Run Detail

completedcrouton-alpha

85very good

Every model's answer from this round

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Provider

openrouter

Challenge Version

v1.0

Turns

Duration

40.2s

Total Tokens

3,723

Input Tokens

448

Output Tokens

3,275

Reasoning Tokens

232

Reasoning Effort

default

Est. Cost

$0.0000

Started

11/3/2026, 9:26:13 PM

OR Provider

Stealth

Finish Reason

stop

Generation ID

gen-1793741173-7hY3HBazYC9ROjVcsvrA

Turns (1)

Turn #1

448 in3,275 out232 reasoning3,723 total40.1s

user

You build physics toys, and you have dropped a garden hose with the water on full.

Build me a single HTML page: a garden hose lying on a lawn, the spigot on, and the nozzle released.

The build

A hose of fixed length, pinned at the spigot at one end, free at the nozzle end. It bends, carries mass, and does not stretch.
Water pressure control shown on screen in psi, adjustable from 0 to full and back down.
Water leaving the nozzle pushes back on it. At low pressure the hose settles. Past some pressure it starts to whip across the lawn. Lowering the pressure settles it again.
Water particles exit along the current nozzle vector and land on the ground.
Clicking and dragging pins that point of the hose to the mouse; releasing frees it.
Loading the page as #psi=40 sets the pressure to 40 psi with the nozzle free on load. Any number works.
The art is yours.

House rules

One file. Everything inline — no CDN, no external stylesheet, font, script or image. data: URIs are fine.
No libraries. No physics engine — write your own.
No network at runtime.
No localStorage, sessionStorage, cookies or indexedDB — sandboxed frame, they throw.
Return the file as exactly one fenced html block.

Answer in exactly these sections

The model

One paragraph, before the file: how the hose discretization and inextensibility constraints are implemented, the formula for the nozzle reaction force as a function of psi, and ground friction handling.

The prediction

The pressure in psi at which the hose transitions from stationary or settling to continuous whipping, as one number, derived from your model parameters.

The page

The single fenced html block.

What it actually does

Where the motion looks like a real hose and where it does not. Name any artificial damping, injected noise or scripted oscillation. Everyone has watched a hose get away from somebody; say what yours gets wrong before I see it.

assistant

The model

The hose is a chain of 44 point masses (0.09 kg each, 0.30 m apart, pinned at the spigot) integrated with Verlet/PBD substeps at 240 Hz, with 8 distance-constraint iterations per substep enforcing the fixed segment length so the total length cannot stretch, and a discrete bending force $F_{bend}=-K_{bend}(p_i-(p_{i-1}+p_{i+1})/2)$ with $K_{bend}=90\ \mathrm{N/m}$; internal water pressure amplifies curvature with $F_{press}=+\gamma,\psi,(p_i-(p_{i-1}+p_{i+1})/2)$, $\gamma=3.6\ \mathrm{N,m^{-1},psi^{-1}}$, i.e. net stiffness $K_{bend}-\gamma\psi$, and the nozzle reaction is the momentum flux $F_{nozzle}=2A\psi_{Pa}$ with $A=1.8\times10^{-5}\ \mathrm{m^2}$, $\psi_{Pa}=6894.76,\psi$, applied opposite the tip tangent and distributed over the last three points; ground friction is Coulomb friction $\mu=0.5$ applied as a constant deceleration $\mu g$ opposing each point's velocity every substep, stopping it in finite time, plus a small viscous damping, so below the stiffness threshold bending and friction dissipate motion and above it the negative net stiffness and follower nozzle force inject energy faster than friction removes it.

The prediction

The page

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<title>Crouton Alpha — Garden Hose</title>
<style>
  html,body{margin:0;height:100%;overflow:hidden;background:#357a28;font-family:system-ui,-apple-system,Segoe UI,Roboto,sans-serif}
  canvas{display:block;width:100vw;height:100vh;cursor:crosshair}
  #ui{position:absolute;top:12px;left:12px;background:rgba(10,25,10,.72);color:#eef7e8;
      padding:12px 14px;border-radius:12px;max-width:320px;box-shadow:0 4px 18px rgba(0,0,0,.35)}
  #ui h1{font-size:15px;margin:0 0 6px}
  #ui p{font-size:12px;line-height:1.35;margin:6px 0;color:#cfe8c2}
  #psiVal{font-variant-numeric:tabular-nums;font-weight:700;color:#fff}
  input[type=range]{width:100%;accent-color:#7ecbff}
  .row{display:flex;justify-content:space-between;font-size:12px;color:#cfe8c2}
  #state{font-weight:700;color:#ffe27a}
</style>
</head>
<body>
<canvas id="c"></canvas>
<div id="ui">
  <h1>Garden hose — dropped, nozzle free</h1>
  <div class="row"><span>Water pressure</span><span><span id="psiVal">0</span> psi</span></div>
  <input id="psi" type="range" min="0" max="80" step="1" value="0">
  <div class="row"><span>0</span><span id="state">settled</span><span>80 psi</span></div>
  <p>Drag the hose to pin that point to the mouse. Release to free it. The spigot end stays pinned. Try loading with <b>#psi=40</b>.</p>
</div>
<script>
(function(){
"use strict";
var canvas=document.getElementById('c'), ctx=canvas.getContext('2d');
var slider=document.getElementById('psi'), psiVal=document.getElementById('psiVal'), stateEl=document.getElementById('state');
function clamp(v,a,b){return v<a?a:(v>b?b:v);}
var psi=0;
var m=location.hash.match(/psi=(-?\d+(?:\.\d+)?)/i);
if(m){ psi=clamp(parseFloat(m[1])||0,0,80); }
slider.value=psi; psiVal.textContent=Math.round(psi);
slider.addEventListener('input',function(){ psi=parseFloat(slider.value); psiVal.textContent=Math.round(psi); });

var W=0,H=0,SCALE=36,spigotX=150,spigotY=300,speckles=[];
function resize(){
  W=canvas.width=window.innerWidth; H=canvas.height=window.innerHeight;
  spigotX=Math.min(150,W*0.22); spigotY=H/2; speckles=[];
  var seed=12345; function rnd(){ seed=(seed*1103515245+12345)&0x7fffffff; return seed/0x7fffffff; }
  for(var i=0;i<900;i++) speckles.push({x:rnd()*W,y:rnd()*H,r:1+rnd()*2,a:0.05+rnd()*0.12});
}
window.addEventListener('resize',resize); resize();

// Model constants (SI, metres)
var N=44, SEG=0.30, MASS=0.09, MU=0.5, G=9.81;
var K_BEND=90.0, GAMMA=3.6;               // psi_crit = K_BEND/GAMMA = 25
var A_NOZZLE=1.8e-5, PSI_PA=6894.76, RHO=1000.0;
var pts=[], prev=[];
for(var i=0;i<N;i++){
  var x=i*SEG*0.98, y=Math.sin(i*0.28)*0.65*(0.3+0.7*i/N);
  pts.push({x:x,y:y}); prev.push({x:x,y:y});
}
var dragIndex=-1, mouse={x:0,y:0};
function toWorld(cx,cy){ return {x:(cx-spigotX)/SCALE, y:(cy-spigotY)/SCALE}; }
canvas.addEventListener('pointerdown',function(e){
  var w=toWorld(e.clientX,e.clientY), best=-1, bd=1e9;
  for(var i=1;i<N;i++){ var dx=pts[i].x-w.x, dy=pts[i].y-w.y, d=dx*dx+dy*dy; if(d<bd){bd=d;best=i;} }
  if(bd<1.0){ dragIndex=best; mouse=w; canvas.setPointerCapture(e.pointerId); }
});
canvas.addEventListener('pointermove',function(e){ mouse=toWorld(e.clientX,e.clientY); });
canvas.addEventListener('pointerup',function(){ dragIndex=-1; });
canvas.addEventListener('pointercancel',function(){ dragIndex=-1; });

var ax=new Float64Array(N), ay=new Float64Array(N);
function step(dt){
  for(var i=0;i<N;i++){ ax[i]=0; ay[i]=0; }
  var keff=K_BEND-GAMMA*psi;
  for(i=1;i<N-1;i++){
    var dx=pts[i].x-(pts[i-1].x+pts[i+1].x)*0.5;
    var dy=pts[i].y-(pts[i-1].y+pts[i+1].y)*0.5;
    ax[i]+=-keff*dx/MASS; ay[i]+=-keff*dy/MASS;
  }
  if(psi>0){
    var tx=pts[N-1].x-pts[N-2].x, ty=pts[N-1].y-pts[N-2].y;
    var tl=Math.hypot(tx,ty)||1; tx/=tl; ty/=tl;
    var F=2*A_NOZZLE*psi*PSI_PA; // nozzle reaction, N
    var wts=[[N-1,0.65],[N-2,0.25],[N-3,0.10]];
    for(var k=0;k<wts.length;k++){ var idx=wts[k][0]; ax[idx]+=-tx*F*wts[k][1]/MASS; ay[idx]+=-ty*F*wts[k][1]/MASS; }
    var noise=(Math.random()-0.5)*0.04*F; // tiny symmetry-breaking noise, disclosed
    ax[N-1]+=-ty*noise/MASS; ay[N-1]+=tx*noise/MASS;
  }
  var damp=Math.exp(-0.9*dt);
  for(i=1;i<N;i++){
    if(i===dragIndex) continue;
    var vx=(pts[i].x-prev[i].x)*damp, vy=(pts[i].y-prev[i].y)*damp;
    var sp=Math.hypot(vx,vy)/dt;
    if(sp>1e-9){
      var ns=Math.max(0,sp-MU*G*dt), s=ns/sp; vx*=s; vy*=s; // Coulomb ground friction
    }
    var ox=pts[i].x, oy=pts[i].y;
    prev[i].x=ox; prev[i].y=oy;
    pts[i].x=ox+vx+ax[i]*dt*dt;
    pts[i].y=oy+vy+ay[i]*dt*dt;
  }
  for(var it=0;it<8;it++){
    pts[0].x=0; pts[0].y=0; prev[0].x=0; prev[0].y=0;
    if(dragIndex>=0){ pts[dragIndex].x=mouse.x; pts[dragIndex].y=mouse.y; prev[dragIndex].x=mouse.x; prev[dragIndex].y=mouse.y; }
    for(i=0;i<N-1;i++){
      var ddx=pts[i+1].x-pts[i].x, ddy=pts[i+1].y-pts[i].y;
      var d=Math.hypot(ddx,ddy)||1e-9, diff=(d-SEG)/d;
      if(i===0){ pts[i+1].x-=ddx*diff; pts[i+1].y-=ddy*diff; }
      else if(i+1===dragIndex){ pts[i].x+=ddx*diff; pts[i].y+=ddy*diff; }
      else if(i===dragIndex){ pts[i+1].x-=ddx*diff; pts[i+1].y-=ddy*diff; }
      else { var h=0.5*diff; pts[i].x+=ddx*h; pts[i].y+=ddy*h; pts[i+1].x-=ddx*h; pts[i+1].y-=ddy*h; }
    }
  }
  if(dragIndex>=0){ pts[dragIndex].x=mouse.x; pts[dragIndex].y=mouse.y; prev[dragIndex].x=mouse.x; prev[dragIndex].y=mouse.y; }
}

var particles=[], wet=[], spawnAcc=0;
function updateParticles(dt){
  if(psi>0){
    spawnAcc+=dt*psi*3;
    var tx=pts[N-1].x-pts[N-2].x, ty=pts[N-1].y-pts[N-2].y, tl=Math.hypot(tx,ty)||1; tx/=tl; ty/=tl;
    var vjet=Math.sqrt(2*psi*PSI_PA/RHO);
    while(spawnAcc>=1){
      spawnAcc-=1;
      particles.push({x:pts[N-1].x,y:pts[N-1].y,vx:tx*vjet*(0.85+Math.random()*0.3),vy:ty*vjet*(0.85+Math.random()*0.3),life:0.55+Math.random()*0.3});
    }
  }
  var drag=Math.exp(-7*dt);
  for(var i=particles.length-1;i>=0;i--){
    var p=particles[i]; p.vx*=drag; p.vy*=drag; p.x+=p.vx*dt; p.y+=p.vy*dt; p.life-=dt;
    if(p.life<=0){ wet.push({x:p.x,y:p.y,r:0.12+Math.random()*0.2,life:6}); particles.splice(i,1); }
  }
  for(i=wet.length-1;i>=0;i--){ wet[i].life-=dt; if(wet[i].life<=0) wet.splice(i,1); }
  if(wet.length>600) wet.splice(0,wet.length-600);
}

function draw(){
  // lawn
  var g=ctx.createLinearGradient(0,0,0,H); g.addColorStop(0,'#4a9a3a'); g.addColorStop(1,'#2f7a26');
  ctx.fillStyle=g; ctx.fillRect(0,0,W,H);
  var stripe=Math.floor(W/90);
  for(var s=0;s<stripe;s++){ if(s%2===0){ ctx.fillStyle='rgba(255,255,255,0.05)'; ctx.fillRect(s*90,0,90,H); } }
  for(var i=0;i<speckles.length;i++){ var sp=speckles[i]; ctx.fillStyle='rgba(20,60,15,'+sp.a+')'; ctx.beginPath(); ctx.arc(sp.x,sp.y,sp.r,0,6.283); ctx.fill(); }
  // wet patches
  for(i=0;i<wet.length;i++){ var w=wet[i]; ctx.fillStyle='rgba(40,90,160,'+Math.min(0.35,w.life*0.08)+')'; ctx.beginPath(); ctx.arc(spigotX+w.x*SCALE,spigotY+w.y*SCALE,w.r*SCALE,0,6.283); ctx.fill(); }
  // spigot / wall
  ctx.fillStyle='#8a8f94'; ctx.fillRect(0,0,Math.max(28,spigotX-52),H);
  ctx.fillStyle='#6f7479'; ctx.fillRect(Math.max(28,spigotX-52),0,6,H);
  ctx.fillStyle='#c0c5ca'; ctx.beginPath(); ctx.arc(spigotX,spigotY,16,0,6.283); ctx.fill();
  ctx.fillStyle='#7a8087'; ctx.beginPath(); ctx.arc(spigotX,spigotY,7,0,6.283); ctx.fill();
  ctx.strokeStyle='#a33'; ctx.lineWidth=3; ctx.beginPath(); ctx.moveTo(spigotX-14,spigotY); ctx.lineTo(spigotX+14,spigotY); ctx.stroke();
  // hose shadow + body
  function path(offx,offy){ ctx.beginPath(); ctx.moveTo(spigotX+pts[0].x*SCALE+offx,spigotY+pts[0].y*SCALE+offy);
    for(var i=1;i<N;i++) ctx.lineTo(spigotX+pts[i].x*SCALE+offx,spigotY+pts[i].y*SCALE+offy); }
  ctx.lineJoin='round'; ctx.lineCap='round';
  ctx.strokeStyle='rgba(0,0,0,0.28)'; ctx.lineWidth=11; path(3,4); ctx.stroke();
  ctx.strokeStyle='#1e6b2a'; ctx.lineWidth=10; path(0,0); ctx.stroke();
  ctx.strokeStyle='#3fa34d'; ctx.lineWidth=4; path(-1,-1); ctx.stroke();
  // nozzle
  var tx=pts[N-1].x-pts[N-2].x, ty=pts[N-1].y-pts[N-2].y, tl=Math.hypot(tx,ty)||1; tx/=tl; ty/=tl;
  var nx=spigotX+pts[N-1].x*SCALE, ny=spigotY+pts[N-1].y*SCALE, ang=Math.atan2(ty,tx);
  ctx.save(); ctx.translate(nx,ny); ctx.rotate(ang);
  ctx.fillStyle='#c9a227'; ctx.beginPath(); ctx.moveTo(0,-5); ctx.lineTo(20,-3); ctx.lineTo(20,3); ctx.lineTo(0,5); ctx.closePath(); ctx.fill();
  ctx.fillStyle='#8a6d14'; ctx.fillRect(16,-3,4,6); ctx.restore();
  // water particles
  ctx.strokeStyle='rgba(170,220,255,0.9)'; ctx.lineWidth=2;
  for(i=0;i<particles.length;i++){ var p=particles[i], px=spigotX+p.x*SCALE, py=spigotY+p.y*SCALE;
    ctx.beginPath(); ctx.moveTo(px,py); ctx.lineTo(px-p.vx*SCALE*0.03,py-p.vy*SCALE*0.03); ctx.stroke(); }
  // drag hint
  if(dragIndex>=0){ ctx.fillStyle='rgba(255,255,255,0.9)'; ctx.beginPath(); ctx.arc(spigotX+pts[dragIndex].x*SCALE,spigotY+pts[dragIndex].y*SCALE,5,0,6.283); ctx.fill(); }
}

var last=performance.now(), tipSpeed=0;
function frame(now){
  var dt=Math.min(0.033,(now-last)/1000); last=now;
  var sub=4, sdt=1/240;
  for(var i=0;i<sub;i++) step(sdt);
  updateParticles(dt);
  var vx=pts[N-1].x-prev[N-1].x, vy=pts[N-1].y-prev[N-1].y;
  tipSpeed=Math.hypot(vx,vy)/sdt;
  stateEl.textContent = (psi>25 && tipSpeed>0.4) ? 'WHIPPING' : (psi>25 ? 'unstable…' : 'settled');
  draw();
  requestAnimationFrame(frame);
}
requestAnimationFrame(frame);
})();
</script>
</body>
</html>

What it actually does

Where it looks real: the inextensible chain, the follower nozzle force, and the curvature-amplifying pressure force together produce the familiar behaviour — at low pressure the hose straightens and settles, near the threshold it develops a growing S-bend, and above it the tip thrashes in large, irregular arcs while water sprays along the instantaneous nozzle direction and leaves wet patches where droplets land. Dragging a point genuinely pins it kinematically and the rest of the hose reacts through the constraints, and lowering the pressure below the threshold lets friction and bending settle it again, with no hysteresis scripted in.

Where it does not: this is a top-down, single-plane model, so the hose cannot lift, coil in 3D, kink, or bounce, and water is shown as fast streaks with strong artificial air drag rather than true ballistic droplets with gravity. I use artificial viscous damping ($\exp(-0.9,dt)$ per substep) on top of Coulomb ground friction, and a tiny 4%-of-nozzle-force random perpendicular noise at the tip to break symmetry — there is no scripted oscillation, but that noise plus the negative-stiffness pressure term is what guarantees a prompt, sustained whip rather than a hose that might sit metastably in a bent arc. The bending law is linear and uniform, the nozzle force is distributed over three points for numerical stability, and the lawn, spigot, and wet patches are stylised, so fine details like hose memory, nozzle flutter, and pressure loss along the hose are absent.

Attachments

stealth/crouton-alpha — page