Lorenz attractor · step-5-preview

Three.js r128ish. Let me check version string and whether OrbitControls is in there (no, min build only core). So I implement my own orbit controls.

Let me write index.html.

Plan:
- Scene, renderer with antialias, camera perspective.
- Integrate Lorenz with RK4, dt=0.005, with substeps per frame.
- Line geometry: use THREE.Line with BufferGeometry, dynamic draw. Colored via vertex colors based on speed/position. Luminous look: additive blending, maybe a second glow line slightly offset? Use LineBasicMaterial with vertexColors, transparent, additive blending, plus a sprite glow. Also could add points at head.
- Bounded storage: max points (e.g., 20000), use a ring buffer or draw range from beginning. Simple: keep array of points; when exceeds max, we can shift (drop oldest) and update geometry with new buffer, or just cap draw count. I'll implement a fixed-size buffer with head index and use setDrawRange on a non-indexed geometry... but drawing range always starts at 0. Simplest: when full, drop oldest half? Alternative: use two draw calls. Easier: keep points array, when length > MAX, remove first chunk (splice) and re-upload only occasionally. Rebuilding buffer each splice of e.g. 2000 points out of 20000 — every 100 frames. Fine.

Actually a cleaner approach: use a "chunk" approach: keep list of segment batches. But let's just do: points array Float32Array fixed capacity; maintain count; when full, memmove removing oldest K points (K = capacity/4) and re-upload entire buffer once. That's 20000*3 floats copy, cheap.

Colors: hue based on speed, updated.

Camera controls: custom orbit — spherical coords around target (0,25,0) center-ish. Compute bounding box of attractor to frame: x∈[-20,20], y∈[-27,37], z∈[0,50]. Center (0,0,25)? Actually z from 0 to 50. Frame: radius ~ 50. Use fitDistance.

Mouse drag: left button orbit (pointerdown/move/up), wheel zoom distance *= exp(delta*0.001), clamped between minDistance (e.g., 15) and max (500). "without entering the geometry" — keep min distance > bounding sphere radius maybe 60? Attractor bounding sphere radius: center (0,5,25)? Points range x±20, y -25..40, z 0..50. Compute radius ≈ sqrt(20²+35²+25²) ≈ 47. Hmm min distance clamp should be like 60 to avoid entering geometry. That's fine — "without entering the geometry". Set minDistance = 70, max = 600.

Also touch support maybe. Add auto-rotate? Not required; keep off, maybe optional toggle.

Add:
- Buttons: Pause/Resume, Reset.
- Info HUD: points count, elapsed time.
- Also maybe sliders for params? Not required but nice. Keep minimal but maybe add a speed slider? Keep simple, but slight extra: show step count.

Luminous: additive blending Line, plus a sprite at the head with radial gradient texture generated via canvas, and a subtle point cloud glow? Also renderer with a "bloom-like" effect optional — I'll skip postprocessing (UnrealBloomPass requires addons not present). Instead use additive blending and a bright head sprite.

Let me also render with a dark background, and maybe a second wider translucent line for glow.

Frame loading: compute after some points exist? Precompute the bounding box by pre-integrating e.g. 20000 steps before drawing? "Frame the full attractor initially" — I can pre-integrate to compute bounds, then set camera distance to fit. Good: run integration for N steps before to compute bounds, but reset trail afterwards. Better: compute bounds from known analytic-ish estimate via pre-run in a scratch simulation, then reset.

Let me implement:

```
function lorenz(s, out){ out.x = sigma*(s.y-s.x); out.y = s.x*(rho-s.z)-s.y; out.z = s.x*s.y - beta*s.z; }
```
RK4 with dt = 0.005 stable.

Per frame: steps = 20 (configurable via speed select). Each step appends point.

Let's write the code.

Vertex colors: color from speed magnitude → hue via HSL. Need new THREE.Color().setHSL.

Geometry update: use BufferAttribute with usage DynamicDrawUsage, set needsUpdate.

Line rendering with additive blending and vertexColors works. Note LineBasicMaterial linewidth ignored; 1px lines. To be "luminous", add additive blending and maybe draw the same line twice — second with slightly different color scaled brightness. Also add a Points object of the trail with small size and additive blending to give glow dots? That may look noisy. I'll add Points with size 1.5, additive, low opacity — gives a nice glow.

Head sprite: canvas radial gradient texture, sprite scale ~4.

Also add a ground grid? Not needed. Maybe faint grid/axes for context. I'll add a subtle wire box or axes lines — optional; add axes helpers faintly to convey 3D. Let's add a thin box outline (Box3Helper) faint.

Also reset should restore camera? "Reset clears the trail and restores the initial simulation state." Camera: I'll keep camera as-is or reset framing — I'll reset camera too (to initial framing) since "restores the initial simulation state" — the initial view is fine. Actually requirement: reset restores initial simulation state (position 0.1,0,0). I'll reset camera as well for good measure.

Canvas resize handling.

Pointer events on renderer.domElement. Also prevent context menu. Support right-drag pan? Not needed; keep orbit only, plus wheel zoom. Maybe add middle/right drag pan — skip or implement simple pan with shift? Keep orbit only.

Let me write the file.

Also keyboard: Space toggles pause, R resets.

Screenshot inspection after.

Let me write it now.

Detail on bounded storage with proper "trail remains connected": dropping oldest points keeps the newer part connected — fine.

Implementation of ring-free buffer:

```
const MAXP = 24000;
const posArr = new Float32Array(MAXP*3);
const colArr = new Float32Array(MAXP*3);
let count = 0;
```
On push: if count === MAXP: compact: posArr.copyWithin(0, MAXP*0.2*3, MAXP*3); same for col; count = MAXP*0.2; then setAttribute needsUpdate full; mark geo.setDrawRange(0,count).

pushPoint:
```
if(count>=MAXP){ ... }
posArr[count*3]=x; ...
count++;
attr.needsUpdate = true; attr.updateRange = {offset: count*3-3, count:3}? 
```
In r128, attribute.updateRange exists (offset, count) and needsUpdate = true triggers update if updateRange.count !== -1. Simpler: set needsUpdate=true (full re-upload of 24000*3 floats = 288KB per step — that's per step, 20 steps/frame → 5.7MB/frame. Meh but probably fine? Better use updateRange). I'll use updateRange properly: after pushing one vertex, attr.updateRange.offset = (count-1)*3; attr.updateRange.count = 3; attr.needsUpdate = true. On compaction, set full range.

Actually safer: push several points per frame (batch), then set updateRange covering the batch. I'll do batch: within frame, push all steps, track startIndex, then update attrib upload range once.

Also color per vertex computed from speed.

Also, careful: copyWithin on Float32Array works.

Let me also handle Points object sharing same geometry with a PointsMaterial (vertexColors, size, sizeAttenuation false? use size in pixels: size 2, sizeAttenuation:false). Additive blending, depthWrite false, opacity 0.5.

Line material: LineBasicMaterial({vertexColors:true, transparent:true, blending:AdditiveBlending, depthWrite:false}).

Faint box: use Box3Helper with color 0x223344 — Box3Helper available in core. Yes.

HUD overlay with stats: points, t, steps, status.

Now the camera framing: after pre-run compute bounds; center c; radius r = distance from center to farthest corner. distance = r / sin(fov/2) * 1.05. Set spherical from an angle.

Write it.

Also make sure `three.min.js` script tag included with plain src.

Let's write the HTML.

Now let's run it in the browser and check console/screenshot.

Note: Box3Helper constructor takes box and color — yes: Box3Helper(box, color=0xffff00). Good.

Potential issue: `posAttr.setUpdateRange` exists in r128? BufferAttribute.updateRange exists in r128 (removed in r159+). setUpdateRange exists too. Fine. But in r128, WebGLAttributes uses updateRange only if updateRange.count !== -1? Let me check the minified code for "updateRange".

Also `THREE.Box3Helper` fine. Let me check.

updateRange exists but setUpdateRange does not in r128 (it appeared later). So I must set attr.updateRange = {offset:0, count:0} manually. Let me fix.

Also check how r128 uses updateRange in the renderer: it likely does `if (updateRange.count === -1) gl.bufferSubData(full) else bufferSubData(updateRange.offset...)`. Let me grep context.

Confirmed: r128 uses `updateRange = {offset, count}` with count default -1 meaning full upload, and after subdata it resets count = -1. `setUpdateRange` method doesn't exist. I'll write my own helper `setRange(attr, offset, count)` that sets attr.updateRange = {offset, count}.

Let me fix the code accordingly.

Also, since after upload count resets to -1, next upload would be full. I set updateRange each frame, fine.

Let me edit.

It's rendering. But fps = 10 — that's low. The reason: the pre-integration (200000 RK4 steps with heavy Vector3 allocations) blocks the main thread at load (~?), and per-frame the computeBounds. Actually fps=10 measured just at start; possibly it recovers. Let's wait and re-check fps.

Also there's heavy allocation of 3 Vector3 per step → garbage. Should optimize deriv/inlining. Let's rewrite rk4 to use plain numbers to reduce GC pressure, and reduce pre-integration steps (200000 steps with allocations = 800k Vector3 allocs; that takes maybe 0.5-1s). Let's optimize.

Also note the trail appears thin — it's 1px. That's fine with additive glow and points. The screenshot shows the trail as thin bright line. OK.

Let me optimize rk4 with scalar math and check fps after running a while.

Also verify: after the buffer fills (30000 pts at 24 steps/frame = 1250 frames ≈ 20s at 60fps), compaction happens. I should test the compaction path quickly — maybe temporarily test via console by setting stepsPerFrame high and maxPts small. I can do a quick browser test by evaluating JS? The browser tool doesn't support arbitrary evaluate. Hmm — inspect gives DOM. I could add a debug hook... Instead I can reason and test by temporarily setting MAXPTS low in the file, verifying, then restore. That's a reasonable verification approach.

First optimize the integration.

The last edit was a no-op-ish (removed a duplicate blank). Fine.

Now reduce computeBounds cost: 200000 steps of scalar RK4 is fast now (~200k*~50 flops = 10M flops, ~10ms). Good.

Now reload and check fps, then wait for trail growth, orbit, pause, reset.

Note the runner inlines three.min.js; fine.

Also I should double-check the initial framing: screenshot showed the bounding box nicely framed, with trail starting at center-ish. Good — the camera looks from outside. The head sprite at (0.1,0,0) roughly center of box. Good.

Wait: bRadius = distance from center to corner ≈ half diagonal. With box (-21..21, -30..42, -1..52): center (0,6,25.5), half diag = sqrt(441+1296+2800)= sqrt(4537)=67. Hmm bRadius=67 → dist fit with fov 52: 67/sin(26°)=153. In the screenshot the box fills the frame reasonably. Good.

But MIN_DIST = 75 > ... camera dist 153. Zoom in limited to 75 which is just above 67. Good, avoids entering geometry.

Now reload.

My replacement broke it. Just strip that block simply.

Actually simpler: use `node --check`? That doesn't work on HTML. Use the browser console instead: reload and check for console errors. Let's just reload the page and check console output + screenshot.

The trailing `})();` remains, causing syntax error with my Function wrapper. That's expected. So the syntax check failed only due to my hack. Let me instead check syntax by wrapping in a function properly.

fps shows 0 sometimes — the fps counter at startup seems odd; fps 0 means frames*1000/(now-fpsTime) rounded... hmm 10 then 0. Actually the DOM is captured right after reload, where the counters might be from a prior interval? Weird: "t = 0.960 · vertices = 193 · fps = 0" — fps=0 with 193 vertices suggests frames counter low? If frames is e.g. 1 and delta 500ms → 2 fps → "2". Hmm 0 means frames=0 and delta>500: that means the first 500ms window had 0 frames — likely because the pre-integration (computeBounds) plus initial setup took longer than 500ms? No — fpsTime is set at module scope before animate starts, and computeBounds... wait, computeBounds runs before `frameAttractor()` and `animate()`. fpsTime = performance.now() is set in the script, so computeBounds time counts into the first window. But that's just a few tens of ms of scalar RK4 (200k steps → maybe 30-60ms).

Hmm, but fps=0 also happened on first run. Something makes frames 0 in first window — maybe the tab is throttled / the browser screenshot capture blocks. Also "GPU stall due to ReadPixels" repeated.

Actually more concerning: t=0.96 at 193 vertices → 193/24 = 8 frames in ~? If it's ~3 seconds after load, that's 3 fps. Very low. Possibly the browser environment is slow at rendering (software GL / swiftshader) — 30000-vertex additive lines with 3 draw calls at full canvas res in headless. Also the fps counter itself. Let's check with a motion/screenshot after waiting, to see t progress and fps.

Let me wait a few seconds and take a screenshot to see the state.

The butterfly shape is forming nicely. FPS is 13 in this headless environment (software GL). Rendering at devicePixelRatio possibly 1 with a 1200×800 canvas — that should be fine on a GPU. It's likely the readpixels stalls from the harness. Acceptable.

One issue: the trail color gradient seems dominated by a blue-green; slow parts appear cyan-ish blue. Looks fine.

Now test interactions:
1. Drag to orbit.
2. Wheel to zoom.
3. Pause, then drag (trail frozen).
4. Reset, verify restart.

Note: the fps and the trail growth — fine.

Let's do a drag: press at some coordinates and drag. The canvas center is around (600,400). Use drag action from x=600,y=400 to 300,300.

Wait — the drag tool's coordinates: x,y are start, toX,toY end. Let's do that.

Also check that trail remains connected from the new angle. Take a screenshot after drag.

Important: dragging will happen while running; that's fine (verify growth continues but the requirement for pause test is separate).

Let me first test pause behavior via clicking the Pause button, then drag, then screenshot, checking t/vertices frozen.

The Pause button location: in the panel at top-left, roughly x≈55, y≈60. Let's click at (55,62).

Paused: state t=61.560, vertices=12313. Now drag on the canvas (avoid the panel — panel is at top-left, roughly x<330, y<220). Drag from (800,450) to (600,300).

Camera orbited (view changed), trail frozen at t=61.560, 12313 vertices, and both lobes are visible and connected from the new angle. 

Now test wheel zoom: move wheel over canvas at (830,450) with delta. The `drag`/`click` tools don't include wheel; maybe I can use... there's no wheel action in the browser tool. Let me check available actions: reload, inspect, screenshot, motion, click, drag, key, type, scroll. `scroll` has delta parameter — maybe scroll works on the page which would trigger wheel events on the canvas. Let's try scroll with delta -100 at position? The scroll action takes x,y,delta. Let's try that.

Then Reset: click Reset button at (~118, 62).

Let's do scroll then screenshot.

Wheel zoom works (view got closer — attractor fills more, still outside geometry). Note the trail extends outside the bounding box a bit? The box seems to fit — yes, in the image the trail appears to extend slightly beyond the box on the right side. Hmm, the box is drawn from computeBounds sampled sparsely (every 5 steps) so it's approximate but close. The bound radius is based on that box; camera min distance 75 keeps outside. Actually the visible trail sticking out slightly beyond the box suggests bounds slightly under-estimate, but only slightly. The zoom min distance of 75 vs actual radius ~67-70 is fine; the trail's max radius from center is about... in the second image the trail barely exceeds the box. It's fine.

Actually let me improve accuracy slightly: sample every step instead of every 5, and also account for the fact that with 200000 steps of 0.005 = 1000 time units, plenty. Sampling every 5 steps = 0.025 dt — misses maybe 1-2 units. Fine, and it's a helper box only.

But one thing to double check: the camera framing uses this box; if actual attractor extends beyond, initial framing might crop slightly. From the first screenshot at load, the full trail fit inside the frame with margin. Fine. To be safer, I could inflate bounds by 5%. Let me do that for safety: bRadius *= 1.06.

Now test Reset: click the Reset button, then check state/t returns to 0 and vertices small, and trail grows from initial state.

Reset works: state back to (0.1, 0, 0), t=0, vertices=1, trail cleared, camera re-framed to the full attractor box.

Now click Resume and verify growth restarts from the initial state. Then also verify bounded storage / compaction: to do that within time, I can temporarily set MAXPTS small? Better: run long enough to fill 30000 points at 24/frame → 1250 frames at ~10fps = 125s. Too long. Instead, temporarily test with MAXPTS = 3000 and stepsPerFrame 60 to trigger compaction quickly, verify visually and via count staying ≤ 3000 and trail connected. Then restore MAXPTS.

Actually a simpler lower-risk verification: temporarily set MAXPTS to 4000 and speed to 60 in the file, reload, run ~5s (4000/60 = 67 frames ≈ 5-7s), screenshot, and check vertices ≤4000 and trail connected (the older part dropped but the newer contiguous part is a full connected curve). Then restore.

Let me do that. But careful to restore exactly.

Also I should verify the head sprite and compaction don't leave artifacts.

Plan:
1. Edit MAXPTS to 4000 temporarily.
2. Reload, wait ~10s, screenshot/dom.
3. Restore MAXPTS = 30000.

Also apply the bRadius inflation fix now (safer framing). Let me do both edits in one pass? If I change MAXPTS to 4000 for test, then restore later — two edit rounds. Fine.

Let me first resume growth test + apply inflation edit.

Growth restarted from the initial state (t grows from 0, vertices grow). fps 60 here.

Now check the compaction path: MAXPTS is 4000 now, 24 steps/frame → 4000/24 = 167 frames ≈ 3 seconds. Let me wait ~6s and screenshot to see the count capped at 4000 with a connected trail.

Problem! vertices = 8521 > MAXPTS = 4000. So compaction isn't working as expected.

Let me look at the logic:

```
function pushVertex() {
  if (ptsCount >= MAXPTS) {
    var keep = Math.floor(MAXPTS * 0.75);
    var moveN = (MAXPTS - keep) * 3;
    positions.copyWithin(0, moveN, MAXPTS * 3);
    colors.copyWithin(0, moveN, MAXPTS * 3);
    ptsCount = keep;
    ...
  }
  var i3 = ptsCount * 3;
  ...
  ptsCount++;
}
```

That should cap at MAXPTS. Unless... wait — maybe the renderer's `count` of the attribute is used for drawing, and `ptsCount` variable... but the DOM shows `vertices = 8521`. Hmm.

Oh! I see — my edit earlier: `var MAXPTS = 4000; // TEMP-TEST`. Did the edit apply to the right place? Yes, index shows. So MAXPTS=4000 and count 8521?

Wait... maybe there's a second `ptsCount` increment: in `reset()` I call pushVertex() then uploadRange(0) — that's fine.

Hmm, unless the compaction branch has a bug where `pushVertex` is defined... let me check whether the `keep` variable name collides with something. Let me grep for 'keep'.

Actually wait — I declared `function setRange` before `function pushVertex`, fine.

Let me actually read the current pushVertex code in the file.

The logic looks right. But wait: `hud.pn` shows 8521... Unless the drag? No.

Hmm! Wait — MAXPTS is 4000, so `new Float32Array(12000)`. If pushVertex writes beyond, it silently does nothing (typed array out-of-bounds writes are ignored). But ptsCount increments regardless. But the compaction branch should trigger at ptsCount>=4000 and set ptsCount=3000. So ptsCount should never exceed 4000... unless... 

OH. I bet the file on disk was reloaded before the edit? No — the screenshot after my edit... wait, I made the edit changing MAXPTS to 4000, and then clicked Resume (page not reloaded!). The running page still has MAXPTS=30000? No wait — the click "Resume" after edit didn't reload the page. So the page is the OLD instance with MAXPTS=30000, vertices=8521. Right! The browser didn't reload after my edit. So 8521 < 30000 — no compaction happened, correct behavior.

I need to reload to test compaction. Let me reload now (MAXPTS=4000 active) and let it run ~6s.

Compaction works: vertices capped at 3153 (< 4000), t keeps growing, the trail remains a connected polyline (no gaps/breaks visible — the oldest quarter is dropped contiguously).

Hmm, one thing: after compaction, the draw range is set to ptsCount and the attribute's count (attribute.count = MAXPTS*... no, count = array.length/itemSize = 4000, independent). Fine.

Also there's a subtlety: after compaction, `attr.count` stays 4000 but drawRange is ptsCount — OK.

Now restore MAXPTS = 30000 and reload for a final check. Also double check that the visual is good with 30000.

Let me also consider whether the trail being drawn as a single Line of 30000 points across 3 draw objects (line, glow, points) — fine.

One more consideration: "Frame the full attractor initially" — verified in first screenshot.

Also maybe I should verify the keyboard shortcuts (Space/R) work. Let's test with the `key` action after reload.

The page reloaded and is running with MAXPTS=30000. Now let's test keyboard shortcuts: press Space (pause), then 'r' (reset). The key tool: action "key" with text like "Space"? Let's try text "Space" then check DOM, then "r".

Note: keyboard events go to the focused element; the window listener should catch them if the document/body has focus. Let's try.

Space key works — paused. Now press "r" to reset.

Note: one detail in the trajectory: the head sprite is at the newest point, but here the head appears near the top-middle. Fine.

Let's press "r".

All interactions verified. Everything works.

One thing: the initial framing after reset puts the attractor in view — the box occupies the frame. Good.

Final consideration: should I verify the trail at full 30000 cap with the real setting? Compaction logic already verified with 4000 cap, and the code path is identical. Fine.

Also potential concern: the head sprite has depthTest:false which means it draws over everything — acceptable for a glow marker.

Another: `boxHelper` box changed via `boxHelper.box.set(...)` — Box3Helper.updateMatrixWorld recomputes geometry? In r128, Box3Helper.updateMatrixWorld sets position/quaternion/scale from the box each frame, and if the box changed and `this.autoUpdate`/update flag... Let me check: in r128 Box3Helper.updateMatrixWorld:

```
updateMatrixWorld( force ) {
  const box = this.box;
  if ( box.isEmpty() ) return;
  box.getCenter( this.position );
  box.getSize( this.scale );
  this.scale.multiplyScalar( 0.5 );
  super.updateMatrixWorld( force );
}
```
It only updates the transform, not the line geometry positions. But the initial geometry was built from the empty box (zero size?). Then setting `boxHelper.box.set(...)` only changes center/size, so the drawn wireframe would use stale geometry positions (built when box was empty → degenerate, all points at 0?) — In r128 the constructor creates a Box3Helper with a box (default new Box3()) and builds geometry from the box's 8 corners.

But the screenshots show a correct box around the attractor! Because the default `new THREE.Box3()` is empty and `setFromPoints`... hmm, but the box in screenshots matches the attractor bounds with corners at (-21,-30,-1) to (21,42,52) — that's not what a degenerate box would produce... Actually wait, maybe r128's Box3Helper.updateMatrixWorld calls `this.geometry` update? Let me check the actual r128 source:

```js
class Box3Helper extends LineSegments {
	constructor( box, color = 0xffff00 ) {
		...
		this.box = box;
		this.updateMatrixWorld = function(){}
	}
}
```
Hmm — I recall in r128 Box3Helper sets `this.updateMatrixWorld = function(){}` ... Actually no, that's for CameraHelper maybe. Anyway, empirically the box is drawn correctly in the screenshots (it matches the trail extents). Let me verify quickly by grepping the minified code, but the visual evidence is strong: the box in the screenshots surrounds the attractor exactly at the right proportions, and the camera framing (which uses `bRadius`) also matched. So the helper is working as intended.

Actually, to be safe, let me check whether the box is drawn correctly — in the first screenshot the box appears to tightly enclose the visible trail. Since boxHelper.box.set() happened after construction, and the box appears correct, r128's Box3Helper must recompute. Good.

Everything is verified. Let me do a final visual check that the final file (with MAXPTS restored) renders correctly over a longer run — I already ran it ~30s and saw 5065 vertices growing smoothly. Good.

Let me also double check the final file content once (read key parts) and confirm no leftover TEMP comments.

Everything is in place. Final state:
- MAXPTS = 30000 restored.
- No temp markers.
- File size 16.7KB.

Let me do one final reload + brief screenshot to confirm the final artifact renders from a clean load (with the restored cap) and growth continues.