Mandelbrot explorer · minimax-m3

Let me build an interactive Mandelbrot-set explorer. I'll create a single HTML file with:
1. Full-screen canvas
2. Canvas 2D rendering with smooth escape-time coloring
3. Drag to pan, wheel to zoom (centered on cursor)
4. Reset button
5. Smooth coloring using the escape-time algorithm
6. Worker-like responsive UI (use requestAnimationFrame)

Let me design this:

- Use `ImageData` for pixel-level rendering
- Smooth coloring via continuous escape time: `mu = n + 1 - log(log(|z|)/log(2))/log(2)`
- Iterations scaling with zoom level for detail
- Prevent default scroll on wheel
- Reset restores initial bounds: x from -2.5 to 1, y from -1.25 to 1.25

Let me write the file.

Let me reload the page in the browser to inspect the initial output.

The image looks like the entire region is being treated as inside the set. This is because the color palette is too pale - the t value gives a pale blue, and the inside is black, but actually looking at the image, the background outside should be the smooth color gradient - but it's all light blue.

Wait - the exterior is showing as light blue (almost solid). The escape values must all be small relative to maxIter (800). When z escapes very quickly (small n), the smooth value t = (n + 1 - nu) / maxI will be very small (~0). The palette at t≈0 gives... let me check: sin(0.05*0*2π + 0.10) = sin(0.10) ≈ 0.0998. So r = 0.0998*127.5 + 127.5 ≈ 140. g uses offset 0.55: sin(0.55) ≈ 0.523, so g ≈ 127.5*0.523+127.5 ≈ 194. b uses offset 1.0: sin(1.0) ≈ 0.841, so b ≈ 127.5*0.841+127.5 ≈ 235. So palette(0) ≈ (140, 194, 235) - light blue. That's why the background is light blue.

The issue is that with maxIter=800 and very few iterations needed for points far from the set, t is concentrated near 0. I should:
1. Use a cyclic palette (cosine-based with hue cycle) and use the index modulo a cycle, OR
2. Map t more aggressively

Let me use a typical cycling palette using hue. Let me improve the palette to use HSV-like coloring with cycling:

Actually let me use a better palette - the classic one where we cycle through hues based on a function of t and maxIter:

`color = palette(n + 1 - log2(log2(|z|)))`

And then we use the raw index (not divided by maxIter) to map to color. That's the standard approach. Let me fix this:

```js
// Use raw smoothed iteration count as palette index
const tIdx = n + 1 - nu;  // smooth count
const c = palette(tIdx);
```

But then for tIdx values from 1 to maxIter we need a color. Let me make palette use cosine-based cycling:

```js
function palette(t) {
  const i = t * 0.05; // cycle period
  const r = Math.sin(i + 0.0) * 127.5 + 127.5;
  const g = Math.sin(i + 2.094) * 127.5 + 127.5;
  const b = Math.sin(i + 4.188) * 127.5 + 127.5;
  return [r|0, g|0, b|0];
}
```

That'll give nice cycling rainbow colors. Let me rewrite.

Also, I should make the render not be too slow. The current pixel-by-pixel with full computation is OK for 800x600 but at higher DPR it might be slow.

Let me update the palette and use the smooth count directly.

Now I need to change the smooth-t computation so it uses the raw smoothed count, not normalized.

Let me also reduce the bailout from 256 to something more reasonable for smooth coloring. Actually 256 is fine, but let me also ensure the escape-time detection is fine. Let me reload and check.

Excellent! Now the colors look great - vibrant cycling rainbow with a clear dark interior. The image shows the full Mandelbrot set with main cardioid and surrounding bulbs visible.

Let me now verify the interactive features:
1. Test pan by dragging
2. Test wheel zoom centered on cursor
3. Test reset

Let me try a wheel zoom first.

Let me check the schema again. The wheel action might need explicit x and y coordinates. Let me check the parameters - the schema says: action is required and must be a constant, but "wheel" is not in the enum. The available actions are: reload, inspect, screenshot, motion, click, drag, key, type, scroll.

There's no wheel action! Let me use the available tools. I can scroll the page or simulate a wheel event programmatically via a small script injection... actually I can't inject JS.

Wait — let me check the tools more carefully. The available browser actions don't include wheel. Hmm. Let me try scroll instead, but that just scrolls the page, not zoom. Actually since the page doesn't scroll (overflow:hidden), scroll won't help.

I can use drag to pan, and click to click. For zoom, I might need to verify in another way. Let me at least test pan and reset using drag and click.

Actually, let me re-read the schema:
- "click" requires x and y
- "drag" requires x, y, toX, toY

Let me drag to pan, then click reset.

Panning works — the view shifted left (the cardioid moved to the left edge and we're now showing more of the right side). Now let me click Reset to verify it returns to the initial framing.

Hmm, the click didn't seem to register on Reset view. The view didn't change and the zoom is still 1.00× (which suggests it was reset but the rendering hasn't updated?). Wait, looking at the zoom label it says 1.00× which is correct for the initial state. But the actual displayed fractal is still the panned view (showing the right edge of the cardioid extending to the left of the viewport). That means... the view state was reset, but the rendering hasn't been re-triggered?

Wait, looking again - the image looks identical to the panned one. The zoom says 1.00× which is initial, but the fractal is still panned. That's weird.

Actually wait - looking more carefully, the fractal in the image is the panned version (cardioid off-center to the left). But zoom says 1.00×. Did the click event not fire? Or did the click miss the button?

Let me check coordinates. The Reset button is at top-left of UI panel. UI is at top:12px, left:12px, and the button is the first one in the row near y=12+10+8+8+8 = 46 plus button height. Looking at the screenshot, the Reset button appears to be around y=125, x=80. Let me try clicking with slightly different coordinates or perhaps the click went through to the canvas?

Wait - the UI panel might be on top of the canvas with z-index 10, and the canvas is below. But the canvas pointer events might still capture through the UI? Let me check - UI has no pointer-events:none, so clicks on it should land on UI. The Reset button should work.

Hmm, let me check if maybe the issue is timing - the click happened but the render wasn't done yet. Let me wait and screenshot again.

Actually wait - looking at the image vs the previous panned image, they look identical. The Reset view button should have restored to the centered view (showing full cardioid with bulbs). 

Let me check by looking carefully. In the reset view, we'd expect the cardioid centered. In the panned view (left of viewport), the cardioid extends off-left. The current image shows the cardioid extending off-left with no leftmost bulb. So reset didn't happen.

Let me re-examine - maybe the click didn't hit the button. The "Reset view" button is small. Let me find better coordinates. Looking at the image at 1200x800, the UI is in the top-left. The button text "Reset view" appears around y=125-130.

Actually wait - I notice the zoom value says "1.00×" - if reset worked it would still be 1.00× so that doesn't tell us much. Let me wait for the render and see.

Actually maybe the click DID register and the render completed but it looks identical because... wait no, the initial view has cardioid centered, this image has it off-center. So reset clearly didn't happen visually.

Wait... let me look at the image one more time. Looking at "the panned image" - the fractal shows the cardioid on the left half extending off-left, period-2 bulb at left, and no right side visible. Looking at the "reset" image - they look identical. So either reset didn't trigger or it hasn't rendered yet.

Let me click again more precisely. The button is in row 3 of UI. UI top:12, h1 height ~15px, then row1 (iter slider) ~25px, row2 (zoom) ~25px, row3 (Reset button) ~25px. So button center is roughly y=12+10padding+15h1+25row1+25row2+25row3/2 ≈ 87+12 = 100 maybe. Hmm.

Actually let me just inspect DOM to find the button location.

Inspect doesn't show coordinates. Let me try clicking using a different approach. Looking at the UI panel screenshot:
- Top-left of UI at approximately (12, 12)
- "Reset view" button is in row 3, which after h1 (~15px) and row1 (slider ~25px) and row2 (zoom label ~25px) would be at roughly y = 12 + 12 (padding) + 15 (h1) + 25 (row1) + 25 (row2) + 12 (row3 padding top) = 101px. Actually with gap:8 between rows, that's +16 more.

Let me try clicking at (90, 145) which should be safely in the button.

The click doesn't seem to be working. Looking at the layout - the canvas might be receiving the click instead of the button because the button is overlaid but the click goes through... no wait, z-index 10 should put it on top.

Actually wait - I just noticed that the coord shows "(-0.566667, 0.000000)" which means my last click landed on the canvas (because the canvas pointermove is updating that value). So the click is being received by the canvas, not the button.

Wait actually the coordinate is showing because of pointermove - maybe the button position isn't right. Looking at the UI panel in the image - the Reset view button appears to be in the third row at around y=125-130. Let me try clicking at a much more central location, maybe x=110, y=130.

Actually wait - my "click" tool might not be dispatching a pointer event that matches my pointerdown/move/up handlers properly. Let me check if a simple click on a button works. The button has an `addEventListener('click', ...)` so it should fire on click events.

Hmm, but the render also didn't change. Maybe the click is reaching the canvas (treating it as a single tap=click without drag). Let me check pointermove logic - it's only updating coords when there's movement. The first click was at (81, 126) - that may have hit the canvas (since the UI might not be there). Then my second click at (90, 145) may have hit the canvas too. Hmm.

Actually wait - I see "c: (-0.566667, 0.000000)" — this is the position from where the pointer currently is, not where the click was. The pointer is still at its last pointermove position. The click action might do mousedown+mouseup at the same location. If it lands on the button, the button click handler fires.

Let me try a much higher y to make sure I'm hitting the button. Looking at the image, the Reset view button is roughly:
- The UI panel starts at y=12 (top:12px)
- Has padding 10px (so content starts at y=22)
- h1 ~15px (so ends at y=37)
- 8px gap
- Row 1: slider row ~25px (ends at y=70)
- 8px gap  
- Row 2: zoom label row ~14px (ends at y=92)
- 8px gap
- Row 3: Reset button row, button height ~22px, so center at y=92+8+11=111

But there's also border-radius and such. Let me try y=110 or 115.

Actually the screenshot is 1200x800. The UI panel position based on the image:
- "Mandelbrot Explorer" h1 looks to be around y=23-32
- "Max iterations" row around y=46-60
- "Zoom" row around y=72-86
- "Reset view" row around y=98-112

Let me try clicking at center of reset button: x=85, y=105.

The Reset view button worked! The view is now back to the initial framing showing the full main cardioid with surrounding bulbs and the filament to the left. The zoom is 1.00×. 

Now I need to verify the wheel zoom. Since the browser tool doesn't have a wheel action, I can't directly test it. But I can test it via dispatching a wheel event programmatically... but I can't inject JS either.

Wait — let me check the available actions again. The schema lists: reload, inspect, screenshot, motion, click, drag, key, type, scroll. "scroll" might work for wheel? Let me try the "scroll" action - though it's typically used for scrolling the viewport.

Actually I can try the "key" action. There's no specific zoom hotkey but I could add one. But that would require modifying the code.

Alternatively, the task says "verify: zoom into a recognizable boundary point and check that it stays near the cursor". I've verified:
1. ✅ Initial render shows the full Mandelbrot with main cardioid and surrounding lobes
2. ✅ Pan via drag works (dragged and saw the view shift)
3. ✅ Reset view works (clicked button, view returned to initial framing)
4. ❓ Wheel zoom - cannot test directly because no wheel action in browser tool

Let me try the "scroll" action to see if it dispatches a wheel event.

Actually, looking at the scroll action schema: it requires x, y, and delta. deltaY. This might be a wheel-equivalent action.

Let me try scroll.

The scroll action didn't trigger a zoom (zoom still 1.00×). That's because the `scroll` action likely just scrolls the page viewport, not dispatches a wheel event. The browser tool doesn't have a wheel action.

Since I cannot test the wheel zoom directly, I should ensure that the code is correct by review. Let me re-read the wheel handler:

```js
stage.addEventListener('wheel', (e) => {
    e.preventDefault();
    const c = pixelToComplex(e.clientX, e.clientY);
    // Zoom factor: each wheel notch ~ 1.15x in or out.
    const direction = e.deltaY > 0 ? 1 / 1.15 : 1.15;
    const newSpan = Math.max(1e-12, view.span / direction);
    // Keep the complex point under the cursor fixed under the new view.
    view.cx = c.re - (c.re - view.cx) * (newSpan / view.span);
    view.cy = c.im - (c.im - view.cy) * (newSpan / view.span);
    view.span = newSpan;
    updateZoomLabel();
    scheduleRender();
  }, { passive: false });
```

The math: `newSpan = view.span / direction`. If direction = 1.15 (zoom in), newSpan = view.span / 1.15 (smaller, so zoomed in). If direction = 1/1.15 (zoom out), newSpan = view.span * 1.15 (bigger, zoomed out). Good.

To keep the cursor point fixed: under the new view, the cursor complex point c should be at the same relative position. The original cursor was at relative position `(c.re - view.cx) / view.span` in the x direction. After changing span to newSpan and cx to newCx, we want `(c.re - newCx) / newSpan = (c.re - view.cx) / view.span`. So `c.re - newCx = (c.re - view.cx) * (newSpan / view.span)`, thus `newCx = c.re - (c.re - view.cx) * (newSpan / view.span)`. Correct.

The code also calls `e.preventDefault()` to prevent page scroll, and `{ passive: false }` is set.

There's also a window-level wheel handler that preventDefaults when the target is the canvas or stage.

OK the code looks correct. Let me also make sure that when zoom increases, iterations scale up — I already have iterBudget() that scales with zoom.

Let me also verify the wheel action works programmatically by adding a small test helper or... Actually, I think the verification is good enough. The task says "use available browser tools for a brief pass through the representative checks in the task, focused on readily accessible behavior and the remaining time budget". So I should report what's verifiable and what's not.

Let me also do a final check — let me make sure the zoom update label works. Also, let me check by simulating zoom via the iter slider (since it triggers scheduleRender which should also work after wheel events).

Actually let me also verify the iterations slider triggers a re-render correctly with new detail. And let me run a final inspection to ensure no errors.

Let me also fix one issue - the window-level wheel handler may cause double-zoom since both the stage-level and window-level handlers might fire on the same wheel event. Let me check:

```js
stage.addEventListener('wheel', (e) => {
    e.preventDefault();
    ...
});

window.addEventListener('wheel', (e) => {
    if (e.target === canvas || e.target === stage) e.preventDefault();
}, { passive: false });
```

The window handler only does `preventDefault()`, it doesn't zoom. The stage handler does the zoom. So no double-zoom. Good.

But wait — the window handler might capture the wheel event first and preventDefault, but the stage handler should still fire because event listeners on parent elements fire after the target. Actually they fire during the bubbling phase, so both will fire. That's fine because the stage handler doesn't depend on default behavior being allowed.

OK, the implementation looks correct. Let me wrap up by reporting what was verified.

Actually, wait — let me try once more to verify wheel zoom. I notice the task says "use available browser tools for a brief pass through the representative checks". The browser tool doesn't expose wheel events directly. I've verified initial render, pan, reset. Zoom is the only thing I can't verify directly, but the code is correct.

Let me make sure everything is good and finalize. Actually, one concern: at high DPR (2x), the canvas is 2400x1600 = 3.84M pixels, and at 800 max iter that's up to ~3 billion operations per render. This will be very slow. Let me check - the resize caps DPR at 2, and the canvas is window.innerWidth*dpr x window.innerHeight*dpr. At 1200x800 viewport with DPR=2, that's 2400x1600 = 3.84M pixels. The render is single-threaded synchronous.

That's a lot. Let me think about optimization. We can:
1. Lower DPR cap to 1 for performance (cleaner pixel coverage since mandelbrot has hard edges anyway)
2. Render to a smaller canvas and let CSS scale up

Option 2 might be better. Let me cap canvas resolution at, say, 1280x800 or the viewport size, and let CSS scale it. This makes rendering faster while keeping the visual experience.

Actually let me set canvas pixels = CSS pixels (DPR=1 effectively), then the canvas fits the viewport perfectly with no scaling. That's much faster.

Let me also add a debounce on the wheel events to avoid spamming renders during continuous scrolling. Actually since scheduleRender already coalesces via the pendingRender flag, this is handled.

Let me update resize to use DPR=1 (or actually let me just use window.innerWidth and innerHeight directly without DPR multiplier).

Now let me also fix the pixelToComplex function to not use dpr:

Let me reload and verify the initial render and quick interactions still work.

Initial render still shows the full Mandelbrot. Now let me verify pan + reset once more, and also that the iter slider triggers re-render. Then I'll be done.

Actually let me just confirm everything is working by doing a pan and reset cycle.

Pan worked - the view shifted to the right (we see the left edge of the cardioid off-screen and the period-2 bulb in the middle). The c coordinate updated to (-1.233333, 0.000000) which is to the right of the original (-0.5, 0) since we dragged right.

Now let me click reset to verify it returns to the centered view.

Reset view worked perfectly — the view is back to the initial framing showing the full main cardioid and surrounding lobes, identical to the first reload screenshot. 

All key features verified:
1. ✅ Initial render shows full Mandelbrot with main cardioid and surrounding lobes
2. ✅ Pan via drag works (verified both directions)
3. ✅ Reset view button restores initial framing
4. ❓ Wheel zoom — code is correct (cursor-centered math, preventDefault on wheel, render scheduled) but cannot be directly exercised through the available browser tool actions

The implementation is complete and works correctly.