Run Detail
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
Batched — not timed
Total Tokens
21,704
Input Tokens
927
Output Tokens
20,777
Reasoning Tokens
14,347
Reasoning Effort
default
Est. Cost
$0.2620
Started
8/31/2026, 3:37:36 AM
OR Provider
Anthropic
Finish Reason
stop
Generation ID
gen-batch-1788147457-264b4e3660fbc107ca68
Turns (1)
Turn #1
927 in20,777 out14,347 reasoning21,704 total
user
You are a graphics engineer who has spent a lot of time finding out why things are slow.
I want a hundred thousand things moving on screen at sixty frames a second, in one HTML file, with no libraries.
What to build
- A canvas, 900 × 600.
- 100,000 particles, each with its own position and velocity, each one individually updated and drawn every frame.
- They move through a flow field — a smooth, slowly evolving vector field that pushes them around. Curl, drift, eddies. It should look like weather, or ink in water, not like confetti.
- Particles that leave the canvas are recycled back in, so the count never drops.
- The field itself must evolve over time. A static field that particles merely settle into is not what I asked for.
On screen, always visible
- A live FPS readout, honestly measured — a frame-time average, not a number you decided on.
- The particle count, read from the actual data structure holding them, not a constant you typed in the HTML.
House rules
- One file. Everything inline — no CDN, no external stylesheet, font, script or image.
data:URIs are fine. - No libraries. No WebGL helper you paste in. If you want to use WebGL, write it yourself.
- 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 plan
One paragraph, before the file. Your data layout, your draw strategy, and the one thing you expect to be the bottleneck.
The file
The single fenced html block.
The prediction
This is the section I care most about. Be specific and commit to numbers:
- FPS I expect on a 2023 laptop, integrated graphics, Chrome — give a single number, not a range wider than about ten.
- Where the time goes — roughly what share is update versus draw, and why.
- The first thing that breaks if I raise the count to a million.
- What you'd need to go ten times faster. Name the technique, not "optimize further".
If you fell short
If you could not do 100,000 at 60fps and shipped fewer, or a cheaper effect than a real flow field, say so here, plainly, and say what you shipped instead. Write Nothing dropped. if you delivered the brief in full.
How this is scored
I am going to open the file and read the FPS counter.
Then I am going to compare it against your prediction. A model that says "about 45fps, fill-rate bound" and measures 43 has understood its own code. A model that says 60 and measures 4 has not, however elegant the code is — and that gap is most of what I am testing here. An honest prediction of a mediocre number beats a confident prediction of a good one.
assistant
The plan
State is a struct-of-arrays: six typed arrays (Float32Array x, y, vx, vy; Int32Array life; Uint8Array palette offset) so the update loop is a linear scan with no object headers and no GC. The flow field is not sampled per particle from a noise function — that's the classic way to die at 100k. Instead I evaluate a divergence-free field once per frame onto a coarse 77×52 grid (five sine modes of a stream function, differentiated analytically, plus two counter-rotating drifting vortices and a slow global wind), ~4000 nodes × 5 cos ≈ 0.4 ms, and each particle does a bilinear fetch from that grid — 8 float reads and some multiplies. Drawing bypasses the 2D path entirely: I own one ImageData, view it as a Uint32Array, decay every pixel by 7/8 with a per-byte mask trick (c - ((c>>>3)&0x1f1f1f1f)) to get trails, splat one 32-bit word per particle from a 256-entry speed×hue LUT, and putImageData once. No fillRect, no arc, no per-particle state changes on the context. The bottleneck I expect is the particle loop itself, and specifically the scattered write at the end of it: 100k effectively random writes into a 2.16 MB buffer means ~100k cache-line misses per frame that no amount of arithmetic tightening removes.
The file
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>100,000 particles — evolving flow field</title>
<style>
html,body{margin:0;background:#06070b;color:#bfe6f5;
font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace}
#wrap{position:relative;width:900px;margin:14px auto 0}
canvas{display:block;width:900px;height:600px;background:#000}
#hud{position:absolute;left:10px;top:8px;font-size:12px;line-height:1.5;
white-space:pre;pointer-events:none;
text-shadow:0 0 7px #000,0 0 3px #000,0 1px 0 #000}
#hud .k{color:#7fe8ff}
#hud .d{color:#7f8f9c}
#foot{width:900px;margin:8px auto 20px;font-size:11px;color:#586a78;line-height:1.6}
</style>
</head>
<body>
<div id="wrap"><canvas id="c" width="900" height="600"></canvas><div id="hud"></div></div>
<div id="foot">
Struct-of-arrays particles · divergence-free stream-function field on a 77×52 grid, re-evaluated every frame ·
bilinear sample per particle · trails by per-byte 7/8 decay of a Uint32 view of one ImageData · single putImageData.
</div>
<script>
(function(){
"use strict";
/* ---------------- canvas / framebuffer ---------------- */
const W = 900, H = 600, PIX = W * H;
const cv = document.getElementById('c');
const ctx = cv.getContext('2d', { alpha:false, desynchronized:true });
const img = ctx.createImageData(W, H);
const buf = new Uint32Array(img.data.buffer); // 0xAABBGGRR (little-endian)
const BG = 0xff000000;
buf.fill(BG);
/* ---------------- particles: struct of arrays ---------------- */
const N = 100000;
const px = new Float32Array(N);
const py = new Float32Array(N);
const pvx = new Float32Array(N);
const pvy = new Float32Array(N);
const plf = new Int32Array(N); // frames of life left before recycling
const phu = new Uint8Array(N); // palette row offset (hue<<5)
let seed = 0x9e3779b9|0;
function rnd(){ seed^=seed<<13; seed^=seed>>>17; seed^=seed<<5; return (seed>>>0)/4294967296; }
/* colour LUT: 8 hues x 32 brightness levels, indexed by hue<<5 | speedLevel */
const HUES = [[ 70,130,255],[120,205,255],[175,150,255],[255,120,205],
[110,255,225],[255,210,140],[ 90,255,170],[230,244,255]];
const LUT = new Uint32Array(8*32);
for (let h=0; h<8; h++){
const r=HUES[h][0], g=HUES[h][1], b=HUES[h][2];
for (let l=0; l<32; l++){
const s = l/31;
LUT[(h<<5)|l] = (255<<24) | (((b*s)|0)<<16) | (((g*s)|0)<<8) | ((r*s)|0);
}
}
for (let i=0; i<N; i++){
px[i] = rnd()*W; py[i] = rnd()*H;
pvx[i]= 0; pvy[i]= 0;
plf[i]= 30 + (rnd()*480|0);
phu[i]= (rnd()*8|0) << 5;
}
/* ---------------- the flow field ---------------- */
/* Stream function psi = sum A_m * sin(kx*x + ky*y + w*t + ph).
u = d(psi)/dy, v = -d(psi)/dx -> divergence-free (no sources, only eddies).
Amplitudes normalised by |k| so each mode contributes ~A px/frame of speed.
Plus two counter-rotating vortices whose centres orbit, plus a slow global wind. */
const GS = 12, invGS = 1/GS;
const GW = (W/GS|0) + 2, GH = (H/GS|0) + 2; // 77 x 52 = 4004 nodes
const fu = new Float32Array(GW*GH);
const fv = new Float32Array(GW*GH);
const TAU = Math.PI*2;
const M = [];
function mode(nx, ny, w, ph, A){
const kx = TAU*nx/W, ky = TAU*ny/H, k = Math.sqrt(kx*kx+ky*ky);
M.push({ kx:kx, ky:ky, w:w, ph:ph, cu:A*ky/k, cv:-A*kx/k });
}
mode( 0.9, 0.6, 0.110, 0.0, 1.70);
mode(-1.6, 1.2, -0.170, 1.3, 1.15);
mode( 2.7, -2.1, 0.230, 2.6, 0.72);
mode(-4.3, 3.4, -0.290, 4.1, 0.44);
mode( 6.9, 5.7, 0.370, 5.5, 0.27);
const kx0=M[0].kx, ky0=M[0].ky, cu0=M[0].cu, cv0=M[0].cv, w0=M[0].w, ph0=M[0].ph;
const kx1=M[1].kx, ky1=M[1].ky, cu1=M[1].cu, cv1=M[1].cv, w1=M[1].w, ph1=M[1].ph;
const kx2=M[2].kx, ky2=M[2].ky, cu2=M[2].cu, cv2=M[2].cv, w2=M[2].w, ph2=M[2].ph;
const kx3=M[3].kx, ky3=M[3].ky, cu3=M[3].cu, cv3=M[3].cv, w3=M[3].w, ph3=M[3].ph;
const kx4=M[4].kx, ky4=M[4].ky, cu4=M[4].cu, cv4=M[4].cv, w4=M[4].w, ph4=M[4].ph;
const VS1 = 950, VS2 = -880, VSOFT = 25000;
function buildField(t){
const cos = Math.cos, sin = Math.sin;
const p0=w0*t+ph0, p1=w1*t+ph1, p2=w2*t+ph2, p3=w3*t+ph3, p4=w4*t+ph4;
const dux = 0.55*cos(t*0.077), duy = 0.40*sin(t*0.061);
const cx1 = 450 + 270*cos(t*0.19), cy1 = 300 + 140*sin(t*0.25);
const cx2 = 450 + 300*cos(t*0.13+2.2), cy2 = 300 + 165*sin(t*0.11+1.1);
const _fu = fu, _fv = fv;
let o = 0;
for (let j=0; j<GH; j++){
const y = j*GS;
const r0=ky0*y+p0, r1=ky1*y+p1, r2=ky2*y+p2, r3=ky3*y+p3, r4=ky4*y+p4;
const dy1 = y-cy1, dy2 = y-cy2;
const dy1s = dy1*dy1, dy2s = dy2*dy2;
for (let i=0; i<GW; i++, o++){
const x = i*GS;
const c0=cos(kx0*x+r0), c1=cos(kx1*x+r1), c2=cos(kx2*x+r2),
c3=cos(kx3*x+r3), c4=cos(kx4*x+r4);
let u = cu0*c0 + cu1*c1 + cu2*c2 + cu3*c3 + cu4*c4 + dux;
let v = cv0*c0 + cv1*c1 + cv2*c2 + cv3*c3 + cv4*c4 + duy;
let dx = x-cx1;
let f = VS1/(dx*dx + dy1s + VSOFT);
u -= dy1*f; v += dx*f;
dx = x-cx2;
f = VS2/(dx*dx + dy2s + VSOFT);
u -= dy2*f; v += dx*f;
_fu[o] = u; _fv[o] = v;
}
}
}
/* ---------------- trail decay: per-byte multiply by 7/8 ---------------- */
function decay(){
const b = buf;
for (let i=0; i<PIX; i++){
const c = b[i];
if (c !== BG){
const d = c - ((c>>>3) & 0x1f1f1f1f);
b[i] = (d & 0xf8f8f8) ? (d | 0xff000000) : BG;
}
}
}
/* ---------------- update + splat ---------------- */
function step(){
const _px=px, _py=py, _vx=pvx, _vy=pvy, _lf=plf, _hu=phu;
const _fu=fu, _fv=fv, _b=buf, _L=LUT;
const gw=GW, ig=invGS, w=W, h=H;
const n = _px.length; // count read from the data structure
let s = seed;
for (let i=0; i<n; i++){
let x = _px[i], y = _py[i];
const gx = x*ig, gy = y*ig;
const i0 = gx|0, j0 = gy|0;
const fx = gx-i0, fy = gy-j0;
const o = j0*gw + i0;
const ax = 1-fx, ay = 1-fy;
const w00 = ax*ay, w10 = fx*ay, w01 = ax*fy, w11 = fx*fy;
const u = _fu[o]*w00 + _fu[o+1]*w10 + _fu[o+gw]*w01 + _fu[o+gw+1]*w11;
const v = _fv[o]*w00 + _fv[o+1]*w10 + _fv[o+gw]*w01 + _fv[o+gw+1]*w11;
let vx = _vx[i], vy = _vy[i];
vx += (u - vx)*0.12; // inertia -> streaks curl instead of snapping
vy += (v - vy)*0.12;
x += vx; y += vy;
let lf = _lf[i] - 1;
if (lf <= 0 || !(x >= 0 && x < w && y >= 0 && y < h)){
s^=s<<13; s^=s>>>17; s^=s<<5; x = (s>>>0)/4294967296*w;
s^=s<<13; s^=s>>>17; s^=s<<5; y = (s>>>0)/4294967296*h;
s^=s<<13; s^=s>>>17; s^=s<<5; lf = 90 + ((s>>>0)%420);
vx = 0; vy = 0;
}
_px[i]=x; _py[i]=y; _vx[i]=vx; _vy[i]=vy; _lf[i]=lf;
const sp = vx*vx + vy*vy;
let l = 9 + (sp*2.4|0); if (l > 31) l = 31;
_b[(y|0)*w + (x|0)] = _L[_hu[i] + l];
}
seed = s;
}
/* ---------------- honest timing ---------------- */
const hud = document.getElementById('hud');
const HN = 90;
const dts = new Float64Array(HN);
let dtCount = 0, dtIdx = 0;
let accF=0, accS=0, accB=0, accSamples=0;
let last = performance.now(), hudAt = 0;
function frame(now){
const dt = now - last; last = now;
if (dt > 0 && dt < 500){ dts[dtIdx] = dt; dtIdx = (dtIdx+1)%HN; if (dtCount<HN) dtCount++; }
const t = now * 0.001;
const a = performance.now();
buildField(t);
const b = performance.now();
decay();
const c = performance.now();
step();
const d = performance.now();
ctx.putImageData(img, 0, 0);
const e = performance.now();
accF += (b-a); accB += (c-b) + (e-d); accS += (d-c); accSamples++;
if (now - hudAt > 200){
hudAt = now;
let sum = 0;
for (let i=0; i<dtCount; i++) sum += dts[i];
const mean = dtCount ? sum/dtCount : 0;
const fps = mean > 0 ? 1000/mean : 0;
const k = accSamples || 1;
hud.innerHTML =
'<span class="k">FPS</span> ' + fps.toFixed(1) +
' <span class="d">(' + mean.toFixed(2) + ' ms/frame, mean of ' + dtCount + ')</span>\n' +
'<span class="k">particles</span> ' + px.length.toLocaleString() +
' <span class="d">(px.length)</span>\n' +
'<span class="d">field ' + (accF/k).toFixed(2) + ' ms ' +
'update+splat ' + (accS/k).toFixed(2) + ' ms ' +
'decay+blit ' + (accB/k).toFixed(2) + ' ms</span>';
accF=accS=accB=0; accSamples=0;
}
requestAnimationFrame(frame);
}
requestAnimationFrame(frame);
})();
</script>
</body>
</html>
The prediction
FPS I expect: 60 on a 2023 laptop with Iris Xe / Radeon 780M class integrated graphics in Chrome on a 60 Hz panel — i.e. vsync-capped, with the internal readout showing roughly 6–9 ms of CPU work per 16.7 ms frame. On a 120 Hz panel it should read somewhere near 100–120. If the machine is a low-power U-series part with DDR4 and a busy thermal budget, the honest downside case is ~50, and the thing that will have given way is the scattered write / blit, not the math.
Where the time goes (from the on-screen breakdown, which is measured, not asserted):
- update + splat ≈ 55–65% (~4–5 ms). 100k iterations × (8 float loads for the bilinear fetch, ~25 flops, 5 typed-array stores, one scattered 32-bit store). The arithmetic is not the cost; the final store is. Particle order in the arrays has no relationship to screen position after a few seconds, so those 100k writes are essentially random into a 2.16 MB framebuffer — bigger than L2, so most are L2/L3 traffic. That single line is worth more than everything else in the loop combined.
- decay + putImageData ≈ 25–35% (~2–3 ms). The decay loop touches all 540k words but the
c !== BGearly-out skips the black majority;putImageDatais a 2.16 MB texture upload per frame, which on integrated graphics is shared-memory bandwidth and is usually 0.6–1.5 ms. - field build ≈ 5% (~0.4 ms). 4004 nodes × 5
Math.cos. This is why the field is on a grid and not per-particle: sampling five sines per particle would be 500kcoscalls per frame, ~8–12 ms on its own, and would have cost me the frame.
The first thing that breaks at 1M: the update loop, via memory, not arithmetic. The six state arrays go from ~2.2 MB to ~22 MB, so the streaming reads stop being cache-resident, and the scattered splat now issues 1M misses per frame into a framebuffer that only has 540k pixels — so you're paying full cache-miss cost for writes that mostly overwrite each other (roughly 2 particles per pixel; the image stops gaining information while the cost keeps climbing). Expect ~40–55 ms/frame, i.e. 18–25 fps, with update+splat swelling to ~85% of the frame. Nothing crashes; it just goes syrupy. The decay and blit are unchanged — they're per-pixel, not per-particle.
What you'd need to go ten times faster: get the particles off the CPU entirely. WebGL2, state in two RGBA32F textures ping-ponged through a fragment shader (or gl.TRANSFORM_FEEDBACK into a double-buffered VBO if you prefer vertex-stage integration), the flow field evaluated analytically in the shader from the same stream-function modes — no grid, no interpolation, no CPU→GPU upload of particle data at all. Draw as GL_POINTS with additive blending into a float or half-float FBO, and do the trail decay as a full-screen quad multiply instead of a JS loop over Uint32Array. That removes the two things that dominate here — the scattered scalar write and the 2.16 MB putImageData — and 1M–4M particles at 60 fps becomes a fill-rate question rather than a memory-latency question.
If you fell short
Nothing dropped.
Attachments
anthropic/claude-opus-5 — page