Fun_With_Math/experiments/basic/collatz.html at main · SimiaCryptus/Fun_With_Math · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
  <meta name="description" content="Explore the Collatz Conjecture: the 3n+1 problem visualized." />
  <title>Collatz Conjecture – Fun With Math</title>
  <link rel="stylesheet" href="../../css/style.css" />
  <style>
    canvas { display: block; background: #0d1117; }
    #resultBox {
      font-family: 'Fira Code', Consolas, monospace;
      font-size: .8rem;
      color: var(--accent);
      word-break: break-all;
      line-height: 1.9;
      max-height: 180px;
      overflow-y: auto;
      padding: .5rem;
      background: var(--bg);
      border: 1px solid var(--border);
      border-radius: 6px;
    }
    #statsRow {
      display: flex;
      flex-wrap: wrap;
      gap: 1rem;
      font-size: .85rem;
      color: var(--text-muted);
      padding: .5rem 0;
    }
    #statsRow strong { color: var(--text); }
    table {
      width: 100%;
      border-collapse: collapse;
      font-size: .82rem;
    }
    th, td {
      text-align: right;
      padding: .3rem .5rem;
      border-bottom: 1px solid var(--border);
    }
    th { color: var(--text-muted); font-weight: 600; }
    td:first-child, th:first-child { text-align: left; }
    tr:hover td { background: rgba(88,166,255,.05); }
    .peak-row td { color: var(--accent2); }
  </style>
</head>
<body>

<nav>
  <a class="brand" href="../../index.html">∑ Fun With Math</a>
  <a href="../../index.html">← All Experiments</a>
</nav>

<div class="page-header">
  <h1>Collatz Conjecture</h1>
  <p>Pick any positive integer. Apply the rule. Will you always reach 1?</p>
</div>

<div class="experiment-layout">
  <div>
    <div id="statsRow">
      <span>Steps: <strong id="stepsEl">—</strong></span>
      <span>Peak value: <strong id="peakEl">—</strong></span>
      <span>Starting at: <strong id="startEl">—</strong></span>
    </div>
    <div class="canvas-wrapper">
      <canvas id="canvas"></canvas>
    </div>
    <div class="info-box" style="margin-top:1rem">
      <h4>Sequence</h4>
      <div id="resultBox">—</div>
    </div>
  </div>

  <aside class="controls">
    <h3>Controls</h3>

    <label>
      Starting Number
      <input type="number" id="startInput" value="27" min="1" max="100000" />
    </label>

    <div style="display:flex;gap:.5rem;flex-wrap:wrap">
      <button class="btn btn-primary"   id="goBtn">▶ Compute</button>
      <button class="btn btn-secondary" id="randomBtn">🎲 Random</button>
    </div>

    <label>
      Compare Range: 2 – <span id="rangeLabel">50</span>
      <input type="range" id="rangeSlider" min="10" max="500" step="10" value="50" />
    </label>
    <button class="btn btn-secondary" id="compareBtn">📊 Compare Range</button>

    <div class="info-box">
      <h4>The Rule</h4>
      <p>
        Given a positive integer <code>n</code>:<br/>
        • If <code>n</code> is even → <code>n / 2</code><br/>
        • If <code>n</code> is odd  → <code>3n + 1</code><br/>
        Repeat until <code>n = 1</code>.
      </p>
    </div>

    <div id="compareTable"></div>
  </aside>
</div>

<footer>
  <p><a href="../../index.html">← Back to all experiments</a></p>
</footer>

<script>
(function () {
  const canvas     = document.getElementById('canvas');
  const ctx        = canvas.getContext('2d');
  const wrap       = canvas.parentElement;
  const startInput = document.getElementById('startInput');
  const goBtn      = document.getElementById('goBtn');
  const randomBtn  = document.getElementById('randomBtn');
  const rangeSlider= document.getElementById('rangeSlider');
  const rangeLabel = document.getElementById('rangeLabel');
  const compareBtn = document.getElementById('compareBtn');
  const resultBox  = document.getElementById('resultBox');
  const stepsEl    = document.getElementById('stepsEl');
  const peakEl     = document.getElementById('peakEl');
  const startEl    = document.getElementById('startEl');
  const compareTable = document.getElementById('compareTable');

  // ── Collatz sequence ─────────────────────────────────────
  function collatz(n) {
    const seq = [n];
    while (n !== 1) {
      n = n % 2 === 0 ? n / 2 : 3 * n + 1;
      seq.push(n);
    }
    return seq;
  }

  // ── Canvas sizing ────────────────────────────────────────
  function resize() {
    canvas.width  = wrap.clientWidth;
    canvas.height = Math.round(wrap.clientWidth * 0.55);
  }

  // ── Draw sequence ────────────────────────────────────────
  function drawSequence(seq) {
    const W = canvas.width, H = canvas.height;
    ctx.fillStyle = '#0d1117';
    ctx.fillRect(0, 0, W, H);

    if (!seq || seq.length < 2) return;

    const maxVal = Math.max(...seq);
    const pad = { top: 24, bottom: 24, left: 8, right: 8 };
    const pw   = W - pad.left - pad.right;
    const ph   = H - pad.top  - pad.bottom;

    const xStep = pw / (seq.length - 1);

    // Grid lines
    ctx.strokeStyle = 'rgba(255,255,255,.05)';
    ctx.lineWidth   = 1;
    for (let i = 0; i <= 4; i++) {
      const gy = pad.top + (ph / 4) * i;
      ctx.beginPath(); ctx.moveTo(pad.left, gy); ctx.lineTo(W - pad.right, gy); ctx.stroke();
      const val = Math.round(maxVal * (1 - i / 4));
      ctx.fillStyle = 'rgba(255,255,255,.2)';
      ctx.font = '10px system-ui';
      ctx.fillText(val.toLocaleString(), pad.left + 2, gy - 3);
    }

    // Gradient line
    const grad = ctx.createLinearGradient(pad.left, 0, W - pad.right, 0);
    grad.addColorStop(0,   '#58a6ff');
    grad.addColorStop(0.5, '#bc8cff');
    grad.addColorStop(1,   '#58a6ff');

    ctx.beginPath();
    seq.forEach((val, i) => {
      const x = pad.left + i * xStep;
      const y = pad.top  + ph * (1 - val / maxVal);
      i === 0 ? ctx.moveTo(x, y) : ctx.lineTo(x, y);
    });
    ctx.strokeStyle = grad;
    ctx.lineWidth   = 2;
    ctx.stroke();

    // Peak marker
    const peakIdx = seq.indexOf(maxVal);
    const px = pad.left + peakIdx * xStep;
    const py = pad.top  + ph * (1 - maxVal / maxVal);
    ctx.beginPath(); ctx.arc(px, py, 5, 0, Math.PI * 2);
    ctx.fillStyle = '#bc8cff'; ctx.fill();
    ctx.fillStyle = '#bc8cff';
    ctx.font = 'bold 11px system-ui';
    ctx.fillText(maxVal.toLocaleString(), Math.min(px + 7, W - 80), py + 4);
  }

  // ── Show sequence ────────────────────────────────────────
  function showSequence(n) {
    const seq = collatz(n);
    const peak = Math.max(...seq);
    stepsEl.textContent = seq.length - 1;
    peakEl.textContent  = peak.toLocaleString();
    startEl.textContent = n.toLocaleString();
    resultBox.textContent = seq.join(' → ');
    resize();
    drawSequence(seq);
  }

  // ── Compare table ────────────────────────────────────────
  function buildCompareTable(limit) {
    const rows = [];
    for (let i = 2; i <= limit; i++) {
      const seq  = collatz(i);
      const peak = Math.max(...seq);
      rows.push({ n: i, steps: seq.length - 1, peak });
    }
    rows.sort((a, b) => b.steps - a.steps);
    const top10 = rows.slice(0, 10);

    let html = '<table><thead><tr><th>n</th><th>Steps</th><th>Peak</th></tr></thead><tbody>';
    top10.forEach((r, idx) => {
      html += `<tr class="${idx === 0 ? 'peak-row' : ''}">
        <td>${r.n}</td>
        <td>${r.steps}</td>
        <td>${r.peak.toLocaleString()}</td>
      </tr>`;
    });
    html += '</tbody></table>';
    compareTable.innerHTML = `<div class="info-box"><h4>Top 10 by step count (2–${limit})</h4>${html}</div>`;
  }

  // ── Events ───────────────────────────────────────────────
  goBtn.addEventListener('click', () => {
    const n = parseInt(startInput.value);
    if (n > 0) showSequence(n);
  });
  startInput.addEventListener('keydown', e => {
    if (e.key === 'Enter') goBtn.click();
  });
  randomBtn.addEventListener('click', () => {
    const n = Math.floor(Math.random() * 9999) + 2;
    startInput.value = n;
    showSequence(n);
  });
  rangeSlider.addEventListener('input', () => {
    rangeLabel.textContent = rangeSlider.value;
  });
  compareBtn.addEventListener('click', () => {
    buildCompareTable(parseInt(rangeSlider.value));
  });

  // ── Init ─────────────────────────────────────────────────
  new ResizeObserver(() => {
    const n = parseInt(startInput.value);
    if (n > 0) showSequence(n);
  }).observe(wrap);
  showSequence(27);
})();
</script>
</body>
</html>