Lorenz attractor · nex-n2-mini

Using the pre-provided three.min.js (global THREE), visualize the Lorenz attractor as a glowing 3D butterfly trajectory that draws over time, with orbit-drag camera controls.

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user

Using the pre-provided three.min.js (global THREE), visualize the Lorenz attractor as a glowing 3D butterfly trajectory that draws over time, with orbit-drag camera controls.

assistant

thinking

We need respond by creating index.html self-contained with inline CSS/JS, use pre-provided three.min.js global THREE via script src="three.min.js". Need current dir /tmp/ws. Need inspect? We need create file. Need maybe list? Use bash ls. Need ensure three.min.js exists. Need write index.html. Need no external resources. Need implement Lorenz attractor glowing 3D butterfly trajectory draws over time, orbit-drag camera controls. Since no OrbitControls external, implement own camera controls around target using spherical coords, mouse drag/pan? Need visualize. Need maybe use BufferGeometry, line segments, additive blending, fog, points, gradient? Need no external textures. Need maybe use WebGLRenderer. Need draw over time: update line geometry segments from computed points over time, maybe glowing trail. Could use Line2? No Line2. Use THREE.Line with material AdditiveBlending, transparent. For glow, maybe draw line twice: thick white/blue core and larger transparent cyan? In Three.js line widths not reliable. Could use multiple lines? Maybe create PointCloud with Points and line. "glowing 3D butterfly trajectory" can use emissive material? LineBasicMaterial has color, transparent, blending, depthWrite false. Could create duplicate lines with different sizes? line material linewidth ignored. Could use TubeGeometry? But dynamic. Better use Points with Sprite? No external.

Need maybe use shader? Custom ShaderMaterial for glowing line with additive blending. We can create BufferGeometry with positions for many line segments, update each frame. Use ShaderMaterial vertex/fragment. Could make line glow by using fragment color with alpha falloff based on gl_PointCoord for Points, but for line segments need width? WebGL line width limited. Maybe use custom line shader with gl_PointSize for points if we use Points. Another approach: render trajectory as many small glowing spheres along path (small sprites/circles) using custom Points shader with additive blending, plus line core. That will glow. For line path, use line with additive blending. For "draws over time" update maxSegments as time progresses. Use Lorenz equations.

Need maybe include UI overlay with instructions. Need camera orbit drag controls. Implement pointer events:
- camera target vector, spherical radius, theta, phi; update camera position; lookAt.
- pointerdown drag, pointermove adjust theta/phi; wheel zoom; maybe auto rotate checkbox? Not necessary.
- touch? support.
- prevent context menu.

Need ensure script load order: <script src="three.min.js"></script> then inline. If file absent? User says pre-provided. But maybe current dir no file? Need check.

→ bash {"command":"ls -la","timeout":10}

toolResult

total 592 drwxr-sr-x. 2 node node 26 Aug 1 20:12 . drwxrwsrwx. 3 root node 16 Aug 1 20:12 .. -rw-r--r--. 1 node node 603445 Aug 1 20:12 three.min.js

assistant

thinking

Need write index.html. Need maybe inspect version? Not necessary. Need create full HTML. Need robust. Need maybe use CSS. Need no external. Need maybe no modules. Need handle WebGL unavailable? Maybe display fallback.

Need plan code.

HTML:
<!doctype html><html lang="en"><head><meta charset...><title>Lorenz Attractor</title><style> html body margin 0 overflow hidden background #02030a font ... #app full. canvas display block. .hud top left etc. .badge. .controls small. @media.

<body><div id=app></div><div class=hud> ... </div><div class=hint>Drag... </div><script src="three.min.js"></script><script> (()=> { ... })(); </script></body></html>

JS:
const container=document.getElementById('app');
const renderer = new THREE.WebGLRenderer({antialias:true, alpha:false, powerPreference:'high-performance'});
renderer.setPixelRatio(Math.min(window.devicePixelRatio,2));
renderer.setSize(window.innerWidth, window.innerHeight);
renderer.outputEncoding = THREE.sRGBEncoding? Actually three.min.js maybe r?? Need support. Use if ('outputEncoding' in renderer) renderer.outputEncoding = THREE.sRGBEncoding; maybe.
renderer.setClearColor(0x02030a, 1). Append.

scene = new THREE.Scene(); scene.fog = new THREE.FogExp2(0x02030a, 0.0035?) maybe.
camera = new THREE.PerspectiveCamera(60, aspect, 0.1, 2000);
target = new THREE.Vector3(0,0,0); radius=58; theta=0.75; phi=1.18; updateCamera().

lights: ambient, point lights.

Lorenz params:
sigma=10, rho=28, beta=8/3; dt=0.015 maybe; stepsPerFrame=1; initial x=1,y=1,z=1; maybe integrate with RK4? Simple Euler enough but use RK4 for accuracy.
function lorenz(x,y,z): dx=sigma*(y-x), dy=x*(rho-z)-y, dz=x*y-beta*z.
integrateRK4.

Path:
Need "draws over time". We can maintain arrays of vertices for line and points. Need update at render interval.

Option A: Precompute? Dynamic. Use positions Float32Array length MAX_SEGMENTS*3*2? For line segments. Each frame add maybe 2 segments? If dt=0.025, segments per frame = Math.ceil(60*dt) ~1.5. To avoid jitter use segment accumulator. But "draws over time" can use elapsed time.

We can use dynamic BufferGeometry with max segments. Each segment has 2 vertices: total maxSegments*2*3. positions attr. But if we draw partial, fill unused with zeros? Three line will connect last valid to first unused if attr includes zeros. Need use drawRange with count = segments*2? For BufferGeometry drawRange counts vertices, but for Line, drawRange can limit vertices? Yes geometry.setDrawRange(0, usedVertices). Need ensure all vertices initially zeros. Good.
lineGeo = new THREE.BufferGeometry();
lineGeo.setAttribute('position', new THREE.BufferAttribute(linePositions,3).setUsage(THREE.DynamicDrawUsage));
lineGeo.setDrawRange(0,0);
lineMat = new THREE.ShaderMaterial({
 uniforms { uTime, uGlowColor, uCoreColor },
 vertexShader: `attribute vec3 position; varying vec3 vPosition; void main(){ vPosition=position; gl_Position=projectionMatrix*modelViewMatrix*vec4(position,1.0); }`,
 fragmentShader: `varying vec3 vPosition; uniform float uTime; void main(){ float t = fract(vPosition.x*0.025 + uTime*0.08); vec3 col = mix(uCoreColor, uGlowColor, t); gl_FragColor=vec4(col,1.0); }`,
 blending: THREE.AdditiveBlending, transparent:true, depthWrite:false
});
line = new THREE.LineSegments(lineGeo,lineMat);
scene.add(line).

For glow points:
Need draw many small glowing dots along trajectory. Use BufferGeometry with maxPoints maybe maxSegments*2? But if line segments endpoints duplicate. Use Points with custom shader:
attribute float aSize; varying float vAlpha; uniform float uTime; void main() { vec4 mv = modelViewMatrix*vec4(position,1.0); gl_PointSize = aSize * (300.0 / -mv.z); gl_Position=projectionMatrix*mv; vAlpha = 0.85; } fragment: gl_PointCoord, d=length(gl_PointCoord-0.5)*2; alpha=smoothstep(1.0,0.0,d)*vAlpha; color = mix core/glow based on alpha? Additive.
Need create positions for maxPoints = MAX_SEGMENTS*2 maybe. attributes size. set drawRange.
But for points, if drawRange counts vertices. Need setDrawRange(0, usedPoints).
But if points are line segment endpoints, duplicate. Fine.

Maybe use Points for "glow". Also add a "head" particle bigger.

Could also add rings/axes? "orbit-drag camera controls" no axes required. Maybe add subtle grid? External resources no. Could create 3D coordinate rings? Nice but not needed. Avoid clutter.

Need update geometry. Need dynamic with maxSegments maybe 120000? If segments per frame ~2, points 240k, positions 720k floats ~2.9MB, size attr ~1MB. Fine. But line segment attr 3*2*maxSegments. If maxSegments 100000, 600k floats ~2.4MB. Good.
But if max points maxSegments*2 = 200k. Good.

Need draw over time. Maybe reset button? User didn't ask. Could include "R reset". But maybe not. Simpler.

Potential issue: THREE.BufferAttribute.setUsage exists? yes.
Potential issue: custom shader in three.min.js older version: uses gl_FragColor. Fine.

Lorenz integration:
let x=0.1,y=0.1,z=1.0;
const maxSegments=120000; const pointsPerSegment=2; const maxPoints= maxSegments*2;
const linePositions = new Float32Array(maxSegments*2*3);
const pointPositions = new Float32Array(maxPoints*3);
const pointSizes = new Float32Array(maxPoints);
let segmentCount=0, pointCount=0;
let lastTime=performance.now();
let segmentAccumulator=0;
const targetSegmentsPerSecond=90; maybe.

function advance(dt) {
  let steps = Math.min(500, Math.floor(dt*120)); // at 60fps 2 steps.
  for i:
    integrate x y z dt
    addSegment(x,y,z)
}
function addSegment(x,y,z) {
 if (segmentCount >= maxSegments) return;
 const base = segmentCount*2*3;
 linePositions[base] = x;...
 linePositions[base+3]=x2...
 segmentCount++;
 if (pointCount >= maxPoints) { // shift? maybe if too many, not. }
 addPoint(x2,y2,z2, size)
}
If max reached, maybe slow? Could loop? If reached, maybe keep x? Or reset? For indefinite, if max reached, shift arrays by 2 vertices each time expensive. Could use ring buffer? But user wants over time. Could choose maxSegments high enough. 120k segments * dt=0.012 * 90 fps = 129600 seconds ~36h. Good.

Need maybe use a moving "head" point:
headGeo = new THREE.BufferGeometry(); position attribute 3, size attr 1. Add point with ShaderMaterial maybe bigger. Update head position. Use Points.
But line/points already include head. Need maybe bright dot. Use custom Points with size.

Need maybe add a faint "core line" with a LineSegments material LineBasicMaterial (not shader) and a glow Points. But line shader can be enough. Need maybe add a second LineSegments with transparent additive. But line width not reliable. Shader with gl_FragColor for LineSegments uses fragment per pixel of line. Good.

Need maybe draw a "nebula" background? Could create points random? But no external. Could generate random star field with Points. But not necessary. Maybe create background star field with Points for depth. Use random positions in cube/sphere. Since no network. Need maybe not distract.

Need maybe use CSS overlay with "Lorenz Attractor" etc. Good.

Need maybe ensure if THREE undefined, show error. Since script src loaded. Need check.

Need maybe create "butterfly wings" by viewing angle. Lorenz attractor naturally. Need maybe set initial camera to show wings. Need maybe rotate? The Lorenz attractor is in x/y plane with z vertical. Camera at x=50,y=50,z=60 looking at origin gives 3D. Maybe set theta=0.75, phi=1.25, radius=65. Good. Need maybe maybe scale.

Need maybe camera controls:
const controls = {
 target: new THREE.Vector3(),
 radius: 64,
 theta: 0.75,
 phi: 1.25,
 minRadius: 12,
 maxRadius: 160,
 minPhi: 0.15,
 maxPhi: Math.PI-0.15,
 dragging: false,
 lastX, lastY,
 moved: false
};
function updateCamera() {
 phi = Math.max(minPhi, Math.min(maxPhi, phi));
 const sinPhi = Math.sin(phi);
 camera.position.x = target.x + radius * sinPhi * Math.sin(theta);
 camera.position.y = target.y + radius * Math.cos(phi);
 camera.position.z = target.z + radius * sinPhi * Math.cos(theta);
 camera.lookAt(target);
}
pointerdown if button 0:
dragging true; moved=false; lastX = event.clientX; lastY = event.clientY; setPointerCapture;
pointermove: if dragging:
dx,dy; theta -= dx*0.005; phi -= dy*0.005? Need sign. Try.
if |dx+dy|>2 moved true.
pointerup.
wheel: preventDefault; radius *= Math.exp(deltaY*0.001); clamp.
Need maybe passive false. Add listener.

Maybe include keyboard:
R reset path, Space pause? Not necessary but can include.

Need maybe pause? no.

Need maybe UI buttons? Could include overlay with "Reset path" maybe. But user didn't ask. We can include but not too much. Need maybe "Drag to orbit • Wheel to zoom". Maybe reset button optional. Since single page.

Need maybe implement reset path:
function resetPath() { x=y=z=0.01; segmentCount=pointCount=0; setDrawRange; }
Could add button in HUD. Need event listener. But maybe not.

Need maybe "draw over time" dynamic. Need maybe if tab inactive dt huge, clamp to 0.05. Good.
Need maybe integration uses dt=0.012; steps per frame 2. Each frame segmentCount += steps. At 60fps, 120 segments/sec; max 120k -> 16.7 min. Good. Maybe max 250k. Fine.
Need maybe if max reached, reset? That would violate draw over time. Could if reached, slow down or loop? Better no. But if reaches, continue with no draw? Maybe no.

Need maybe make "glowing" via shader. Need maybe use additive blending. Need maybe star field with additive.

Let's craft code carefully. Need test in browser? We can't run WebGL in shell maybe. But can use node to check syntax? Could use `node --check` on JS? But script includes browser DOM. Node --check only syntax. We can run. Need maybe no external. Good.

Potential issue: in shader, if using `gl_PointSize = aSize * (300.0 / -mvPosition.z);` with negative z. Good. For transparent additive, need `gl_FragColor = vec4(color, alpha);`.

Shader for line:
vertex:
```
attribute float aDepth;
varying float vDepth;
void main() {
 vec4 mvPosition = modelViewMatrix * vec4(position, 1.0);
 gl_Position = projectionMatrix * mvPosition;
 vDepth = -mvPosition.z;
}
```
fragment:
```
uniform float uTime;
uniform vec3 uCoreColor;
uniform vec3 uGlowColor;
uniform float uAlpha;
varying float vDepth;
void main() {
 float flow = fract(vDepth * 0.035 + uTime * 0.08);
 vec3 color = mix(uGlowColor, uCoreColor, flow);
 gl_FragColor = vec4(color, uAlpha);
}
```
LineSegments material with additive. `side` not relevant. `depthTest: true` maybe. DepthWrite false.

For points:
```
attribute float aSize;
uniform float uPixelRatio;
uniform float uTime;
varying float vPulse;
void main(){
 vec4 mvPosition = modelViewMatrix * vec4(position,1.0);
 float dist = max(1.0, -mvPosition.z);
 gl_PointSize = aSize * uPixelRatio * (220.0 / dist);
 gl_Position = projectionMatrix * mvPosition;
 vPulse = 0.75 + 0.25*sin(uTime*4.0 + position.x*0.3);
}
```
fragment:
```
float d = length(gl_PointCoord - vec2(0.5));
float halo = smoothstep(0.5, 0.0, d);
float core = smoothstep(0.18, 0.0, d);
vec3 color = mix(uGlowColor, uCoreColor, core);
float alpha = halo * uAlpha * vPulse;
gl_FragColor = vec4(color, alpha);
```
Need pointSizes set. For line endpoints, sizes maybe 5-11. For head maybe 18.

Could create head point:
```
const headPosition = new Float32Array(3);
const head = new THREE.Points(new THREE.BufferGeometry(), new THREE.PointsMaterial? custom)
```
But point shader can handle head. Maybe use same points with maxPoints includes head? Simpler create separate Points with position and size, material. But need update each frame.

Head material:
vertex:
```
attribute float aSize;
varying float vPulse;
void main(){...}
```
fragment:
```
float d=...; gl_FragColor=vec4(1.0,0.92,0.72,alpha);
```
But not necessary. Add a small "comet head" maybe nice.

Need maybe create "ghost trail" with line. Good.

Potential issue: `renderer.outputEncoding = THREE.sRGBEncoding` might not exist in older version? Need check. Use `if (THREE.sRGBEncoding !== undefined) renderer.outputEncoding = THREE.sRGBEncoding;`. But if undefined, property maybe exists? Good.
Potential issue: `renderer.setClearColor(0x02030a, 1)`.
Potential issue: `renderer.setAnimationLoop(animate)` or requestAnimationFrame. Use `renderer.setAnimationLoop(animate)`.

Need maybe create star field:
```
const starCount = 900;
const starPositions = new Float32Array(starCount*3);
for i: random sphere radius 120-220; z? 
starGeo.setAttribute('position', new THREE.BufferAttribute(starPositions,3));
starMat = new THREE.PointsMaterial({color:0x7aa7ff,size:0.45,transparent:true,opacity:0.45,blending:THREE.AdditiveBlending,depthWrite:false});
scene.add(stars);
```
No external. Good.
Need maybe create axes? no.

Need maybe create "orbit ring" around target? Could create three TorusGeometry rings? But "orbit-drag camera controls" maybe not. Could add faint orbit guide? Not necessary.

Need maybe maybe implement "orbit-drag camera controls" by dragging. Could include overlay. Good.

Need maybe make scene background not pure black. Use CSS radial gradient? Canvas clear color. CSS background. Good.

Need maybe no external resources except script. Need "Use NO external resources, CDNs or network requests: artifact runs fully sandboxed with no network. End with index.html present. These library file(s) are ALREADY present in current directory — load each with plain <script src="NAME"> exact filename: three.min.js." We comply.

Need maybe maybe mention file created. Final concise.

Need write file. Use write. Need maybe include comments? Fine. Need ensure no `type=module`. Need maybe if `THREE` not loaded, display. Since script order.

Let's write.

→ write /tmp/ws/index.html (17721 bytes)

toolResult

Successfully wrote 17721 bytes to /tmp/ws/index.html

assistant

thinking

Need maybe verify file exists. Use ls and maybe node --check? Need maybe no need but good. Need maybe check syntax of inline JS. Could use node --check with extracting? Node --check index.html fails because HTML. Need maybe use bash with grep? Could use `node --check <(grep -A...`? Simpler maybe use Python to extract script and node check. But final can mention. Need maybe use bash `test -f index.html && wc -c index.html` maybe. Also maybe run a quick static check by extracting inline script with Python and node --check. Let's do.

→ bash

{"command":"python3 - <<'PY'\nfrom pathlib import Path\nimport re, subprocess, sys\nhtml = Path('index.html').read_text()\nscript = re.searc

toolResult

/bin/bash: line 1: python3: command not found node:internal/modules/cjs/loader:1520 throw err; ^ Error: Cannot find module '/tmp/index_inline.js' at node:internal/modules/cjs/loader:1517:15 at node:internal/main/check_syntax:33:20 { code: 'MODULE_NOT_FOUND', requireStack: [] } Node.js v24.18.1 -rw-r--r--. 1 node node 17724 Aug 1 20:13 index.html

assistant

thinking

Oops python3 absent. Need maybe use node script to extract.

→ bash

{"command":"node - <<'NODE'\nconst fs = require('fs');\nconst html = fs.readFileSync('index.html', 'utf8');\nconst m = html.match(/<script>(

toolResult

-rw-r--r--. 1 node node 17724 Aug 1 20:13 index.html

assistant

thinking

Output missing node --check? It succeeded with no output. Good. Need maybe perhaps `node --check` exit 0. Good.

Need maybe consider code issues in browser:
- `pointGeometry.attributes.position.array.fill(0)` after reset? `headGeometry.attributes.position.array` is Float32Array length 3, fill(0) works.
- In `animate`, `animate.lastTime` property on function okay. On first call dtNow = (now - now)/1000 = 0, max(0.001) -> 0.001. Good.
- `resetTrail(); startedAt = performance.now();` in reset button after reset. But in animate, startedAt used only elapsed. Reset button sets startedAt now, but if paused? okay.
- `pauseBtn.textContent` initial "Pause". Good.
- `lineGeometry.setDrawRange(0, segmentCount * 2);` count in vertices. For LineSegments, drawRange count vertices. Good.
- `pointGeometry.setDrawRange(0, pointCount);` points. Good.
- `linePositions` initial zeros; drawRange excludes. Good.
- `pointSizes` for unused zeros. drawRange excludes. Good.
- `addSegment` returns false if no segment. If segmentCount max, integration stops. Good.
- Potential issue with `BufferAttribute.setUsage` returns this? Yes returns this.
- Potential issue: `renderer.domElement.releasePointerCapture` may throw if not captured. Catch.
- Potential issue: `event.code === 'Space'` okay. But if space scroll? Body overflow hidden. Fine.
- Potential issue: in shader, `gl_PointSize` may exceed max point size, but okay. Some GPUs max 64, point size maybe 230*2/depth ~4.6 to 38, okay. Head 285/depth ~14.25*2=28.5. Fine.
- Potential issue: line shader no lineWidth. okay.
- Potential issue: `THREE.DynamicDrawUsage` exists. yes.
- Potential issue: `THREE.FogExp2` exists. yes.
- Potential issue: `renderer.outputEncoding = THREE.sRGBEncoding` in older three min? Need check version maybe r? If sRGBEncoding undefined but renderer.outputEncoding property exists? It might be undefined. We guard.
- Potential issue: script src exact `three.min.js` relative. Good.
- Potential issue: user asked "using pre-provided three.min.js (global THREE)" loaded. Good.

Need maybe maybe use `three.min.js` file exact. Good.

Need final concise with file path. But maybe mention syntax checked? Could say created. Need not include code. Final answer.

Created `index.html` in `/tmp/ws`. It is a self-contained single-page Lorenz attractor visualization using `three.min.js`, with: - glowing additive trajectory trail that draws over time - real-time Lorenz integration - orbit-drag camera controls - wheel/pinch zoom - reset and pause controls - no external assets, CDNs, or network requests

TAKE IT TO CODE

A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.

RUN

modelnex-n2-mini

vendorNex AGI

harnesspi-agent

generated2026-08-01

EVALUATION

★★★★★ 1/5 broken

Only a dark starfield background with UI text/buttons visible; no visible Lorenz attractor or trajectory rendered.

off-prompt

Vision grade · anthropic/claude-sonnet-5

MEASUREMENTS

Raw readings from the capture, not a verdict — the grade above is the only judgement. Percentages are how much of the screen changed; the measure under-reports sparse motion on a dark background.

idle motion0.0%

on click0.0%

on drag0.0%

on wheel0.0%

on enter + space0.1%

on arrow keys0.0%

on w/a/s/d0.0%

frame spread6.5 / 255

console errors0

js errors none

METRICS

runtime54.4s

tokens in41k

tokens out11k

cached12k

cost / run$0.0019