Run Detail
completedgpt-6.1-terraRecorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
58.1s
Total Tokens
5,915
Input Tokens
738
Output Tokens
5,177
Reasoning Tokens
2,305
Reasoning Effort
default
Est. Cost
$0.0266
Started
10/26/2026, 6:37:21 PM
OR Provider
OpenAI
Finish Reason
stop
Generation ID
gen-1793039841-yG6VE8HadVzFYsSs50Ki
Turns (1)
Turn #1
738 in5,177 out2,305 reasoning5,915 total58.1s
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
Immediately after release, the top will accelerate downward rapidly while the bottom remains almost level with the marker. The loss of support travels down the spring as a disturbance; for these parameters it should reach the bottom at roughly 200–250 ms. The bottom should then begin to fall, and the slinky will continue to collapse and oscillate. The transition will not be perfectly sharp because this is a discrete, damped chain.
The setup
- 50 point masses, each 0.01 kg, joined by 49 springs.
- Spring constant: 500 N/m; unstretched length: 1.5 mm.
- Neighbour-to-neighbour damping: 0.02 kg/s.
- Gravity: 9.81 m/s². Timestep: 0.2 ms, using semi-implicit Euler integration.
- Initially the top mass is held fixed. Each spring is extended by the weight of all masses below it divided by the spring constant, giving the exact static equilibrium of this chain.
- After release, all masses use the same integration rules. The endpoint masses naturally have only one neighbour.
The file
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>The falling slinky</title>
<style>
:root {
color-scheme: dark;
font-family: system-ui, sans-serif;
background: #101823;
color: #eef5fa;
}
* { box-sizing: border-box; }
body {
margin: 0;
padding: 20px;
}
main {
max-width: 1000px;
margin: 0 auto;
}
h1 {
margin: 0 0 6px;
font-size: 1.7rem;
}
p {
color: #b9cbd8;
line-height: 1.45;
}
.intro { margin: 0 0 16px; }
.controls {
display: flex;
flex-wrap: wrap;
align-items: center;
gap: 12px;
margin-bottom: 12px;
}
button {
border: 1px solid #9cc5d7;
border-radius: 6px;
background: #27536a;
color: white;
padding: 9px 16px;
font: inherit;
font-weight: 650;
cursor: pointer;
}
button:hover:not(:disabled) { background: #376d86; }
button:disabled {
cursor: default;
opacity: 0.5;
}
.speed {
display: flex;
align-items: center;
flex-wrap: wrap;
gap: 8px;
}
input[type="range"] {
width: 160px;
accent-color: #75d8e7;
}
output { font-variant-numeric: tabular-nums; }
.readouts {
display: flex;
flex-wrap: wrap;
gap: 8px 24px;
margin-bottom: 12px;
color: #d7e7f0;
}
.clock {
font-size: 1.2rem;
font-weight: 700;
}
canvas {
display: block;
width: 100%;
height: auto;
border: 1px solid #506574;
border-radius: 6px;
background: #172635;
}
.note {
margin: 10px 0 0;
font-size: 0.9rem;
}
</style>
</head>
<body>
<main>
<h1>The falling slinky</h1>
<p class="intro">
Release the hanging chain and watch its bottom against the dashed line.
</p>
<div class="controls">
<button id="release" type="button">Release</button>
<button id="reset" type="button">Reset</button>
<label class="speed" for="speed">
Speed
<input id="speed" type="range" min="0.05" max="1"
step="0.05" value="0.25">
<output id="speedValue" for="speed">0.25×</output>
</label>
</div>
<div class="readouts">
<div class="clock">Since release: <output id="clock">0 ms</output></div>
<div id="status">Hanging at equilibrium</div>
</div>
<canvas id="view" width="900" height="720"
aria-label="A hanging slinky and a horizontal line marking the initial height of its bottom">
</canvas>
<p class="note">
The clock measures simulated time. The dashed line stays at the bottom’s
release height; the view does not follow the slinky as it falls.
</p>
</main>
<script>
"use strict";
(() => {
const N = 50;
const MASS = 0.01; // kg per point mass
const K = 500; // N/m
const DAMPING = 0.02; // N s/m, between neighbours
const REST_LENGTH = 0.0015; // m
const GRAVITY = 9.81; // m/s^2
const DT = 0.0002; // s
const canvas = document.getElementById("view");
const ctx = canvas.getContext("2d");
const releaseButton = document.getElementById("release");
const resetButton = document.getElementById("reset");
const speedSlider = document.getElementById("speed");
const speedValue = document.getElementById("speedValue");
const clock = document.getElementById("clock");
const status = document.getElementById("status");
// Downward is positive; positions are in metres.
const y = new Float64Array(N);
const v = new Float64Array(N);
const a = new Float64Array(N);
let released = false;
let markerY = 0;
let steps = 0;
let accumulator = 0;
let lastFrame = null;
// A fixed view: neither the reference line nor the camera follows the chain.
const centerX = 450;
const anchorPixelY = 64;
const pixelsPerMetre = 900;
const toPixelY = metres => anchorPixelY + metres * pixelsPerMetre;
function reset() {
released = false;
steps = 0;
accumulator = 0;
lastFrame = null;
y[0] = 0;
v.fill(0);
// Spring i supports the N-1-i masses below it.
for (let i = 0; i < N - 1; i++) {
const supportedMass = (N - 1 - i) * MASS;
const extension = supportedMass * GRAVITY / K;
y[i + 1] = y[i] + REST_LENGTH + extension;
}
markerY = y[N - 1];
releaseButton.disabled = false;
status.textContent = "Hanging at equilibrium";
updateClock();
draw();
}
function step() {
// Every mass receives gravity, and each spring exerts equal and
// opposite forces on its two neighbours.
a.fill(GRAVITY);
for (let i = 0; i < N - 1; i++) {
const extension = y[i + 1] - y[i] - REST_LENGTH;
const relativeVelocity = v[i + 1] - v[i];
const force = K * extension + DAMPING * relativeVelocity;
a[i] += force / MASS;
a[i + 1] -= force / MASS;
}
// Semi-implicit Euler: update velocity, then position.
for (let i = 0; i < N; i++) {
v[i] += a[i] * DT;
y[i] += v[i] * DT;
}
steps++;
}
function updateClock() {
clock.textContent = Math.round(steps * DT * 1000) + " ms";
}
function draw() {
const w = canvas.width;
const h = canvas.height;
ctx.clearRect(0, 0, w, h);
// Fixed reference height.
const markerPixel = toPixelY(markerY);
ctx.save();
ctx.strokeStyle = "#ffcf70";
ctx.lineWidth = 1.5;
ctx.setLineDash([9, 7]);
ctx.beginPath();
ctx.moveTo(20, markerPixel);
ctx.lineTo(w - 20, markerPixel);
ctx.stroke();
ctx.setLineDash([]);
ctx.fillStyle = "#ffcf70";
ctx.font = "15px system-ui, sans-serif";
ctx.fillText("Bottom at release", 24, markerPixel - 9);
ctx.restore();
// Fixed support; only the unreleased chain is attached to it.
ctx.strokeStyle = "#a9bdca";
ctx.lineWidth = 3;
ctx.beginPath();
ctx.moveTo(centerX - 42, 31);
ctx.lineTo(centerX + 42, 31);
ctx.moveTo(centerX, 31);
ctx.lineTo(centerX, 50);
ctx.stroke();
ctx.beginPath();
ctx.arc(centerX, 54, 4, 0, Math.PI * 2);
ctx.stroke();
if (!released) {
ctx.beginPath();
ctx.moveTo(centerX, 58);
ctx.lineTo(centerX, anchorPixelY);
ctx.stroke();
}
// Coil-like marks represent the point masses. Their vertical positions
// are the simulated positions, not an independently animated shape.
ctx.save();
ctx.beginPath();
ctx.rect(0, 0, w, h);
ctx.clip();
for (let i = 0; i < N; i++) {
const py = toPixelY(y[i]);
if (py < -10 || py > h + 10) continue;
ctx.beginPath();
ctx.ellipse(centerX, py, 48, 4, 0, 0, Math.PI * 2);
ctx.strokeStyle = "#74d6e5";
ctx.lineWidth = 2;
ctx.stroke();
}
// Visual labels for the ends; they do not change the dynamics.
function endLabel(index, label, color) {
const py = toPixelY(y[index]);
if (py < 10 || py > h - 10) return;
ctx.fillStyle = color;
ctx.beginPath();
ctx.arc(centerX + 48, py, 4, 0, Math.PI * 2);
ctx.fill();
ctx.font = "15px system-ui, sans-serif";
ctx.fillText(label, centerX + 61, py + 5);
}
endLabel(0, "top", "#f7fbff");
endLabel(N - 1, "bottom", "#ffcf70");
ctx.restore();
if (toPixelY(y[N - 1]) > h || toPixelY(y[0]) > h) {
ctx.fillStyle = "#d7e7f0";
ctx.font = "15px system-ui, sans-serif";
ctx.fillText("The chain continues below the view.", 24, h - 20);
}
}
releaseButton.addEventListener("click", () => {
if (released) return;
markerY = y[N - 1];
released = true;
accumulator = 0;
lastFrame = null;
releaseButton.disabled = true;
status.textContent = "Released";
draw();
});
resetButton.addEventListener("click", reset);
speedSlider.addEventListener("input", () => {
speedValue.textContent = Number(speedSlider.value).toFixed(2) + "×";
});
// Do not try to simulate a long interval while the page is hidden.
// The clock remains a clock of simulated, rather than wall, time.
document.addEventListener("visibilitychange", () => {
lastFrame = null;
});
function frame(now) {
if (released && !document.hidden) {
if (lastFrame !== null) {
const elapsed = (now - lastFrame) / 1000;
accumulator += elapsed * Number(speedSlider.value);
while (accumulator >= DT) {
step();
accumulator -= DT;
}
}
lastFrame = now;
updateClock();
draw();
} else {
lastFrame = null;
}
requestAnimationFrame(frame);
}
reset();
requestAnimationFrame(frame);
})();
</script>
</body>
</html>
What it actually shows
The code is set up to produce the predicted delayed motion of the bottom at the default parameters. I have not run the file here, so I cannot verify the visible timing or appearance against the marker; that remains a prediction rather than an observed result.
Attachments
openai/gpt-6.1-terra — page