Run Detail
completedmercury-3Recorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
201.7s
Total Tokens
85,282
Input Tokens
709
Output Tokens
84,573
Reasoning Tokens
81,398
Reasoning Effort
default
Cached Input Tokens
1
Est. Cost
$0.0297
Started
10/21/2026, 9:35:16 PM
OR Provider
Inception
Finish Reason
stop
Generation ID
gen-1792618515-bBdBIVgo97EXTqVWJCHe
Turns (1)
Turn #1
709 in84,573 out81,398 reasoning1 cached85,282 total201.7s
user
You build physics demonstrations for a science museum. The exhibits have to be right, because there is usually a physicist in the room.
Build me the falling slinky.
The exhibit
A single HTML page. A slinky — at least 40 coupled segments — hangs from a fixed point at the top of the canvas, at rest, under gravity. Then it is released.
Controls:
- Release — lets go of the top. Reset — hangs it back up, at rest.
- A speed slider from full speed down to about 1/20th, so a visitor can watch the interesting part.
- A marker line drawn across the canvas at the height of the bottom of the slinky at the instant of release, staying where it was put. Visitors need something to compare against.
- A running clock in milliseconds since release.
The physics, and I will be checking it
- Model it properly: masses connected by springs, with gravity and a little damping. Hooke's law between neighbours, integrated over small time steps.
- The hanging state must be the true equilibrium. A real slinky at rest is not evenly spaced — the coils near the top carry the weight of everything below them and are stretched further apart than the coils at the bottom. Your initial condition must have this. Solve for it or relax into it, but do not start from even spacing and call it hanging.
- The integrator must be stable at the stiffness you choose. If it explodes, lower the stiffness or shorten the step — do not add a fudge factor that clamps velocities and hides it.
- No scripted behaviour. Every segment obeys the same rules. Nothing is pinned, frozen, delayed or special-cased once you press Release. If any segment is treated differently from its neighbours at any point after release, that is scripting, and you must say so.
House rules
- One file. Everything inline — no CDN, no external stylesheet, font, script or image.
data:URIs are fine. - No libraries. No physics engine.
- No network at runtime.
- No
localStorage,sessionStorage, cookies orindexedDB— sandboxed frame, they throw. - Return the file as exactly one fenced
htmlblock.
Answer in exactly these sections
The prediction
Before the file, and before you write it. In one paragraph: what will this simulation show in the first few hundred milliseconds after release, and why does the physics require that? Be concrete about what each end of the slinky does and roughly when.
Commit to this. It is the claim I am going to test your simulation against.
The setup
Your parameters — segment count, mass, spring constant, damping, timestep, integrator — and how you found the hanging equilibrium.
The file
The single fenced html block.
What it actually shows
Now be honest. Having written it, does the simulation reproduce what you predicted?
Say plainly if it does not. Say if you are unsure. Say if it only works at some parameter settings and falls apart at others.
Do not tell me it shows the right thing because the physics says it should. I am going to open the file, press Release, and watch it against the marker line. If your prediction and your simulation disagree, the answer I want is the one that says so — that is a working scientist noticing their model is wrong, and it scores far above a confident write-up of a result the code does not produce.
assistant
The prediction
On release, the top end accelerates downward far faster than the bottom end. The top mass starts with a downward acceleration of about (N g \approx 440\ \mathrm{m/s^2}) because it is still carrying the tension of the spring below it; within about 15 ms it has compressed the first spring almost to its minimum separation. The compression/unloading disturbance then travels down the chain at a finite speed. For the parameters below, the fastest signal takes roughly (N/\sqrt{k/m} \approx 0.22\ \mathrm{s}) to reach the bottom, so the bottom mass should remain essentially at the marker line for about 200–250 ms while the upper part of the slinky visibly bunches. After that front arrives, the bottom begins to descend and the whole compacted slinky falls under gravity, with the bottom leaving the marker.
The setup
- 45 masses, each (m = 0.01\ \mathrm{kg}), connected by 44 springs.
- Spring stiffness (k = 400\ \mathrm{N/m}), rest length (L_0 = 0.013\ \mathrm{m}).
- Damping (c = 0.05\ \mathrm{N\cdot s/m}) between neighbouring masses, resisting relative velocity.
- Gravity (g = 9.81\ \mathrm{m/s^2}).
- Timestep (\Delta t = 0.0001\ \mathrm{s}).
- Integrator: semi-implicit Euler (symplectic Euler): compute all accelerations, update velocities, then update positions.
Equilibrium was solved analytically, not relaxed. With (y) measured downward from the support, spring (j) between masses (j) and (j+1) carries tension ((N-1-j)mg), so its extension is that tension divided by (k). I set (y_0=0) and
[ y_i = y_{i-1} + L_0 + (N-i)\frac{mg}{k}. ]
Velocities are zero. This gives the true non-uniform hanging shape: springs near the top are stretched much more than springs near the bottom. The only support constraint is the top end before Release; after Release every mass uses the same force loop.
The clock reports simulated milliseconds since release; at a 1× slider speed this is real time. The marker line is set from the bottom mass position at the instant Release is pressed and remains visible through Reset.
The file
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Falling Slinky</title>
<style>
* { box-sizing: border-box; }
body {
margin: 0;
min-height: 100vh;
display: flex;
align-items: center;
justify-content: center;
background: #0a0d13;
font: 15px/1.3 system-ui, -apple-system, "Segoe UI", sans-serif;
color: #d8e1ec;
}
.wrap {
width: 940px;
max-width: 96vw;
background: #141a23;
border-radius: 14px;
padding: 18px;
box-shadow: 0 10px 40px rgba(0,0,0,.45);
}
h1 {
margin: 0 0 12px;
font-size: 1.15rem;
letter-spacing: .5px;
}
.controls {
display: flex;
flex-wrap: wrap;
gap: 10px 16px;
align-items: center;
margin-bottom: 12px;
}
button {
background: #27313d;
border: 0;
color: #e8eef5;
padding: 9px 16px;
border-radius: 7px;
font: inherit;
cursor: pointer;
transition: background .15s;
}
button:hover:not(:disabled) { background: #334153; }
button:disabled { opacity: .35; cursor: default; }
.speed {
display: flex;
align-items: center;
gap: 8px;
}
input[type=range] {
width: 130px;
accent-color: #ffcf5a;
}
.clock {
font-variant-numeric: tabular-nums;
background: #0c1118;
padding: 7px 12px;
border-radius: 7px;
border: 1px solid #232d3a;
}
#clock { color: #ffcf5a; font-weight: 600; }
.canvas-wrap {
border: 1px solid #26303d;
border-radius: 10px;
overflow: hidden;
}
canvas {
display: block;
width: 100%;
height: auto;
background: #090d13;
}
.foot {
margin-top: 10px;
color: #7e8da0;
font-size: 12px;
}
</style>
</head>
<body>
<div class="wrap">
<h1>Falling slinky</h1>
<div class="controls">
<button id="releaseBtn" type="button">Release</button>
<button id="resetBtn" type="button" disabled>Reset</button>
<div class="speed">
<label for="speedSlider">Speed</label>
<input id="speedSlider" type="range" min="0.05" max="1" step="0.01" value="1">
<span id="speedVal">1.00×</span>
</div>
<div class="clock">sim time <span id="clock">0</span> ms</div>
</div>
<div class="canvas-wrap">
<canvas id="canvas" width="900" height="650"></canvas>
</div>
<div class="foot">45 masses, Hooke springs, semi-implicit Euler, dt = 0.1 ms.</div>
</div>
<script>
(() => {
'use strict';
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
const W = canvas.width;
const H = canvas.height;
const releaseBtn = document.getElementById('releaseBtn');
const resetBtn = document.getElementById('resetBtn');
const speedSlider = document.getElementById('speedSlider');
const speedVal = document.getElementById('speedVal');
const clockEl = document.getElementById('clock');
const N = 45;
const m = 0.01;
const k = 400;
const L0 = 0.013;
const g = 9.81;
const dampC = 0.05;
const DT = 0.0001;
const supportX = W / 2;
const supportY = 70;
const y = new Float64Array(N);
const v = new Float64Array(N);
const a = new Float64Array(N);
function restingState() {
y[0] = 0;
v[0] = 0;
for (let i = 1; i < N; i++) {
v[i] = 0;
const ext = (N - i) * m * g / k;
y[i] = y[i - 1] + L0 + ext;
}
}
restingState();
const slackLength = y[N - 1];
const scale = (H - supportY - 40) / slackLength;
const toCanvasY = p => supportY + p * scale;
let released = false;
let simTime = 0;
let accumulator = 0;
let markerY = null;
let lastNow = 0;
let speed = 1;
speedSlider.addEventListener('input', () => {
speed = parseFloat(speedSlider.value);
speedVal.textContent = speed.toFixed(2) + '×';
});
speed = parseFloat(speedSlider.value);
speedVal.textContent = speed.toFixed(2) + '×';
// After Release this is the only physics: the same force law for every mass.
function physicsStep(dt) {
for (let i = 0; i < N; i++) {
let f = m * g;
if (i > 0) {
const dy = y[i] - y[i - 1];
const ext = dy - L0;
const relV = v[i] - v[i - 1];
f += -k * ext - dampC * relV;
}
if (i < N - 1) {
const dy = y[i + 1] - y[i];
const ext = dy - L0;
const relV = v[i + 1] - v[i];
f += k * ext + dampC * relV;
}
a[i] = f / m;
}
for (let i = 0; i < N; i++) {
v[i] += a[i] * dt;
y[i] += v[i] * dt;
}
}
function drawSupport() {
ctx.save();
ctx.fillStyle = '#526479';
ctx.fillRect(supportX - 22, supportY - 20, 44, 10);
ctx.fillStyle = '#8b9bb0';
ctx.fillRect(supportX - 4, supportY - 10, 8, 8);
ctx.fillStyle = '#cdd8e5';
ctx.beginPath();
ctx.arc(supportX, supportY, 4, 0, Math.PI * 2);
ctx.fill();
ctx.restore();
}
function drawMarker() {
if (markerY === null) return;
ctx.save();
ctx.strokeStyle = '#ffcf5a';
ctx.lineWidth = 1.5;
ctx.setLineDash([8, 5]);
ctx.beginPath();
ctx.moveTo(0, markerY);
ctx.lineTo(W, markerY);
ctx.stroke();
ctx.setLineDash([]);
ctx.fillStyle = '#ffcf5a';
ctx.font = '12px ui-monospace, SFMono-Regular, Menlo, monospace';
ctx.textBaseline = 'alphabetic';
ctx.fillText('release bottom', 14, markerY - 8);
ctx.restore();
}
function drawSlinky() {
ctx.lineCap = 'round';
ctx.lineJoin = 'round';
for (let i = 0; i < N - 1; i++) {
const py0 = toCanvasY(y[i]);
const py1 = toCanvasY(y[i + 1]);
const len = Math.max(1, Math.abs(py1 - py0));
const amp = Math.min(7, Math.max(2.5, len * 0.22));
const turns = 2;
const steps = 20;
ctx.beginPath();
ctx.moveTo(supportX, py0);
for (let s = 1; s <= steps; s++) {
const t = s / steps;
const yy = py0 + (py1 - py0) * t;
const xx = supportX + amp * Math.sin(t * Math.PI * 2 * turns);
ctx.lineTo(xx, yy);
}
ctx.strokeStyle = '#79a7d8';
ctx.lineWidth = 2;
ctx.stroke();
}
ctx.fillStyle = '#ffd57a';
for (let i = 0; i < N; i++) {
const py = toCanvasY(y[i]);
ctx.beginPath();
ctx.arc(supportX, py, 3, 0, Math.PI * 2);
ctx.fill();
}
}
function draw() {
ctx.clearRect(0, 0, W, H);
ctx.strokeStyle = '#1c2531';
ctx.lineWidth = 1;
ctx.beginPath();
ctx.moveTo(supportX, 0);
ctx.lineTo(supportX, H);
ctx.stroke();
drawSupport();
drawSlinky();
drawMarker();
ctx.fillStyle = '#7e8da0';
ctx.font = '12px ui-monospace, SFMono-Regular, Menlo, monospace';
ctx.fillText('N = ' + N + ' masses, k = ' + k + ' N/m', 14, 24);
ctx.fillText('dt = 0.1 ms, semi-implicit Euler', 14, 42);
}
function release() {
if (released) return;
released = true;
releaseBtn.disabled = true;
resetBtn.disabled = false;
accumulator = 0;
simTime = 0;
markerY = toCanvasY(y[N - 1]);
clockEl.textContent = '0';
lastNow = performance.now();
}
function reset() {
released = false;
releaseBtn.disabled = false;
resetBtn.disabled = true;
accumulator = 0;
simTime = 0;
clockEl.textContent = '0';
restingState();
lastNow = performance.now();
}
releaseBtn.addEventListener('click', release);
resetBtn.addEventListener('click', reset);
function frame(now) {
if (!lastNow) lastNow = now;
let realDt = (now - lastNow) / 1000;
lastNow = now;
if (realDt < 0) realDt = 0;
if (realDt > 0.1) realDt = 0.1;
if (released) {
accumulator += realDt * speed;
while (accumulator >= DT) {
physicsStep(DT);
accumulator -= DT;
simTime += DT;
}
clockEl.textContent = Math.floor(simTime * 1000);
}
draw();
requestAnimationFrame(frame);
}
requestAnimationFrame(frame);
})();
</script>
</body>
</html>
What it actually shows
Honest report: I have not been able to run this page in a browser from this environment, so I cannot claim an observed verification. The code is a direct transcription of the model above, and the prediction follows from that model’s finite wave speed, but “the model says so” is not the same as having watched the rendered output. I am therefore unsure until the file is actually opened and run.
The one thing I would check on screen is the first compression transient: the top spring is the most violently compressed, and if the chosen rest length and stiffness did not prevent the top masses from passing through one another, that would be a visible failure. With the stated parameters the analytic overshoot bound is safely below the initial top spacing, so I expect it not to happen, but I would want to see that frame-by-frame before claiming the simulation reproduces the prediction.
Attachments
inception/mercury-3 — page