Run Detail
completeddeepseek-v4-pro-0813Recorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
503.3s
Total Tokens
39,641
Input Tokens
822
Output Tokens
38,819
Reasoning Tokens
33,581
Reasoning Effort
default
Est. Cost
$0.1548
Started
8/15/2026, 1:47:31 AM
OR Provider
Novita
Finish Reason
stop
Generation ID
gen-1786758452-J0FdHktP6Drc30CfDNao
Turns (1)
Turn #1
822 in38,819 out33,581 reasoning39,641 total503.2s
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
In the first few hundred milliseconds after release, the top of the slinky accelerates downward much faster than gravity alone, while the bottom remains essentially at the marker line. This is because the hanging slinky is in a true stretched equilibrium: upper coils support the weight of everything below them, so they are stretched much more than lower coils. When the top is released, only the top mass initially has a large unbalanced force; the lower masses still have balanced spring forces and zero initial acceleration. The release disturbance travels down as a longitudinal wave. With the parameters below, that wave reaches the bottom after about (N-1)*sqrt(m/k) = 49*0.01 ≈ 0.49 s of simulated time. So the top collapses almost immediately, the bottom stays near the marker for roughly half a second, and then the whole collapsed slinky falls away from the marker.
The setup
- Segments:
N = 50masses. - Mass:
m = 1in pixel-mass units. - Gravity:
g = 1000 px/s². - Spring rest length / solid coil spacing:
L0 = 8 px. - Spring stiffness:
k = 10000(chosen viam g / k = 0.1 px, so the hanging stretch is visible but not huge). - Damping: main spring damping coefficient
c = 20. - Coil collision: when adjacent masses are closer than
L0, a short-range repulsive contact force is added identically for every neighbouring pair, with stiffnesskContact = 500000and dampingcContact = 1000. This prevents coils from passing through each other without scripting any individual segment. - Timestep:
dt = 0.0002 s(1/5000 s), with semi-implicit Euler integration. - Hanging equilibrium: solved algebraically. With the top mass held at
y0, the extension of springiise_i = (N - 1 - i) * m * g / k. Positions are theny[i+1] = y[i] + L0 + e_i. This gives zero net force on every mass except the top one, which is held by the support. Velocities start at zero. No velocity clamping is used.
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>
body {
margin: 0;
background: #111;
color: #eee;
font-family: monospace;
display: flex;
justify-content: center;
align-items: center;
min-height: 100vh;
}
.wrap {
display: flex;
flex-direction: column;
align-items: center;
gap: 8px;
}
canvas {
background: #222;
border: 1px solid #444;
}
.controls {
display: flex;
align-items: center;
gap: 12px;
flex-wrap: wrap;
justify-content: center;
}
button {
background: #333;
color: #eee;
border: 1px solid #555;
padding: 6px 12px;
cursor: pointer;
font-family: monospace;
}
button:disabled {
opacity: 0.5;
cursor: default;
}
input[type="range"] {
vertical-align: middle;
}
#clock {
min-width: 70px;
display: inline-block;
text-align: right;
}
</style>
</head>
<body>
<div class="wrap">
<canvas id="c" width="600" height="680"></canvas>
<div class="controls">
<button id="releaseBtn">Release</button>
<button id="resetBtn">Reset</button>
<label>Speed
<input type="range" id="speed" min="0.05" max="1" step="0.01" value="0.2">
</label>
<span id="speedLabel">0.20x</span>
<span>Clock: <span id="clock">0 ms</span></span>
</div>
</div>
<script>
(() => {
const canvas = document.getElementById('c');
const ctx = canvas.getContext('2d');
const w = canvas.width;
const h = canvas.height;
const cx = w / 2;
// Physics parameters, length units are pixels.
const N = 50;
const m = 1;
const g = 1000;
const L0 = 8;
const mgPerK = 0.1;
const k = m * g / mgPerK; // 10000
const c = 20;
const kContact = 500000;
const cContact = 1000;
const dt = 0.0002;
const topY = 50;
const coilR = 4;
const y = new Float64Array(N);
const v = new Float64Array(N);
const initialY = new Float64Array(N);
const forces = new Float64Array(N);
let released = false;
let simTime = 0;
let markerY = 0;
let accumulated = 0;
let lastTime = performance.now();
const releaseBtn = document.getElementById('releaseBtn');
const resetBtn = document.getElementById('resetBtn');
const speedInput = document.getElementById('speed');
const speedLabel = document.getElementById('speedLabel');
const clockEl = document.getElementById('clock');
function updateClock() {
clockEl.textContent = Math.round(simTime * 1000) + ' ms';
}
function setInitial() {
y[0] = topY;
for (let i = 0; i < N - 1; i++) {
const extension = (N - 1 - i) * mgPerK;
y[i + 1] = y[i] + L0 + extension;
}
initialY.set(y);
v.fill(0);
markerY = y[N - 1] + coilR;
simTime = 0;
accumulated = 0;
released = false;
releaseBtn.disabled = false;
updateClock();
}
function computeForces() {
for (let i = 0; i < N; i++) forces[i] = m * g;
for (let i = 0; i < N - 1; i++) {
const dx = y[i + 1] - y[i];
const dv = v[i + 1] - v[i];
// Spring + dashpot between neighbouring masses.
let F = k * (dx - L0) + c * dv;
// Short-range contact, active only when coils are compressed
// below solid spacing. Applied identically to every pair.
if (dx < L0) {
F += kContact * (dx - L0) + cContact * dv;
}
forces[i] += F;
forces[i + 1] -= F;
}
}
function stepPhysics() {
computeForces();
for (let i = 0; i < N; i++) {
v[i] += (forces[i] / m) * dt;
}
for (let i = 0; i < N; i++) {
y[i] += v[i] * dt;
}
simTime += dt;
}
function draw() {
ctx.clearRect(0, 0, w, h);
// Marker line: bottom of slinky at release.
ctx.strokeStyle = 'rgba(255, 90, 90, 0.85)';
ctx.lineWidth = 1.5;
ctx.setLineDash([6, 5]);
ctx.beginPath();
ctx.moveTo(0, markerY);
ctx.lineTo(w, markerY);
ctx.stroke();
ctx.setLineDash([]);
ctx.fillStyle = '#ff5a5a';
ctx.font = '12px monospace';
ctx.fillText('bottom at release', 10, markerY - 6);
// Slinky coils.
for (let i = 0; i < N; i++) {
const yy = y[i];
if (yy < -20 || yy > h + 20) continue;
ctx.beginPath();
ctx.ellipse(cx, yy, 22, coilR, 0, 0, Math.PI * 2);
ctx.strokeStyle = `hsl(${205 - i * 2.5}, 35%, ${62 - i * 0.4}%)`;
ctx.lineWidth = 1.4;
ctx.stroke();
}
// Support while hanging.
if (!released) {
ctx.strokeStyle = '#bbbbbb';
ctx.lineWidth = 2;
ctx.beginPath();
ctx.moveTo(cx, 0);
ctx.lineTo(cx, y[0] - coilR);
ctx.stroke();
ctx.beginPath();
ctx.arc(cx, y[0] - coilR, 5, 0, Math.PI * 2);
ctx.stroke();
}
}
function frame(now) {
let realDelta = (now - lastTime) / 1000;
lastTime = now;
if (realDelta < 0) realDelta = 0;
if (realDelta > 0.05) realDelta = 0.05;
if (released) {
const speed = parseFloat(speedInput.value);
accumulated += realDelta * speed;
const steps = Math.floor(accumulated / dt);
for (let s = 0; s < steps; s++) {
stepPhysics();
}
accumulated -= steps * dt;
updateClock();
}
draw();
requestAnimationFrame(frame);
}
releaseBtn.addEventListener('click', () => {
if (released) return;
released = true;
releaseBtn.disabled = true;
markerY = y[N - 1] + coilR;
simTime = 0;
accumulated = 0;
updateClock();
});
resetBtn.addEventListener('click', setInitial);
speedInput.addEventListener('input', () => {
speedLabel.textContent = parseFloat(speedInput.value).toFixed(2) + 'x';
});
setInitial();
requestAnimationFrame(frame);
})();
</script>
</body>
</html>
What it actually shows
The simulation is built to reproduce the prediction. I have not executed it in this environment, so I cannot claim visual verification. The initial hanging state is exact, the integrator is stable at the chosen step, and the bottom delay should be close to the discrete-chain propagation time (N-1)*sqrt(m/k) ≈ 0.49 s. The part most likely to need tuning is the short-range contact force: if its stiffness were much lower, coils could overlap; if much higher, the timestep would need to be shortened. At the parameters above, I expect the bottom to stay at the marker for roughly the predicted half-second, then fall once the collapse wave reaches it.
Attachments
deepseek/deepseek-v4-pro-0813 — page