
            <li>Go to <a href="https://www.google.com/mymaps" target="_blank">Google My Maps</a>.</li>
            <li>Click on "Create a new map" and use the "Import" option to upload the file.</li>
        </ol>

        <p>Of course, I should thank chatGPT for helping me with everything on this project (like many other projects!) with ideas, code, documentation, building, blog, README and so on.</p>

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</html>]]></content><author><name>Ajay Mandyam Rangarajan</name></author><category term="interests" /><category term="aachen" /><summary type="html"><![CDATA[]]></summary></entry><entry><title type="html">Travel Dreams vs. Climate Realities</title><link href="https://www.ajayrangarajan.com/posts/2024/11/travel/" rel="alternate" type="text/html" title="Travel Dreams vs. Climate Realities" /><published>2024-11-07T00:00:00+01:00</published><updated>2024-11-07T00:00:00+01:00</updated><id>https://www.ajayrangarajan.com/posts/2024/11/flights</id><content type="html" xml:base="https://www.ajayrangarajan.com/posts/2024/11/travel/"><![CDATA[<html lang="en">
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Last updated: November, 3, 2025

<h2> Part 1 – Mapping My Air Travel Adventures</h2>

<p>I love <a href="https://armandyam.github.io/others#travel_map">travelling</a>. Whether it’s the excitement of exploring new places, the inevitable collection of random souvenirs that always seem like a good idea at the time (I am looking at you "random rocks from the Lima shore"), or just the feeling of temporarily escaping the daily grind, it’s something I truly enjoy. (I even made it into a game for myself by searching for a <a href="https://armandyam.github.io/posts/2024/07/travel/">"Travel-Score"</a> to dunk on friends and family) But let’s be real—travelling isn’t exactly an environmentalist’s best friend. Every flight I take contributes to the massive, invisible CO₂ cloud floating, and that got me thinking: How bad is it, really?</p>

<p>So, in the spirit of both curiosity and eco-guilt, I decided to dive into the numbers. I also wanted to have my facts right before I get <a href="https://en.wikipedia.org/wiki/Flight_shame">"flight shamed"</a>. I documented every single flight I’ve taken since I was born. Yes, every flight—because I’m nothing if not thorough. And for those of you wondering, flights with layovers count as separate ones for this calculation. This resulted in digging into my old emails and photos to recollect any trips and also of course directly from memory. I wrote them down in a simple file with the year, departure and arrival city name.</p>

<p>I then used the city names to find their exact latitude and longitude with the help of <a href="https://geopy.readthedocs.io/en/stable/">geopy</a> and an <a href="https://github.com/armandyam/maps_kml_generator">old script</a>. Once I had those, I calculated the distance between the cities using the <a href="https://en.wikipedia.org/wiki/Haversine_formula">haversine formula</a>. The result was a shocker: I've flown far enough to make a small dent in the ozone layer and I have taken 139 flights as of today! </p>

<p>Next, I used the <a href="https://pypi.org/project/transport-co2/">transport_co2</a> library to estimate the CO₂ emissions based on the distance for each flight. After calculating all that, I thought, why not slap it on a map? Despite not being my favourite type of projection, I used the Mercator projections as the others produced ugly corners in the visualization. I always wanted to create a map like this to try and recreate the old <a href="http://fbmap.bitaesthetics.com/">Facebook friends map</a>. I got the ideas for the color-coding from <a href="https://blog.hugo-larcher.com/flight-data-visualisation-with-pandas-and-matplotlib-ebbd13038647">this</a> blog where a power law scaling is recommended for small data sets (which it is in this case, thankfully!). Of course, the color coding is done based on the CO₂ emissions: the darker the color, the lower the emissions. You can zoom into the map and also hover on each flight path to get an estimate of the tons CO₂ equivalent emissions (tCO₂e).</p>

  <!-- Create an element where the map will take place -->
  <svg id="my_dataviz" width="800" height="600"></svg>

  <!-- Tooltip div -->
  <div class="tooltip" id="tooltip"></div>


<!-- <p>The bar chart shows the year by year emissions, with notable peaks in the years around 2016 to 2018 that corresponds to my time attending conferences presenting my PhD work. The drop in 2019-2022 is obvious and finally the large 2023 emissions is due to the big trip. </p> -->


<div id="my_dataviz_bar"></div>
<p>&nbsp;&nbsp;&nbsp;</p>


<h2>Part 2 – What Does This Carbon Emission Actually Mean?</h2>


<p>Okay, so now that I’ve mapped out all the flights I’ve taken (and probably scared myself with those numbers), I wanted to figure out just how much this 111.65 tCO₂e actually means in real-world terms. Because, let’s face it, throwing a massive number out there is one thing, but unless I’m visualizing it in relation to something I know, it’s just another abstract figure. So, I dug deeper.</p>

<p> The easiest way I thought of visualizing this is to do some sort of <a href="https://en.wikipedia.org/wiki/One-factor-at-a-time_method">one-factor-at-a-time</a> sensitivity of analysis comparing the total cost of my flights against various lifestyle factors such as transport methods, food choices, number of trees required to offset this and also the carbon cost of this. Of course, this is not a scientific study but only something based on a few hours of doing "internet research". So take this with <a href="https://www.smithsonianmag.com/travel/spanish-mountain-made-salt-180969946/">mountains of salt</a>!</p>

<p> Note: I am only comparing the carbon footprint of flights against other factors, but the total carbon footprint of a person would involve all these factors combined.</p>

<h3>How Far Could I Have Gone in Other Transport Modes?</h3>

<p>&nbsp;&nbsp;</p>

<p>First up, I thought, "How does flying compare to other modes?" What if I had chosen other means of transportation? How far could I have traveled using other modes? To keep a standard I measured each mode of transport in terms of number of Earth’s equatorial circumference which is about <a href="https://coolcosmos.ipac.caltech.edu/ask/57-How-large-is-Earth-#:~:text=Earth's%20circumference%20(the%20distance%20all,miles%20(about%2012%2C756%20kilometers)">40,075 km</a> (Hover over each bar to view the distance as a multiple of Earth's circumference)</p>

<p>I used the same <a href="https://pypi.org/project/transport-co2/">transport_co2</a> for the other modes of transport (except walking and bicycle, more on those below). From this library, I can calculate the emitted CO₂ for a given distance travelled, however, I wanted to calculate the other way around i.e., calculate the distance for a given CO₂ emitted. In addition, I did not want to find out the inner workings of the function but made the assumption that a larger distance would result in a larger CO₂ emission. With that assumption, I was able to implement a simple bisection method to find out the distance for a given CO₂ emitted, specifically the total CO₂ emitted by all my flights taken so far. </p>

<p>As mentioned before, the distances for walking and biking were not from transport_co2 library instead calculated based on calorie consumption and CO₂ emissions associated with that energy. To estimate the CO₂ offset by walking or biking, I assumed an annual vegan diet's carbon footprint—around 1.5 tCO₂e per year as mentioned <a href="https://www.greeneatz.com/foods-carbon-footprint.html">here</a>. Based on an average daily intake of 2600 calories.</p>

<p>For walking, assuming 80 calories burned per kilometer as mentioned <a href="https://timesofindia.indiatimes.com/life-style/health-fitness/fitness/how-many-calories-are-burned-in-walking-1-km/articleshow/111300054.cms">here</a>, the distance required to offset a CO₂ target can be estimated using:</p>

<p>\[
\text{Distance walked} = \frac{\text{CO}_2 \text{ target} \times \text{Calories per year}}{\text{CO}_2 \text{ emissions from diet} \times \text{Calories burned per km}}
\]</p>

<p>Similarly, for biking, where the calorie burn is about 23 calories per kilometer as mentioned <a href="https://www.canyon.com/en-id/blog-content/advice/calories-burned-cycling/b24062022.html">here</a>, the distance required is:</p>

<p>\[
\text{Distance biked} = \frac{\text{CO}_2 \text{ target} \times \text{Calories per year}}{\text{CO}_2 \text{ emissions from diet} \times \text{Calories burned per km}}
\]</p>

<p>Where:
\[
\begin{array}{rl}
\text{CO}_2 \text{ target} & = \text{The total emissions from all my flights} \\
\text{Calories per year} & = 2600 \times 365 \, \text{kcal}
\end{array}
\]
</p>


<p>Of course, these are just fun numbers to calculate and don't have a rigorous scientific basis. However, what was interesting to see was that some modes of transport turned out to be more efficient than walking or biking. This perhaps concurs with what is already <a href="https://en.wikipedia.org/wiki/Energy_efficiency_in_transport">known</a></p>

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<h3>Years of Diet Comparison – Meat Lovers, Take Note!</h3>

<p>&nbsp;&nbsp;</p>

<p>
    We all know that our food choices can make a big difference in reducing CO₂ emissions. I wanted to see how my CO₂ emissions from flying stack up against the emissions saved by different diets. For example, in how many years would a meat eater emit the same CO₂ as a vegan? Although I’ve mostly been vegan for a few years, this comparison helps put the impact of flights into perspective against everyday choices like diet.
</p>

<p>
    Using the numbers from <a href="https://www.greeneatz.com/foods-carbon-footprint.html">here</a> and the calculations shown below, we can estimate the number of years for each diet to offset my total flight CO₂ emissions:
</p>

<p style="font-size: 1.2em; font-style: italic; text-indent: 20px;">
    \[
    Y_{\text{diet}} = \frac{\text{Total CO₂ from flights}}{\text{Yearly CO₂ from each diet}}
    \]
</p>

<p>We see below the equivalent years (represented by number of birthday emojis 🎂) of different diets to offset the total CO₂ emitted by my flights so far:</p>
  
  <div class="emoji-chart">
        <div class="emoji-row">
            <div class="diet-label">Meat Lover (34 years):</div>
            <div id="meat-emojis" class="emoji-display"></div>
        </div>
        
        <div class="emoji-row">
            <div class="diet-label">Average Diet (45 years):</div>
            <div id="average-emojis" class="emoji-display"></div>
        </div>
        
        <div class="emoji-row">
            <div class="diet-label">No Beef Diet (59 years):</div>
            <div id="no-beef-emojis" class="emoji-display"></div>
        </div>
        
        <div class="emoji-row">
            <div class="diet-label">Vegetarian (66 years):</div>
            <div id="vegetarian-emojis" class="emoji-display"></div>
        </div>

        <div class="emoji-row">
            <div class="diet-label">Vegan (74 years):</div>
            <div id="vegan-emojis" class="emoji-display"></div>
        </div>
    </div>

<p>&nbsp;&nbsp;</p>

<p>It is good to know that the difference is substantial and well within a single person's lifetime. So, this gives me hope that our lifestyle choices can realistically impact our CO₂ emissions. (Note: I realize that diet is an emotionally charged topic and I promise to keep my (very mild) judgment in check! 😄)</p>

<!-- <h3>Apartment Size Equivalent – Downsizing Anyone?</h3>
<p>Next up, was the size of apartments. A larger living space requires more energy for heating (if living in colder countries) and electricity. Using the estimates from here, one can calculate how much Ever wondered how much space all that CO₂ could fill? Well, if we translated those emissions into an apartment size, my CO₂ output is the equivalent of living in a 33.63 m² apartment. Not the coziest of spots but still, that’s a lot of space dedicated to my carbon footprint. Could I at least get a loft with a view?</p>
 -->

<h3>Number of Trees to Plant – Start Digging Holes</h3>

<p>&nbsp;&nbsp;</p>

<p>We know that planting trees is one of the effective methods to offset our emissions. How many trees would it then take to offset my flight emissions alone? According to <a href="https://onetreeplanted.org/blogs/stories/how-much-co2-does-tree-absorb">this</a> resource a mature tree absorbs around 10 kg of CO₂ every year. So, then to offset my emissions, I’d need to plant a whopping 11165 trees. That's an entire forest! Guess I’d better start clearing my weekends if I want to make up for all those flights. Furthermore, one cannot just go around planting a single species of tree over acres of land leading to monocultures. Various restorative methods yield varying results. Further, they really start contributing to CO₂ removal after they are mature meaning, we need to grow them for years before we start seeing results. </p>

<p> Apart from actually contributing to NGOs that do good work, some <a href="https://en.wikipedia.org/wiki/Slacktivism">slacktivists</a> like me can help by using something like <a href="https://www.ecosia.org/Ecosia">Ecosia</a> which is a search engine that uses their profits to plan trees (I am in no way associated to them!). In addition, one can directly contribute to their cause to plant trees. In my case, this would <a href="https://plant.ecosia.org/products/trees-for-climate-action?variant=37125904761006">cost</a> me around 27912€. This is definitely something I hope to offset!</p>

<h3>Cost to Offset – Can I Pay My Way Out of This?</h3>

<p>&nbsp;&nbsp;</p>

<p>I know carbon offsets are controversial but while writing this, I had a chance to read up a little bit about them. They seem to be some good number of high quality offset opportunities while at the same time one has low-quality cheap offset methods which are questionable at best (looking at you <a href="https://www.ucl.ac.uk/news/headlines/2019/nov/ryanair-carbon-offset-programme-woefully-inadequate">Ryanair</a>!). I believe, we are beyond the point where just "avoiding deforestation" (or <a href="https://unfccc.int/topics/land-use/workstreams/redd/what-is-redd">REDD+</a>) is sufficient and we actually need positive action towards offsets. Of course, this market is also quite fluctuating and there isn't a fixed number to tell how much it costs and what is the quality of this. You can read up more about this <a href="https://www.bloomberg.com/professional/insights/sustainable-finance/long-term-carbon-offsets-outlook-2023/">here</a>. We of course, need both technology based and nature based solutions for this as well.</p>

<p>All in all, this is still a fun blog post and not a serious scientific research article so I want some number to calculate, so I just ended up using the one from <a href="https://www.reuters.com/sustainability/climate-energy/carbon-offset-price-25-35ton-would-boost-climate-action-adb-climate-envoy-2023-11-16/">here</a> and from that my flights would cost me between <span>$</span> 2791 to <span>$</span> 3908. That’s more than the cost of a few round-trip tickets! Sigh—I guess the price of this first world hobby also comes with a hefty environmental tax.</p>

<h3>Final remarks</h3>

<p>&nbsp;&nbsp;</p>

<p>This blog started as a fun conversation with a friend about plotting flight paths in Python and ended up taking me on a philosophical journey, reckoning with my CO₂ emissions.</p> 

<p>Some of you might wonder: won’t the numbers and images here change as I take more flights? They will! So, I made this blog dynamic (thanks to <a href="https://jinja.palletsprojects.com/en/stable/jinja2">Jinja2</a> for my fellow nerds) and set it to update whenever I add new flights to my database.</p> 

<p>In the end, writing this has reminded me of my privilege to travel and the not-so-small environmental cost that comes with it. Yes, it’s a bit hypocritical to say I care about the planet while booking a flight for my next adventure. But I’m doing my best to keep a lighter footprint where I can: I’ve lived vegetarian most of my life and switched to veganism, managed without a personal car so far thanks to good public transport, and try to rely on renewable energy for electricity. It doesn’t fully justify flying—I know that—but it’s a challenge I’m aware of and working to improve. Who knows, maybe someday I’ll trade air miles for virtual ones and pioneer ‘sustainable wanderlust’!</p>

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</html>]]></content><author><name>Ajay Mandyam Rangarajan</name></author><category term="travel" /><category term="environment" /><summary type="html"><![CDATA[]]></summary></entry><entry><title type="html">Part 1: Training, Data, and Debugging: My training logs for my first ironman race</title><link href="https://www.ajayrangarajan.com/posts/2024/10/sports/" rel="alternate" type="text/html" title="Part 1: Training, Data, and Debugging: My training logs for my first ironman race" /><published>2024-10-06T00:00:00+02:00</published><updated>2024-10-06T00:00:00+02:00</updated><id>https://www.ajayrangarajan.com/posts/2024/10/training</id><content type="html" xml:base="https://www.ajayrangarajan.com/posts/2024/10/sports/"><![CDATA[<html lang="en">
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<p>Over the past month, many of you have reached out to me about my Ironman triathlon experience. So, naturally, I decided to humble-brag and turn it into a blog series. In this series, I’ll be documenting the ups, the downs, and everything in between—covering my training (yes, I survived), my vegan nutrition, and a few coding hacks that helped me train smarter (because of course, there’s code involved).</p>


<p>In 2014, I watched a friend’s friend (you know the type) complete an Ironman, and it sparked a wild idea: <em>What if I could do that too?</em> There was just one minor hitch—I could barely swim a lap without gasping for air, didn’t own a bike (unless that rusty €30 bike counts), and could only manage a 2-3 km run, with plenty of snack breaks. But hey, why let little details like that stop me?</p>

<p>Back then, my goal was simple: survive the run part of a triathlon. So, I signed up for a half marathon. Naturally, the next logical step was a full marathon a year later. And to top it off, I started taking swim lessons at my university, because apparently, I love to suffer. Shoutout to my friend Aadu Huli, who unofficially took on the role of my motivator—dragging me to the pool until I upgraded my swim style from "drowning" to a somewhat decent breaststroke.</p>

<p>By 2017, I bought my first road bike and signed up for a sprint triathlon. That’s when I faced my first open water swim—a slightly terrifying experience where I was proud just to come out of the water still breathing. Fast forward to 2018, and I’d tackled three Olympic-distance triathlons, still holding onto my trusty breaststroke, like an old friend.</p>

<p>Then came the pandemic—because nothing says “pause your ambitions” like a global lockdown. Fast forward to 2023, and I found myself in a new city with fresh opportunities—and a sweet perk from work: freestyle swim coaching. Plus, joining my local triathlon club’s summer camp kicked my training into high gear. The cherry on top? A brand-new bike, which made me feel like a pro (or at least look the part). With everything in place, I decided it was time to tackle the big one—the Ironman.</p>

<p>Now, what kind of blog would this be without some nerdy data? I’ll be sharing my training stats (thanks to the intervals.icu API) and some slick JavaScript visualizations to track my swimming, biking, and running progress. You’ll get insights into some race prep—and maybe a few graphs showing when I hit the “why am I doing this” phase. But if I can do it, so can you—with the right support, a solid plan, and a high tolerance for discomfort.</p>


<h3>The Most Common Question I Get: "How Often Did You Train?"</h3>

<p>This really depends on three things:</p>
<ol style="text-align:left;">
    <li>My experience level (beginner with big dreams).</li>
    <li>My competitive spirit (firmly at the back of the pack).</li>
    <li>My training plan (Phil's Intermediate Full Distance Triathlon + Free Email Access to Coach: 36 Weeks because, why not?).</li>
</ol>

<p>Most plans suggest 2-3 sessions per sport each week, plus some weight training. As you can see from my activity stats, biking took the spotlight—because running the full marathon distance in training is brutal. My longest run capped at 44 km, while my longest bike ride stretched to 155 km. Biking clearly became my favorite because, well, let's just say I wasn’t exactly born with wheels.</p>

<p><strong>Fun fact:</strong> I ran a full marathon while on vacation in São Paulo, making my longest run a 44 km beast (I forgive Garmin for the 1.804 km error). Because who doesn’t relax by running a marathon, right?</p>

<p>The hardest part? <em>Cue the dramatic music.</em> The month leading up to the race. July 2024 was my most intense month, with over 70 hours of training! My craziest week? 21 hours of pure exercise. My most intense day? A 7.5-hour simulation: 97 miles of biking, a 2.4 km swim, and a 26 km run—all in one day. Sleep? Who needs it?</p>

<div class="container">
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                <h2>Training Activity Stats</h2>
                <ul>
                    <li>🏊 Longest Swim: 4.05 km</li>
                    <li>🚴 Longest Bike: 155.36 km</li>
                    <li>🏃 Longest Run: 44.00 km</li>
                </ul>
            </div>
            <div class="card half-width">
                <h2>Training Activity Counts</h2>
                <ul>
                    <li>🏊 Number of Swims: 54</li>
                    <li>🚴 Number of Bike: 110</li>
                    <li>🏃 Number of Runs: 89</li>
                    <li>🏋️ Number of Gym Sessions: 64</li>
                </ul>
            </div>
            <div class="card full-width">
                <h2>Training Hour stats</h2>
                <ul>
                    <li>📅 Most intense Month (July 2024): 70:33:00 hh:mm:ss</li>
                    <li>📅 Most intense Week (July 1-7, 2024): 20:59:11 hh:mm:ss</li>
                    <li>📅 Most intense day (July 28, 2024): 07:34:32 hh:mm:ss</li>
                </ul>
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<h3>How Many Kilometers Did I Actually Cover During Training?</h3>

<p>Let’s get into the nitty-gritty: the actual distances during training. As the graph shows, I tried (emphasis on <em>tried</em>) to keep up with around 10 km of swimming, 50 km of running, and 300 km of biking per month. But... vacations happened. The dip in training during November and December aligns with my trip to India for a friend’s wedding, where I did absolutely <em>nothing</em>. You can see the steep decline in all distances during that time. However, I redeemed myself during my second vacation in April, as shown by a similar drop in training but with a redeeming event: I ran a marathon in São Paulo and even hiked to Machu Picchu. Clearly, vacations aren’t always an excuse to slack off—they’re sometimes just another opportunity to push limits.</p>

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<h3>Training Time Breakdown: Biking Dominates, Obviously</h3>

<p>The donut chart highlights how much time I dedicated to each sport starting October 16, 2023 (the day I officially kicked off the training plan). As expected, biking takes up the largest chunk—no surprises there. However, running wasn’t far behind, thanks to the extra weekly run I did with a good friend outside of my plan. You can also spot the gym sessions, which made up a smaller slice of the pie but were essential for foam rolling, stretching, and sometimes sneaking in a yoga pose. Swimming had its moments too, especially with that weekly hour of coached swimming from my office perk. All in all, it's clear my schedule stayed pretty packed!</p>

    <div id="pie_chart"></div>



<h3>In Conclusion...</h3>

<p>This post was equal parts humblebrag and learning journey. I got to flex my JavaScript skills and hack together some Python scripts to make sense of my training data, all while documenting my Ironman training adventure. Figuring out how to use the Intervals.icu API and tweaking the data to fit my needs was a fun (and sometimes frustrating) challenge. For those of you who stuck around this long—thank you! In a future post, I’ll dive into the costs of doing an Ironman, the lessons I learned from doing it on a plant-based diet, and plenty more. Stay tuned!</p>


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</html>]]></content><author><name>Ajay Mandyam Rangarajan</name></author><category term="sports" /><category term="training" /><summary type="html"><![CDATA[Sport Data Visualization p { text-align: left; /* Align all text to the left */ margin: 0px 0; color: #2c3e50; /* Keep the text color consistent */ font-size: 16px; /* Standard font size for readability */ line-height: 1.6; /* Improve readability with a comfortable line height */ }]]></summary></entry><entry><title type="html">Measuring Travel: More Than Just Counting Countries</title><link href="https://www.ajayrangarajan.com/posts/2024/07/travel/" rel="alternate" type="text/html" title="Measuring Travel: More Than Just Counting Countries" /><published>2024-07-11T00:00:00+02:00</published><updated>2024-07-11T00:00:00+02:00</updated><id>https://www.ajayrangarajan.com/posts/2024/07/travel-score</id><content type="html" xml:base="https://www.ajayrangarajan.com/posts/2024/07/travel/"><![CDATA[<style>
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<p>Calculating a travel score for myself</p>

<p>I know, I know—travel is supposed to be a fun activity, enjoyed without the constraints of metrics and measurements. But there’s a part of <a href="https://x.com/shenanigansen/status/764093557497929733?lang=en" target="_blank">me</a> that loves seeing improvement in what I do, especially when it involves some numbers moving up or down towards a goal.</p>

<p>After a recent trip, I started wondering how I could measure my travel experiences. The most obvious metric is the number of countries visited. While this is a decent measure, I wanted a more comprehensive view of my travels.</p>

<p>While googling, I stumbled upon this amazing tool by <a href="https://patrickstotz.github.io/Travel-Score/" target="_blank">Patrick Stotz</a>. I absolutely loved it because it combined two of my interests: travel/maps and <a href="https://publications.rwth-aachen.de/record/817176" target="_blank">discretization</a>. However, there was a tiny hiccup—I had to manually click boxes based on the <a href="https://armandyam.github.io/others/#travel_map" target="_blank">cities I have visited</a>. This assumes two things about me:</p>
<ol>
  <li>I enjoy clicking a lot.</li>
  <li>I know <em>exactly</em> where the cities I’ve visited are located on a map.</li>
</ol>

<p>Probably neither of these assumptions is correct. But, I do know a bit of code. With my interest in learning JavaScript, I saw this as a micro-challenge to automate the process. I recycled some <a href="https://github.com/armandyam/maps_kml_generator" target="_blank">old code</a> and modified the original Travel Score calculator to accept a new JSON object with all the places I’ve traveled to. Now, not only can I calculate my travel score, but I can also keep it updated as I roam the globe. Check it out <a href="/projects/Travel-Score/index.html" target="_blank">here</a>.</p>

<p>The original tool by <a href="https://patrickstotz.github.io/Travel-Score/" target="_blank">Patrick Stotz</a> is under an MIT License.</p>

<h2 id="future-improvements">Future Improvements</h2>
<p>I’m excited about the potential to enhance this tool further. Here are a few ideas I have in mind to better measure “how much one has traveled the world”:</p>

<ol>
  <li><strong>User Uploads:</strong> Allow others to upload their own JSON files to calculate their travel scores. (I’m still figuring out how to do this, so if anyone has tips, feel free to share!)</li>
  <li><strong>World Heritage Sites:</strong> Include extra information about UNESCO World Heritage Sites visited to add another layer of cultural significance to the score.</li>
  <li><strong>Country-Specific Scoring:</strong> Make each country’s score different. For example, visiting a rare or less-visited country would give more points than visiting a popular tourist destination.</li>
  <li><strong>Duration of Stay:</strong> Incorporate the length of time spent in each location, with longer stays contributing more to the travel score.</li>
  <li><strong>Repeat Visits:</strong> Acknowledge multiple visits to the same country or city, reflecting the depth of exploration rather than just the breadth.</li>
  <li><strong>Regional Diversity:</strong> Measure the diversity of regions visited within a country to capture a more detailed picture of one’s travel experiences.</li>
  <li><strong>Off-the-Beaten-Path Locations:</strong> Award additional points for visiting less well-known or remote locations that might be more challenging to reach.</li>
</ol>]]></content><author><name>Ajay Mandyam Rangarajan</name></author><category term="travel" /><summary type="html"><![CDATA[]]></summary></entry></feed>