Overview › Code › R83
Code · blind round

R83 · Fourier epicycles tracing a shape

blind round 9/11 local models answered

Every answer below carries the name of the model that wrote it. Blind refers to the scoring: the review was done without knowing which model produced which answer — the published result names them.

2 of the 11 local models delivered nothing through our test harness in this round — for reasons that lie with our setup, not with the models. Those cards are marked DNF like any other, but they are not evidence about those models — the reason is noted on the card itself.

Show task 
Create ONE self-contained HTML file (STRICT LIMIT: max 7000 characters in total — this is a budget on characters, not on lines, so removing line breaks does not help) that draws a closed shape with rotating Fourier epicycles on a <canvas>. Build a chain of circles whose radii and speeds come from the Fourier coefficients of a simple target outline, draw the chain rotating, and let the tip of the last circle trace out the shape over time. Keep the traced path visible as it is drawn, and show the number of epicycles used. Smooth requestAnimationFrame animation, NO user input, starts immediately and keeps running (restart with a fresh random instance when finished). No external libraries, no comments needed. Output ONLY the HTML file content, nothing else.

The answers

Local models (Brain cluster) — identical prompt, shuffled order (the sequence is not a ranking)
mistral-small:24bOKFORMAT
Show code
```html
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Fourier Epicycles</title>
<style>
body {display:flex; justify-content:center; align-items:center; height:100vh; margin:0;}
#canvasContainer {position:relative;}
#epicycleCount {position:absolute; top:20px; left:50%; transform:translateX(-50%); background:#fff; padding:5px 10px; border-radius:5px; font-family:Arial, sans-serif;}
</style>
</head>
<body>
<div id="canvasContainer">
<canvas id="canvas" width="600" height="600"></canvas>
<span id="epicycleCount">Number of Epicycles: 0</span>
</div>
<script>
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
let nEpicycles = Math.floor(Math.random() * 15) + 5;
document.getElementById('epicycleCount').innerText = `Number of Epicycles: ${nEpicycles}`;

function drawShape() {
    const shapePoints = [];
    let t = 0;
    for (let i = 0; i < nEpicycles * 2; i += 2) {
        shapePoints.push({
            x: Math.cos(i / 10),
            y: Math.sin(i / 10)
        });
    }
    return shapePoints;
}

function getFourierCoefficients(shapePoints, n) {
    const a = new Array(n).fill(0);
    const b = new Array(n).fill(0);
    for (let t = 0; t < shapePoints.length; t++) {
        for (let m = 1; m <= n; m++) {
            a[m - 1] += Math.cos(2 * Math.PI * (t / shapePoints.length) * (m)) * shapePoints[t].x;
            b[m - 1] += Math.sin(2 * Math.PI * (t / shapePoints.length) * (m)) * shapePoints[t].y;
        }
    }
    return { a, b };
}

const shapePoints = drawShape();
let fourierCoefficients = getFourierCoefficients(shapePoints, nEpicycles);
const a = fourierCoefficients.a;
const b = fourierCoefficients.b;

function draw() {
    ctx.clearRect(0, 0, canvas.width, canvas.height);
    const t = new Date().getTime() * (1 / 60) % 10000;
    let x = 300, y = 300;
    for (let i = 0; i < nEpicycles; i++) {
        const freq = i + 1;
        const radius = Math.sqrt(a[i] * a[i] + b[i] * b[i]);
        ctx.beginPath();
        ctx.arc(x, y, radius, 0, 2 * Math.PI);
        ctx.strokeStyle = 'black';
        ctx.stroke();
        x += radius * Math.cos(2 * Math.PI * freq * t / 1000 + Math.atan(b[i] / a[i]));
        y += radius * Math.sin(2 * Math.PI * freq * t / 1000 + Math.atan(b[i] / a[i]));
    }
    ctx.beginPath();
    ctx.moveTo(x, y);
    ctx.lineTo(x - canvas.width/2 ,y-canvas.height/2 );
    ctx.strokeStyle = 'red';
    ctx.stroke();
    requestAnimationFrame(draw);
}

function restart() {
    nEpicycles = Math.floor(Math.random() * 15) + 5;
    document.getElementById('epicycleCount').innerText = `Number of Epicycles: ${nEpicycles}`;
    shapePoints = drawShape();
    fourierCoefficients = getFourierCoefficients(shapePoints, nEpicycles);
    a.splice(0, a.length, ...fourierCoefficients.a);
    b.splice(0, b.length, ...fourierCoefficients.b);
    setTimeout(draw, 500);
}

draw();

setInterval(() => {
    restart();
}, 30000); // Restart every 30 seconds
</script>
</body>
</html>
```
qwen3-coder:30bSTATFORMAT
Show code
```html
<!DOCTYPE html>
<html>
<head>
<title>Fourier Epicycles</title>
<style>body {margin: 0; overflow: hidden;} #canvas {display: block;}</style>
</head>
<body>
<canvas id="canvas"></canvas>
<script>
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');

let W, H;
let N_COEFFS = 8; // Number of epicycles (Fourier coefficients)
let t = 0;
let pathTrace = [];
let currentCoeffs = [];

function resize() {
    W = window.innerWidth;
    H = window.innerHeight;
    canvas.width = W;
    canvas.height = H * 0.8; // Use 80% height for drawing area
}
window.addEventListener('resize', resize);
resize();

function generateCoefficients() {
    const sampleSize = 100;
    let x = [];
    for (let i = 0; i < sampleSize; i++) {
        x.push(i / sampleSize * Math.PI * 2 - Math.PI); // Sample x from a range
    }

    // Target curve function (e.g., sin^2(x) or simple wave for coefficients)
    const y = x.map(xi => Math.sin(xi) * (1 + Math.cos(xi))); 

    let sum_A = Array(N_COEFFS).fill(0);
    let sum_B = Array(N_COEFFS).fill(0);

    for (let k = 0; k < N_COEFFS; k++) {
        let Ak = 0;
        let Bk = 0;
        let coeff_sum_A = 0;
        let coeff_sum_B = 0;
        for (let j = 0; j < sampleSize; j++) {
            const xj = x[j];
            // Fourier basis functions: cos(k*xj), sin(k*xj)
            coeff_sum_A += y[j] * Math.cos(k * xj);
            coeff_sum_B += y[j] * Math.sin(k * xj);
        }
        Ak = coeff_sum_A / sampleSize;
        Bk = coeff_sum_B / sampleSize;
        sum_A[k] = Ak;
        sum_B[k] = Bk;
    }

    return { A: sum_A, B: sum_B };
}

function init() {
    currentCoeffs = generateCoefficients();
    t = 0;
    pathTrace = [];
}

function drawEpicycles(time) {
    ctx.clearRect(0, 0, W, H);
    ctx.fillStyle = 'rgba(255, 255, 255, 0.1)'; // Fade background trace slightly
    ctx.fillRect(0, 0, W, H);

    // Draw path trace (fainter)
    if (pathTrace.length > 1) {
        ctx.strokeStyle = 'rgba(100, 255, 100, 0.7)';
        ctx.lineWidth = 1;
        ctx.beginPath();
        ctx.moveTo(pathTrace[0].x, pathTrace[0].y);
        for (let i = 1; i < pathTrace.length; i++) {
            ctx.lineTo(pathTrace[i].x, pathTrace[i].y);
        }
        ctx.stroke();
    }

    // Calculate current tip position and draw chain
    let x_tip = W / 2;
    let y_tip = H * 0.85; // Start slightly above the baseline
    let angle_sum = 0;

    for (let k = 0; k < N_COEFFS; k++) {
        // Radii and Speeds derived from coefficients (A and B)
        const Rk = Math.sqrt(Math.abs(currentCoeffs.A[k]) * currentCoeffs.A[k] + Math.abs(currentCoeffs.B[k]) * currentCoeffs.B[k]);
        const Sk = 0.5 + k / N_COEFFS; // Speed increases with order
        
        // Update angle: Angle = initial phase + speed * time
        angle_sum += (Sk * t);

        // Calculate circle center coordinates for drawing the epicycle
        let dx = Math.cos(angle_sum) * (Rk * 0.5);
        let dy = Math.sin(angle_sum) * (Rk * 0.5);

        // Draw the current circle/epicycle
        ctx.strokeStyle = `rgba(30, 150, 255, ${Math.min(1, k / N_COEFFS + 0.5)})`;
        ctx.lineWidth = Math.max(1, Rk * 0.1);
        ctx.beginPath();
        ctx.arc(x_tip + dx, y_tip - dy, Rk * 0.3, 0, Math.PI * 2);
        ctx.stroke();

        // Update position for the next circle (the center of the next circle is on the edge of the current one)
        x_tip += dx;
        y_tip -= dy;
    }

    // The final tip position after all rotations
    const x_final = x_tip;
    const y_final = y_tip;

    // Draw the actual trace point (the tip of the last circle)
    ctx.fillStyle = '#FF4500';
    ctx.beginPath();
    ctx.arc(x_final, y_final, 3, 0, Math.PI * 2);
    ctx.fill();

    // Record and draw path trace (the actual tip)
    const newPoint = { x: x_final, y: y_final };
    pathTrace.push(newPoint);
    if (pathTrace.length > 1000) pathTrace.shift(); // Limit memory usage

    // Display info
    ctx.fillStyle = 'rgba(0, 0, 0, 0.8)';
    ctx.font = '14px monospace';
    const infoText = `Coeffs Used: ${N_COEFFS}. Tip Position: (${x_final.toFixed(1)}, ${y_final.toFixed(1)})`;
    ctx.fillText(infoText, 10, 20);

}

function animate() {
    t += 0.03; // Time step
    drawEpicycles(t);
    requestAnimationFrame(animate);
}

init();
animate();
</script>
</body>
</html>
```
qwen3.5:9bBLANKFORMAT
Show code
```html
<!DOCTYPE html>
<html><head><title>Fourier Epicycles</title><style>body{background:#111;margin:0;overflow:hidden}.canvas{display:block}</style></head><body onload="init()"><canvas id="c" width="600" height="400"></canvas><script>
    const canvas = document.getElementById('c');
    const ctx = canvas.getContext('2d');
    let animationFrameId;

    // Global state
    let phaseOffset = 0;
    let epicycles = [];
    let history = [];
    const MAX_HISTORY = 500;

    function init() {
        history = [];
        epicycles = [];
        phaseOffset = Math.random() * Math.PI * 2;
        drawFourier(10); // Use 10 coefficients for the epicycle chain
        animate();
    }

    // Calculates Fourier coefficients (approximated) and sets up epicycles
    function drawFourier(N) {
        epicycles = [];
        const L = canvas.width;
        const H = canvas.height;
        let sumSq = 0;

        // Simple target source: a sin wave approximation
        for (let x = 0; x < L; x += 5) {
            let y_target = Math.sin(x / 100) * 80 + H / 2 - 40;
            sumSq += 1; // Just normalizing the length
        }

        // Simplified pseudo-Fourier calculation for demonstration purposes:
        // We use the coordinates themselves to generate coefficients (A_k, B_k).
        for (let k = 1; k <= N; k++) {
            const R = Math.abs(Math.sin(0.1 * k) * 50 + 20); // Radius A_k
            const S = Math.abs(Math.cos(0.1 * k) * 40 + 30); // Speed B_k
            epicycles.push({ r: R, s: S });
        }
    }

    function updateAnimation() {
        ctx.clearRect(0, 0, canvas.width, canvas.height);

        // Draw History Trace
        if (history.length > 1) {
            ctx.beginPath();
            ctx.strokeStyle = 'rgba(60, 255, 60, 0.8)';
            ctx.lineWidth = 2;
            ctx.moveTo(history[0].x, history[0].y);
            for (let i = 1; i < history.length; i++) {
                ctx.lineTo(history[i].x, history[i].y);
            }
            ctx.stroke();
        }

        // Draw Epicycles and Tip Path
        const centerX = canvas.width / 2;
        const centerY = canvas.height / 2;
        let currentX = centerX;
        let currentY = centerY;
        
        let epicycleOutput = '';
        
        for (let i = 0; i < epicycles.length; i++) {
            const e = epicycles[i];
            
            // Calculate position based on phase offset and index
            const angle = Math.sin(phaseOffset + i * 0.5) * 2; // Angle calculation
            
            currentX += e.r * Math.cos(angle);
            currentY += e.r * Math.sin(angle);

            // Draw the circle (epicycle)
            ctx.beginPath();
            ctx.arc(currentX, currentY, e.r, 0, 2 * Math.PI);
            ctx.strokeStyle = `hsl(${i * 360 / epicycles.length}, 80%, ${50 + i * 2}%)`;
            ctx.lineWidth = 1;
            ctx.stroke();

            // Update the phase offset for the next circle (simulating coupling)
            phaseOffset += e.s / 100;
        }

        // Draw the final tip point
        ctx.beginPath();
        ctx.arc(currentX, currentY, 3, 0, Math.PI * 2);
        ctx.fillStyle = 'lime';
        ctx.fill();
        
        // Record history and enforce limit
        history.push({ x: currentX, y: currentY });
        if (history.length > MAX_HISTORY) {
            history.shift();
        }

        animationFrameId = requestAnimationFrame(updateAnimation);
    }

    function animate() {
        // Loop management (keeps running indefinitely)
        window.onload = function(){}; // Ensure initialization completes
    }
</script></body></html>
```
gemma4:26bharness
No answer reached us (THIN) — and the reason lies with our setup, not with the model: reasoning consumed the entire token budget (3 min 28 s, zero characters of answer); larger budgets are refused by the gateway Counted as a did-not-finish, but it is not evidence about this model.
llama3.1:8bSTATFORMAT
Show code
```html
<!DOCTYPE html>
<html>
<head>
<title>Fourier Epicycles</title>
<style>
body {
  margin: 0;
  padding: 0;
}
canvas {
  border: 1px solid black;
}
</style>
</head>
<body>
<canvas id="c" width="400" height="300"></canvas>
<script>
var c = document.getElementById('c');
var ctx = c.getContext('2d');
var w = c.width, h = c.height;
var r = 50;
var cx = w / 2, cy = h / 2;
var n = 4; // number of epicycles
var t = 0;

// target shape's Fourier coefficients (example: a circle)
var A = [1];
var B = [];
for (var i = 1; i <= n; i++) {
  var C = Math.cos(2 * i * Math.PI / w);
  var S = Math.sin(2 * i * Math.PI / w);
  B.push(C, S);
}
var A0 = 350, A1 = -150, A2 = 250;

function drawEpi() {
  ctx.clearRect(0, 0, w, h);

  for (var i = 0; i < n + 1; i++) {
    var a = A[i];
    var b = B[2 * i], c = B[2 * i + 1];
    var x = r * a * Math.cos(t) - r * B[2 * i] * Math.sin(t);
    var y = r * a * Math.sin(t) + r * B[2 * i + 1] * Math.cos(t);

    ctx.beginPath();
    ctx.arc(cx + x, cy + y, r, 0, 2 * Math.PI);
    ctx.stroke();
  }
}

function drawPath() {
  var path = '';
  for (var i = 0; i < n + 1; i++) {
    var a = A[i];
    var b = B[2 * i], c = B[2 * i + 1];
    var x = r * a * Math.cos(t) - r * B[2 * i] * Math.sin(t);
    var y = r * a * Math.sin(t) + r * B[2 * i + 1] * Math.cos(t);

    path += `L${cx + x} ${cy + y}`;
  }
  ctx.beginPath();
  ctx.strokeStyle = 'rgba(0,0,0,.5)';
  ctx.lineWidth = 2;
  ctx.lineCap = 'round';
  ctx.lineJoin = 'round';

  var p = path.split(' ');
  ctx.moveTo(p[0].split(' ')[0] + cx, p[0].split(' ')[1] + cy);
  for (var i = 1; i < p.length; i++) {
    var x = p[i].split(' ')[0];
    var y = p[i].split(' ')[1];
    ctx.lineTo(x + cx, y + cy);
  }
  ctx.stroke();
}

function animate() {
  t += 0.01;
  drawEpi();

  if (Math.floor(t) === w) {
    document.getElementById('n').innerHTML = n;
    location.reload();
  } else {
    requestAnimationFrame(animate);
    drawPath();
  }
}
document.addEventListener('DOMContentLoaded', animate, false);

</script>
<span id="n"></span>
</body>
</html>
```
qwen3:14bOKFORMAT
Show code
```html
<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>Fourier Epicycles</title>
    <style>body { margin: 0; overflow: hidden; background: #111; }</style>
</head>
<body>
    <canvas id="c"></canvas>
    <script>
        const canvas = document.getElementById('c');
        const ctx = canvas.getContext('2d');

        let W, H;
        let animationId;

        function resize() {
            W = window.innerWidth;
            H = window.innerHeight;
            canvas.width = W;
            canvas.height = H * 0.8;
        }
        window.addEventListener('resize', resize);
        resize();

        let phase = 0;
        const MAX_EPICYCLES = Math.min(12, Math.ceil(Math.log2(W)/50)); // Adaptive count based on canvas size
        let epicycles = [];
        let trailPoints = [];
        let isRunning = true;

        function initializeEpicycles() {
            epicycles = [];
            trailPoints = [];
            const center = { x: W / 2, y: H * 0.8 - 50 };

            // Simple target function approximation (e.g., approximating a slightly squashed circle/figure)
            for (let i = 0; i < MAX_EPICYCLES; i++) {
                const k = i + 1;
                // Coefficients derived from simple harmonic motion for demonstration
                const R = Math.pow(k, 0.5) * 20 + Math.random() * 10; // Radius increases slightly with index
                const S = (i % 3 === 0 ? 0.02 : 0.01);          // Speed varies
                epicycles.push({ r: R, s: S, x: center.x, y: center.y });
            }
        }

        function draw() {
            ctx.clearRect(0, 0, W, canvas.height);

            if (!isRunning) return;

            // Update and Draw Epicycles
            let currentX = epicycles[0].x;
            let currentY = epicycles[0].y;

            for (let i = 0; i < MAX_EPICYCLES; i++) {
                const e = epicycles[i];

                // Update phase based on speed and time
                e.r += e.s * 0.1; // Simulate radius change/oscillation
                phase += e.s * 0.1;

                // Calculate position (circular motion)
                const xOffset = e.r * Math.cos(phase);
                const yOffset = e.r * Math.sin(phase);

                const nextX = currentX + xOffset;
                const nextY = currentY + yOffset;

                // Draw the circle (epicycle)
                ctx.beginPath();
                ctx.arc(nextX, nextY, e.r * 0.05, 0, Math.PI * 2);
                ctx.strokeStyle = `rgba(100, 200, 255, 0.4)`;
                ctx.stroke();

                // Update current position for the next link
                currentX = nextX;
                currentY = nextY;
            }

            // Draw the tip (end of the chain)
            ctx.beginPath();
            ctx.arc(currentX, currentY, 3, 0, Math.PI * 2);
            ctx.fillStyle = 'red';
            ctx.fill();

            // Update and draw trail (the traced shape)
            trailPoints.push({ x: currentX, y: currentY });
            if (trailPoints.length > 1500) {
                trailPoints.shift(); // Keep the array size manageable
            }

            ctx.beginPath();
            ctx.strokeStyle = 'rgba(255, 255, 255, 0.3)';
            ctx.lineWidth = 1;
            for (let i = 0; i < trailPoints.length - 1; i++) {
                const p1 = trailPoints[i];
                const p2 = trailPoints[i + 1];
                ctx.moveTo(p1.x, p1.y);
                ctx.lineTo(p2.x, p2.y);
            }
            ctx.stroke();

            // Display epicycle count
            ctx.fillStyle = 'white';
            ctx.font = '14px Arial';
            ctx.fillText(`Epicycles Used: ${MAX_EPICYCLES}`, 10, 25);


            animationId = requestAnimationFrame(animate);
        }

        function animate() {
            phase += 0.01; // Global phase shift for continuous rotation
            draw();
        }

        function startSimulation() {
            if (animationId) cancelAnimationFrame(animationId);
            initializeEpicycles();
            phase = 0;
            requestAnimationFrame(animate);
        }


        // Start immediately
        startSimulation();
    </script>
</body>
</html>
```
deepseek-r1:14bERRBLANKFORMAT
Show code
```html
<!DOCTYPE html>
<html><body style="background:#000;margin:0;display:flex;justify-content:center-align-items:center;height:100vh">
<canvas id=c width=600 height=400></canvas>
<script>
function setup() {
  const canvas = document.getElementById('c');
  const ctx = canvas.getContext('2d');
  
  // Setup
  let epicycles = [];
  const count = 20;
  const colors = ['#fff','#f0f','#0ff','#ff0'];
  for(let i=0;i<count;++i) {
    epicycles.push({
      r:Math.random()/3*(.5+.5*i/count),
      speed:(.1 - .02*i/count),
      angle:i%2==0?0:.Math.PI/4,
      x:canvas.width/2,y:canvas.height/2
    });
  }
  
  let path = [];
  let frameCount=0;
  const maxFrames=5000;
  
  function draw() {
    ctx.clearRect(0,0,canvas.width,canvas.height);
    
    // Draw traced path
    if(path.length>1) {
      ctx.beginPath();
      ctx.strokeStyle='rgba(255,255,255,.1)';
      ctx.moveTo(path[0].x,path[0].y);
      for(let i=1,len=path.length;i<len;++i) {
        ctx.lineTo(path[i].x,path[i].y);
      }
      ctx.stroke();
    }
    
    // Update and draw epicycles
    let prevX = canvas.width/2;
    let prevY = canvas.height/2;
    for(let i=0,len=epicycles.length;i<len;++i) {
      const e = epicycles[i];
      e.angle += e.speed;
      
      if(i==0) {
        ctx.beginPath();
        ctx.arc(e.x,e.y,e.r,0,Math.PI*2);
        ctx.strokeStyle=colors[i%colors.length];
        ctx.stroke();
      } else {
        const nextX = prevX + Math.cos(e.angle)*e.r;
        const nextY = prevY + Math.sin(e.angle)*e.r;
        
        e.x = nextX;
        e.y = nextY;
        
        // Draw connecting line
        ctx.beginPath();
        ctx.moveTo(prevX,prevY);
        ctx.lineTo(nextX,nextY);
        ctx.strokeStyle=colors[i%colors.length];
        ctx.stroke();
      }
      
      prevX = e.x;
      prevY = e.y;
    }
    
    // Record path and draw dot
    if(frameCount % 10 == 0) {
      path.push({x:prevX,y:prevY});
    }
    ctx.beginPath();
    ctx.arc(prevX,prevY,2,0,Math.PI*2);
    ctx.fillStyle='rgba(255,255,255,.8)';
    ctx.fill();
    
    // Animation controls
    frameCount++;
    if(frameCount > maxFrames) {
      epicycles.forEach((e,i)=>{
        e.angle = i%2==0?0:.Math.PI/4;
      });
      frameCount=0;
    }
    
    requestAnimationFrame(draw);
  }
  
  document.getElementById('c').addEventListener('click',function(e){
    let rect = canvas.getBoundingClientRect();
    let x = e.clientX - rect.left;
    let y = e.clientY - rect.top;
    if(Math.random()>.5) {
      epicycles.push({
        r:Math.random()/3,
        speed:(.1 - .02*epicycles.length),
        angle:Math.random()*Math.PI/2,
        x:x,y:y
      });
    }
  });
  
  draw();
}

window.onload = setup;
</script><div style="position:absolute;top:10px;left:10px;color:#fff;font-family:sans-serif;font-size:16px">Epicycles used: <span id=count>20</span></div>
</body></html>
```
qwen3:8bharness
No answer reached us (ERR) — and the reason lies with our setup, not with the model: reasoning consumed the entire token budget and the answer stayed empty; the gateway rejects budgets above 3000 tokens Counted as a did-not-finish, but it is not evidence about this model.
deepseek-r1:32bERRBLANKFORMAT
Show code
```html
<!DOCTYPE html><html><body style="background:#000;display:flex;justify-content:center;align-items:center;height:100vh;margin:0"><canvas id="c"></canvas></body>
<script>
const canvas=document.getElementById('c'),ctx=canvas.getContext('2d');
function resize(){canvas.width=window.innerWidth*.8;canvas.height=window.innerHeight*.8;
ctx.translate(canvas.width/2,canvas.height/2);
}resize();window.addEventListener('resize',resize);
let time=0,phase=0,N=40,epicycles=[],targetOutline=[],center=[0,0],radius=.5*canvas.width/max(N,10),running=true;

function computeFourierCoefficients(points){
const N=points.length;
epicycles=new Array(N).fill(0);
for(let k=-N/2;k<=N/2;k++){
let sum_r=0,sum_i=0,freq=k;
for(let n=0;n<points.length;n++){
const t=n/N*2*Math.PI,
x=points[n][0],y=points[n][1];
sum_r+=x*Math.cos(-freq*t)+y*Math.sin(-freq*t);
sum_i+=-x*Math.sin(-freq*t)+y*Math.cos(-freq*t);
}
epicycles[Math.floor(k+N/2)]=[sum_r/N,sum_i/N];
}}

function generateTargetOutline(){
const nVertices=5;
return Array.from({length:nVertices},(v,i)=>[
Math.cos(i/nVertices*2*Math.PI + Math.random()*Math.PI)*radius,
Math.sin(i/nVertices*2*Math.PI + Math.random()*Math.PI)*radius
]);
}

computeFourierCoefficients(generateTargetOutline());

ctx.strokeStyle='#fff';ctx.lineWidth=1;ctx.lineCap='round';
const trace={x:0,y:0},prevTrace={x:0,y:0};
let completed=false;

function drawEpicycles(x=0,y=0,time){
epicycles.forEach((e,i)=>{
const freq=i-(epicycles.length/2),amp=Math.hypot(e[0],e[1]);
if(amp<.01)return;
const angle=freq*time + phase;
ctx.beginPath();
ctx.arc(x,y,amp,.5*Math.PI,-1.5*Math.PI);
ctx.strokeStyle=`hsl(${i*360/epicycles.length},80%,70%)`;
ctx.stroke();
x+=amp*Math.cos(angle);
y+=amp*Math.sin(angle);
});
return {x,y};
}

function animate(){
if(!running)return;
time=(phase+time)%Math.PI/2;
const pos=drawEpicycles(center[0],center[1],time);
if(time>Math.PI*2){
running=false;
setTimeout(()=>{running=true;computeFourierCoefficients(generateTargetOutline());animate();},1e3);
return;
}
ctx.beginPath();
ctx.moveTo(prevTrace.x,prevTrace.y);
ctx.lineTo(trace.x=pos.x,trace.y=pos.y);
ctx.strokeStyle='#fff';ctx.lineWidth=2;ctx.stroke();
prevTrace={x:trace.x,y:trace.y};
phase+=.02;
requestAnimationFrame(animate);
}

animate();
</script>
```
command-r:35bOKFORMAT
Show code
```html
<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>Fourier Epicycles</title>
    <style>
        body {
            margin: 0;
            display: flex;
            justify-content: center;
            align-items: center;
            height: 100vh;
            background-color: #222;
        }
        canvas {
            border: 2px solid #fff;
        }
    </style>
</head>
<body>
    <canvas id="myCanvas"></canvas>

    <script>
        const canvas = document.getElementById('myCanvas');
        const ctx = canvas.getContext('2d');

        let radius = [];
        let speed = [];
        
        function generateRandomFourierCoefficients() {
            // Target shape is a simple closed curve (e.g., circle or square)
            
            const numHarmonics = 5; // Number of Fourier harmonics to use
            const maxRadius = 100; // Maximum radius for the epicycles

            for (let i = 0; i < numHarmonics; i++) {
                radius[i] = Math.random() * maxRadius + 10; // Randomize radii within a range
                speed[i] = -Math.random() * 2 * Math.PI + Math.PI / 4; // Randomize speeds
            }
        }

        function drawShape(ctx, radius, speed) {
            ctx.clearRect(0, 0, canvas.width, canvas.height);
            const centerX = canvas.width / 2;
            const centerY = canvas.height / 2;

            for (let i = 0; i < radius.length; i++) {
                const angle = speed[i] * Date.now() / 1000; // Convert milliseconds to seconds
                ctx.beginPath();
                ctx.arc(centerX + Math.cos(angle) * radius[i], centerY + Math.sin(angle) * radius[i], 2, 0, 2 * Math.PI);
                ctx.strokeStyle = 'white';
                ctx.stroke();
            }

            // Draw the traced path of the last circle's tip
            const angle = speed[radius.length - 1] * Date.now() / 1000;
            const x = centerX + Math.cos(angle) * radius[radius.length - 1];
            const y = centerY + Math.sin(angle) * radius[radius.length - 1];

            ctx.beginPath();
            ctx.moveTo(centerX, centerY);
            ctx.lineTo(x, y);
            ctx.strokeStyle = 'blue';
            ctx.stroke();
        }

        function animate() {
            generateRandomFourierCoefficients();
            drawShape(ctx, radius, speed);

            requestAnimationFrame(animate); // Restart the animation with a fresh random instance when finished drawing          
        }

        // Start the animation immediately
        animate();
    </script>
</body>
</html>
```
qwq:32bSTAT
Show code
<think>

Okay, I need to create a self-contained HTML file that draws a closed shape using rotating Fourier epicycles on a canvas. The user wants a chain of circles based on Fourier coefficients, and the path should be traced by the tip of the last circle. Also, it should have smooth animation with requestAnimationFrame, restart when done, and no external libraries. Let me think through the steps.

First, I need to choose a simple shape. Maybe a square or a triangle? But the example I've seen before uses an ellipse or a star. Wait, the Fourier epicycles are derived from the shape's outline, so I need to parametrize the shape as a set of points. The user mentioned a closed shape, so maybe an ellipse would work since it's easy to compute Fourier coefficients for?

Alternatively, maybe a star-shaped polygon? Hmm. Let's pick a square for simplicity. Wait, but a square might have more Fourier components. Alternatively, an ellipse would have a simpler Fourier series. Let me think. For a circle, the Fourier coefficients would be simple, but the path would just be a circle. The example might need something more interesting.

Wait, the problem says "simple target outline". Let me see, perhaps a square with rounded corners? Or maybe a simpler shape like a triangle? Alternatively, maybe a heart shape? Hmm, but that might complicate things. Let me go with a square. Let me think how to parametrize it.

Alternatively, maybe use a parametric equation for an ellipse. Let me think: for an ellipse, the parametrization is x = a*cos(t), y = b*sin(t), but that's just a circle if a and b are equal. But the Fourier coefficients for an ellipse can be obtained. Wait, but maybe I can choose a shape where I can compute the Fourier series coefficients analytically. That might be better.

Alternatively, perhaps a square wave? But that's more of a 1D function. Maybe a square in 2D? Hmm, maybe better to use a predefined set of points for the shape. Let's see, the problem says "the Fourier coefficients of a simple target outline". To compute those, I need to sample the shape's coordinates over time. So, perhaps first, I can define the target shape as a sequence of points over time, then compute its discrete Fourier transform (DFT) to get the coefficients. 

So, the process is: 

1. Define a target path as a set of (x,y) points over time 't' from 0 to 1 (or 0 to 2π). The shape should be closed, so the start and end points should be the same.

2. Convert this path into a complex number array (since in Fourier transforms, complex numbers are easier), where each point is (x + yi) at time t.

3. Compute the Fourier coefficients (DFT) of this complex array. The result will give the coefficients (amplitude and phase) for each frequency component.

4. Each Fourier coefficient corresponds to an epicycle (circle) with radius equal to the amplitude, and angular velocity proportional to the frequency. The frequencies are integers (n) where n is from 0 to N-1 (for a DFT of size N). The angular velocity would be 2πn per unit time. 

Wait, but the angular velocity (omega) for the nth term in a Fourier series is 2πn*T, where T is the period. Since we're dealing with a closed shape over T=1 (so period 1), then the angular velocity would be 2πn. So each epicycle rotates at n * 2π radians per unit time.

But since we are animating over time, maybe we can have time 't' increase, and each circle's angle is angle = 2πn * t + phase. The radius is the magnitude of the Fourier coefficient for that n.

Wait, but the Fourier series is represented as a sum over terms like A_n * e^(i*(2πn t + phase_n)), so the magnitude is the amplitude, and the phase is added.

So, the process is: for each point in time, the position is the sum of all the epicycles' vectors. The tip of the last epicycle traces the path.

So, in the code, I need to first define the target shape, sample it into points, compute DFT, then use the coefficients to draw the circles.

But since we need to compute this in JavaScript without any libraries, doing a DFT manually might be time-consuming. Alternatively, maybe the user expects a predefined set of Fourier coefficients for a simple shape, so that the code can hardcode them?

Wait, that might be necessary. Because implementing a DFT in JS would take a lot of code, which might not fit in the 7000 character limit. Let me see.

Alternatively, perhaps the user expects us to choose a shape for which the Fourier coefficients can be approximated manually. For example, a square wave has known Fourier coefficients. Alternatively, a rectangle or a star shape?

Hmm. Alternatively, perhaps the user is okay with a hard-coded set of coefficients for a simple shape. Let me think of an example. For instance, a square can be approximated with several terms. Alternatively, a triangle?

Alternatively, maybe a simple shape like an ellipse. Let's consider the ellipse as a parametric equation:

x(t) = cos(2πt)
y(t) = 0.5*sin(2πt)

This is an ellipse with semi-axes 1 and 0.5. The Fourier series for this is straightforward because it's already in terms of sine and cosine. Let's see:

The complex form would be z(t) = cos(2πt) + i 0.5 sin(2πt). Let me write this in complex exponentials.

cos(2πt) = ( e^{i2πt} + e^{-i2πt} ) / 2

0.5 sin(2πt) = 0.5 * ( e^{i2πt} - e^{-i2πt} ) / (2i) ) = (e^{i2πt} - e^{-i2πt}) / (4i )

So combining both terms:

z(t) = [ e^{i2πt} + e^{-i2πt} ] / 2 + i * [ ( e^{i2πt} - e^{-i2πt} ) / (4i) ]

Simplify the second term: i * ( something / 4i ) = ( something ) /4 

Wait, let me compute term by term:

The real part's expression is (e^{i2πt} + e^{-i2πt})/2

The imaginary part's 0.5 sin(2πt) is equal to (e^{i2πt} - e^{-i2πt} )/(4i) ?

Wait, let me recheck:

sin(θ) = (e^{iθ} - e^{-iθ})/(2i)

So 0.5 sin(θ) = (e^{iθ} - e^{-iθ})/(4i)

So when multiplied by i:

i * 0.5 sin(θ) = (e^{iθ} - e^{-iθ})/4

Therefore, the imaginary component multiplied by i (since the original is y(t) = Im(z), but here we have:

Wait, z(t) is x(t) + i y(t). Let me see:

x(t) = cos(2πt)

y(t) =
Outside the Brain cluster — same task, same character budget, collected through their own tooling (response times not comparable)
Claude Opus 5frontier referenceOK
Show code
<!doctype html><html lang=en><head><meta charset=utf-8><meta name=viewport content="width=device-width,initial-scale=1"><title>Fourier Epicycles</title><style>
html,body{margin:0;height:100%;background:#07080e;overflow:hidden}
canvas{display:block}
#i{position:fixed;left:16px;top:14px;font:12px/1.6 ui-monospace,Menlo,monospace;color:#9fdcff;letter-spacing:.14em;text-transform:uppercase;text-shadow:0 0 10px rgba(60,170,255,.6);pointer-events:none}
#i b{color:#fff}
</style></head><body><canvas id=c></canvas><div id=i></div><script>
const T=6.283185307,c=document.getElementById('c'),g=c.getContext('2d'),I=document.getElementById('i'),D=Math.min(2,devicePixelRatio||1);
let W,H,CO,M,NRM,tt,hold,path,hue,last=0;
function rs(){W=c.width=innerWidth*D;H=c.height=innerHeight*D;c.style.width=innerWidth+'px';c.style.height=innerHeight+'px'}
function poly(V){return t=>{const n=V.length,s=t/T*n,i=Math.floor(s),f=s-i,a=V[i%n],b=V[(i+1)%n];return[a[0]+(b[0]-a[0])*f,a[1]+(b[1]-a[1])*f]}}
function ring(n,r1,r2){const V=[];for(let i=0;i<n;i++){const A=T*i/n-1.5708;V.push([(i%2?r2:r1)*Math.cos(A),(i%2?r2:r1)*Math.sin(A)])}return V}
function shape(){const R=Math.random,y=R()*6|0;
if(y==0){const k=3+(R()*5|0),a=.22+R()*.3;return t=>{const r=1+a*Math.cos(k*t);return[r*Math.cos(t),r*Math.sin(t)]}}
if(y==1)return poly(ring(3+(R()*6|0),1,1));
if(y==2){const p=5+(R()*4|0);return poly(ring(2*p,1.15,.42+R()*.16))}
if(y==3)return t=>{const s=Math.sin(t);return[1.2*s*s*s,-.075*(13*Math.cos(t)-5*Math.cos(2*t)-2*Math.cos(3*t)-Math.cos(4*t))]};
if(y==4){const k=6+(R()*8|0);return t=>{const r=1+.18*Math.tanh(5*Math.sin(k*t));return[r*Math.cos(t),r*Math.sin(t)]}}
const e=2.4+R()*4;return t=>{const u=Math.cos(t),v=Math.sin(t),q=Math.pow(Math.pow(Math.abs(u),e)+Math.pow(Math.abs(v),e),-1/e);return[q*u,q*v]}}
function init(){const f=shape(),N=400,P=[];let sx=0,sy=0;
for(let n=0;n<N;n++){const p=f(T*n/N);P.push(p);sx+=p[0];sy+=p[1]}
sx/=N;sy/=N;NRM=.1;
for(const p of P){p[0]-=sx;p[1]-=sy;NRM=Math.max(NRM,Math.hypot(p[0],p[1]))}
const C=[];
for(let k=0;k<N;k++){let re=0,im=0;
for(let n=0;n<N;n++){const A=-T*k*n/N,u=Math.cos(A),v=Math.sin(A);re+=P[n][0]*u-P[n][1]*v;im+=P[n][0]*v+P[n][1]*u}
C.push({f:k>N/2?k-N:k,a:Math.hypot(re,im)/N,p:Math.atan2(im,re)})}
C.sort((u,v)=>v.a-u.a);
M=26+(Math.random()*54|0);CO=C.slice(0,M);
tt=0;hold=0;path=[];hue=Math.random()*360|0;
I.innerHTML='Fourier series &middot; epicycles: <b>'+M+'</b>'}
function frame(now){requestAnimationFrame(frame);
const dt=Math.min(.05,(now-last)/1000);last=now;
g.fillStyle='#07080e';g.fillRect(0,0,W,H);
const S=Math.min(W,H)*.31/NRM,p1=new Path2D(),p2=new Path2D();
g.save();g.translate(W/2,H/2);g.lineJoin='round';g.lineCap='round';
let px=0,py=0;p2.moveTo(0,0);
for(let i=0;i<M;i++){const o=CO[i],r=o.a*S,A=o.f*tt+o.p;
if(r>1.5){p1.moveTo(px+r,py);p1.arc(px,py,r,0,T)}
px+=r*Math.cos(A);py+=r*Math.sin(A);p2.lineTo(px,py)}
g.lineWidth=D*.7;g.strokeStyle='rgba(120,180,255,.17)';g.stroke(p1);
g.lineWidth=D;g.strokeStyle='rgba(200,230,255,.55)';g.stroke(p2);
if(!hold)path.push([px/S,py/S]);
const p3=new Path2D();
for(let i=0;i<path.length;i++){const p=path[i];i?p3.lineTo(p[0]*S,p[1]*S):p3.moveTo(p[0]*S,p[1]*S)}
g.lineWidth=D*1.7;g.shadowBlur=16;g.shadowColor='hsl('+hue+',100%,58%)';g.strokeStyle='hsl('+hue+',100%,68%)';g.stroke(p3);
g.shadowBlur=0;g.fillStyle='#fff';g.beginPath();g.arc(px,py,D*2.2,0,T);g.fill();
g.restore();
if(hold){hold+=dt;if(hold>1.7)init()}else{tt+=dt*.7;if(tt>=T){tt=T;hold=1e-4}}}
rs();addEventListener('resize',rs);init();requestAnimationFrame(frame);
</script></body></html>
GPT-5.5 (Codex)frontier referenceOK
Show code
<!doctype html><html><head><meta charset=utf-8><title>Fourier Epicycles</title><style>html,body{margin:0;height:100%;background:#101418;color:#e9eef2;font:15px system-ui}canvas{display:block;width:100vw;height:100vh}.hud{position:fixed;left:16px;top:12px;background:#0008;padding:8px 11px;border-radius:8px}</style></head><body><canvas id=c></canvas><div class=hud id=h></div><script>
let c=document.getElementById("c"),x=c.getContext("2d"),h=document.getElementById("h"),W,H,pts,coef,path,t=0,N=38;
function sz(){W=c.width=innerWidth*devicePixelRatio;H=c.height=innerHeight*devicePixelRatio;x.setTransform(devicePixelRatio,0,0,devicePixelRatio,0,0);W=innerWidth;H=innerHeight}
onresize=sz;sz();
function target(){
 let a=[],n=520,r1=160+Math.random()*45,r2=55+Math.random()*35,k=3+(Math.random()*4|0),p=Math.random()*7;
 for(let i=0;i<n;i++){let u=i/n*6.2831853,r=r1+r2*Math.sin(k*u+p)+18*Math.cos((k+2)*u);a.push({x:r*Math.cos(u),y:.72*r*Math.sin(u)+28*Math.sin(2*u+p)})}
 return a
}
function fourier(a){
 let n=a.length,o=[];
 for(let m=-N;m<=N;m++){let re=0,im=0;for(let j=0;j<n;j++){let q=-6.2831853*m*j/n,z=a[j],A=Math.cos(q),B=Math.sin(q);re+=z.x*A-z.y*B;im+=z.x*B+z.y*A}re/=n;im/=n;o.push({f:m,r:Math.hypot(re,im),p:Math.atan2(im,re)})}
 return o.sort((a,b)=>b.r-a.r)
}
function reset(){pts=target();coef=fourier(pts);path=[];t=0;h.textContent="Epicycles: "+coef.length}
function step(){
 x.clearRect(0,0,W,H);let ox=W/2,oy=H/2,px=ox,py=oy,dt=6.2831853/pts.length;
 x.lineWidth=1;x.strokeStyle="#51606b";
 for(let z of coef){let nx=px+z.r*Math.cos(z.f*t+z.p),ny=py+z.r*Math.sin(z.f*t+z.p);x.beginPath();x.arc(px,py,z.r,0,7);x.stroke();x.beginPath();x.moveTo(px,py);x.lineTo(nx,ny);x.stroke();px=nx;py=ny}
 path.unshift({x:px,y:py});x.lineWidth=2.4;x.strokeStyle="#45f0b0";x.beginPath();for(let i=0;i<path.length;i++)i?x.lineTo(path[i].x,path[i].y):x.moveTo(path[i].x,path[i].y);x.stroke();
 x.fillStyle="#fff";x.beginPath();x.arc(px,py,3,0,7);x.fill();t+=dt;if(t>6.2831853)reset();requestAnimationFrame(step)
}
reset();step();
</script></body></html>
Claude Sonnet 5frontier referenceOK
Show code
<!DOCTYPE html><html><head><meta charset="utf-8"><title>Epicycles</title>
<style>html,body{margin:0;background:#05060c;overflow:hidden;height:100%}canvas{display:block}
#h{position:fixed;top:8px;left:10px;color:#9fe;font:14px monospace;text-shadow:0 0 4px #000}</style>
</head><body><canvas id="c"></canvas><div id="h"></div>
<script>
const cv=document.getElementById('c'),x=cv.getContext('2d');
let W,H,cx,cy;
function rz(){W=cv.width=innerWidth;H=cv.height=innerHeight;cx=W/2;cy=H*0.42;}
rz();addEventListener('resize',rz);
const M=140,K=44;
let epis,time,trace,scale;
function shapeFn(kind){
  if(kind===0)return t=>({x:16*Math.pow(Math.sin(t),3)/16,y:-(13*Math.cos(t)-5*Math.cos(2*t)-2*Math.cos(3*t)-Math.cos(4*t))/16});
  if(kind===1)return t=>{const r=1+0.35*Math.cos(5*t);return{x:r*Math.cos(t),y:r*Math.sin(t)};};
  return t=>{const r=1+0.45*Math.sin(4*t)*Math.cos(2*t);return{x:r*Math.cos(t),y:r*Math.sin(t)};};
}
function dft(px,py){
  const out=[];
  for(let k=0;k<M;k++){
    let re=0,im=0;
    for(let n=0;n<M;n++){
      const phi=2*Math.PI*k*n/M;
      re+=px[n]*Math.cos(phi)+py[n]*Math.sin(phi);
      im+=py[n]*Math.cos(phi)-px[n]*Math.sin(phi);
    }
    re/=M;im/=M;
    let freq=k;if(freq>M/2)freq-=M;
    out.push({re,im,freq,amp:Math.hypot(re,im),phase:Math.atan2(im,re)});
  }
  out.sort((a,b)=>b.amp-a.amp);
  return out.slice(0,K);
}
function init(){
  const kind=(Math.random()*3)|0;
  const fn=shapeFn(kind);
  const px=[],py=[];
  for(let n=0;n<M;n++){
    const t=n/M*2*Math.PI;
    const p=fn(t);
    px.push(p.x);py.push(p.y);
  }
  scale=Math.min(W,H)*0.32;
  epis=dft(px,py).map(e=>({re:e.re*scale,im:e.im*scale,freq:e.freq,amp:e.amp*scale,phase:e.phase}));
  time=0;trace=[];
  x.fillStyle='#05060c';x.fillRect(0,0,W,H);
}
init();
function step(){
  let px=cx,py=cy;
  x.strokeStyle='rgba(120,170,220,0.28)';
  x.lineWidth=1;
  for(const e of epis){
    const ang=e.freq*time+e.phase;
    const nx=px+e.amp*Math.cos(ang);
    const ny=py+e.amp*Math.sin(ang);
    if(e.amp>1.2){
      x.beginPath();x.arc(px,py,e.amp,0,7);x.stroke();
    }
    x.beginPath();x.moveTo(px,py);x.lineTo(nx,ny);x.stroke();
    px=nx;py=ny;
  }
  trace.push({x:px,y:py});
  if(trace.length>M+2){
    time+=1e-6;
    return {px,py,wrapped:true};
  }
  time+=2*Math.PI/M;
  return {px,py,wrapped:false};
}
function draw(tip){
  x.fillStyle='rgba(5,6,12,0.18)';x.fillRect(0,0,W,H);
  x.strokeStyle='#ffcf6b';x.lineWidth=2.2;
  x.beginPath();
  for(let i=0;i<trace.length;i++){
    const p=trace[i];
    if(i===0)x.moveTo(p.x,p.y);else x.lineTo(p.x,p.y);
  }
  x.stroke();
  x.fillStyle='#ff6b6b';
  x.beginPath();x.arc(tip.px,tip.py,3.5,0,7);x.fill();
  document.getElementById('h').textContent=`epicycles: ${epis.length}   tracing shape...`;
}
function loop(){
  const r=step();
  draw(r);
  if(trace.length>M+40)init();
  requestAnimationFrame(loop);
}
loop();
</script></body></html>
Claude Haiku 4.5frontier referenceOKMINIFIED
Show code
<!DOCTYPE html><html><head><meta charset="utf-8"><style>body{margin:0;background:#000;overflow:hidden}#c{display:block}#i{position:absolute;top:5px;left:5px;color:#0f0;font-family:monospace;font-size:12px}</style></head><body><canvas id="c"></canvas><div id="i"></div><script>const c=document.getElementById('c'),ctx=c.getContext('2d'),i=document.getElementById('i');c.width=800;c.height=600;const mx=c.width/2,my=c.height/2;let path=[];const N=30;let coef=[];for(let k=-N;k<=N;k++){let r=0,im=0;for(let t=0;t<64;t++){let a=t/64*Math.PI*2;let x=150*Math.cos(a)+100*Math.cos(3*a),y=150*Math.sin(a)+100*Math.sin(3*a);r+=x*Math.cos(k*a);im+=x*Math.sin(k*a)}coef.push({r:r/64,i:im/64})}function f(t){let x=0,y=0;for(let k=0;k<coef.length;k++){let ang=k*t;x+=coef[k].r*Math.cos(ang)-coef[k].i*Math.sin(ang);y+=coef[k].r*Math.sin(ang)+coef[k].i*Math.cos(ang)}return{x:x/coef.length,y:y/coef.length}}function dr(){ctx.fillStyle='#000';ctx.fillRect(0,0,c.width,c.height);ctx.strokeStyle='#080';ctx.lineWidth=1;if(path.length>1){ctx.beginPath();ctx.moveTo(mx+path[0].x,my+path[0].y);for(let j=1;j<path.length;j++){ctx.lineTo(mx+path[j].x,my+path[j].y)}ctx.stroke()}let t=(Date.now()/50)%500;let p={x:0,y:0};let r=200;ctx.strokeStyle='#0f0';for(let k=0;k<coef.length;k++){let ang=k*t;let dx=coef[k].r*Math.cos(ang)-coef[k].i*Math.sin(ang);let dy=coef[k].r*Math.sin(ang)+coef[k].i*Math.cos(ang);ctx.beginPath();ctx.arc(mx+p.x,my+p.y,Math.hypot(dx,dy),0,Math.PI*2);ctx.stroke();p.x+=dx;p.y+=dy}ctx.fillStyle='#f00';ctx.fillRect(mx+p.x-2,my+p.y-2,4,4);path.push({x:p.x,y:p.y});if(path.length>800)path.shift();i.textContent=`Epicycles: ${coef.length}`}setInterval(dr,50);</script></body></html>
Results at a glance— every model in this round with score, response time and status.

Who wrote what

ModelBlind scoreLatencyStatus
mistral-small:24b —135.5 sOK
qwen3-coder:30b —26.1 sOK
qwen3.5:9b —38.4 sOK
gemma4:26b ——harness
llama3.1:8b —133.3 sOK
qwen3:14b —40.7 sOK
deepseek-r1:14b —81.1 sOK
qwen3:8b ——harness
deepseek-r1:32b —152.0 sOK
command-r:35b —130.1 sOK
qwq:32b —153.0 sOK