Mandelbrot explorer · minimax-m3.1-flash

Let me write a single-file Mandelbrot explorer with progressive rendering (tiles/rows) to keep UI responsive.

Plan:
- Canvas full-screen, devicePixelRatio aware.
- Progressive rendering: render in chunks using requestAnimationFrame, so zoom increases iterations and shows detail progressively.
- Smooth coloring: escape time with fractional iteration count, log coloring.
- Wheel zoom centered on cursor complex point, with preventDefault.
- Drag pan.
- Reset view button.
- Show status: zoom level, iterations, coords.

Implementation detail: render into ImageData at scaled resolution (e.g., render at 0.5 scale of canvas pixels) and draw scaled? Simpler: render full-res image data in row chunks, put to canvas via putImageData per chunk row. Use an offscreen buffer of full canvas size and putImageData with dirty rect rows.

Let me do: maintain an offscreen canvas (ImageData) sized to canvas. Render row bands of e.g. 32 rows per frame. Display progress overlay.

Smooth color: iterate z, count iterations, continuous escape value: nu = n + 1 - log(log(|z|)/log(2))/log(2). Use that for smooth coloring.

Interior color distinct: dark navy/black.

Zoom: use center complex point and scale (pixels per unit). Wheel: factor = exp(deltaY * 0.0015). Keep point under cursor fixed.

Pan: drag changes center by pixel delta / scale.

Iterations: based on zoom: iter = base + log(scale ratio)* something, e.g. maxIter = 100 + 60*log2(zoom) where zoom = initialScale/scale. Also allow slider for iterations.

Anti-banding: use a simple gamma-correct palette via cosine palette (Inigo Quilez style).

Let me write the code.

Also "keep controls responsive during rendering" — since rendering is in rAF chunks, buttons work. But heavy loop could block. Use chunk of ~16ms budget per frame.

Let's write.

Coordinates: initial view: center (-0.5, 0), span x 3.0 (from -2 to 1), y span 1.5 (aspect 1200/800 = 1.5 → 3.0/1.5 = 2 ✓). Compute from canvas aspect: xspan = 3.0 fixed, yspan = xspan/aspect. Actually with canvas aspect ratio variable, better: use yspan = 1.5 fixed? Just set xspan=3.2 and yspan = xspan*h/w? Hmm for 1200x800, xspan 3.2, yspan 3.2*800/1200=2.13, showing more vertically. Classic is height 2.0? Standard: width 3.2, height 2.0 (aspect 1.6). I'll fix yspan = 2.0 and xspan = 2.0*aspect... at 1200x800 aspect 1.5 → xspan 3.0. Good: main cardioid fits. Use: hSpan = 2.0 fixed, wSpan = hSpan*aspect. But at wide aspect more horizontal, fine.

Actually "Initially show the complete main cardioid and surrounding lobes" — cardioid spans x from -0.75 to 0.25, y ±0.6ish. wSpan 3.0 from -2 to 1 ✓ includes -2 and 0.25. Good.

Center: (-0.5, 0) → x from -2 to 1 ✓.

Pixel mapping: zx = centerX + (px - w/2)/scale, where scale = w/wSpan.

Zoom under cursor: before: z0 = center + (mouse - center_screen)/scale. After scale*=f, center = z0 - (mouse-center_screen)/newScale.

Escape radius 2 (or 4 for smooth). Use bailout 256 for smoother? Use large bailout 1e6 gives better smooth coloring but risk of precision. Use bailout = 2^8=256 with periodic checking? Standard trick: use escape radius 2 but compute smooth value. I'll use bailout 1e10? Mandelbrot with large bailout looks smooth but need high iterations. I'll use radius 2, smooth coloring via log.

Continuous iteration count: mu = n + 1 - log2(log(|z|)/log(bailout)) ... standard: for |z|>2, n_smooth = n - log(log(|z|)/log(2))/log(2). Then t = n_smooth/ maxIter mapped through palette.

Let me write render function per pixel with double loop.

Palette: cosine palette: r = 0.5+0.5*cos(6.28318*(c*d + phase)).

Also handle max iterations interior.

Progressive: after navigation, reset job: iterate count, image buffer, progress bar. Render rows top to bottom. But for interactive zoom, better render from center outward? Simplest: render top-to-bottom, and also render with increasing iterations as it goes? Requirement: "Use sufficient iterations to reveal new detail as the user zooms" — use iteration count formula based on zoom, and progressive refinement: pass 1 with lower iterations coarse, then refine. I'll do: job has iterations target; render band rows at target iterations directly but start with a quick low-iter pass? To keep it simpler: single pass with computed iterations, chunked by rows; plus a "refine" second pass with more iterations after first pass completes (target * 1.5 capped). That shows extra detail.

Let me implement:

state: centerX, centerY, scale (complex units per pixel), maxIter.
renderJob: {iter, row, imageData, buf, phase}

renderLoop(ts): if job active: process rows until 12ms elapsed; putImageData for dirty rows; update progress; if done: if job.iter < targetIter && zoom>1 -> start refine job.

Actually simpler: two-phase: phase 0 draws with iter = min(target, 200) then phase 1 with target. But changing maxIter changes colors for whole image (normalization) — that's fine, standard.

Hmm, but palette normalization by maxIter means the second pass recolors everything. Acceptable, shows "Refining detail".

Let's do: on navigation, start job with iter = target. Chunk rows. On complete, if refineCount < 1 and target > base, run refine with target*1.4? Might be overkill. Instead: progressive iterations: while zooming in, compute target iter; render coarse pass at iter/2 first (fast preview), then final pass at target. I'll implement two jobs queued: queue = [coarse, final].

Keep it manageable.

Code:

```js
const canvas=..., ctx=canvas.getContext('2d');
let W,H,DPR;
function resize(){DPR=min(devicePixelRatio,2); canvas.width=W*DPR...}
```
Use CSS pixels coordinate for mouse; internal pixel scale: px = cssX*DPR. Map complex using internal pixels: zx = centerX + (px - Wpx/2)/scalePx where scalePx = pixels per complex unit. Keep scale in "units per CSS pixel"? Let's keep scale = complex units per internal pixel. Then rendering loops over internal pixels.

Let's define: unitsPerPixel (complex). zx = centerX + (x - Wpx/2)*uPP.

Zoom factor f: uPP /= f, and center = z0 - (mouseInternal - center)*newUPP.

Wheel: e.preventDefault(); f = Math.exp(e.deltaY*0.0015) (deltaY positive → zoom out). Clamp uPP to min 1e-14.

Pan: on pointerdown store start; pointermove → centerX -= dx*uPP (dx in internal pixels).

Also handle pointer events on canvas with setPointerCapture.

Also prevent page scroll: CSS overflow hidden, and wheel listener passive:false.

UI: top bar with title, Reset view button, iteration slider, zoom display, coordinates, status. Style nicely dark.

Let me write the file.

Colors: cosine palette with phase (0.0,0.15,0.20)? Use IQ palette: a=(0.5,0.5,0.5), b=(0.5,0.5,0.5), c=(1,1,1), d=(0.0,0.10,0.20) offset. Fine.

Interior: use distinct color like #0b0b16? Use rgb(8,6,20) plus slight variation. Actually give interior a slightly lighter dark blue.

Also edge detection? not needed.

Write code now.

Rendering chunking: function renderChunk() processes rows from job.row upward, each row computed into job.buf (Uint8ClampedArray full), then putImageData(job.imageData, 0, y, Wpx, rowsDone) — need imageData with dirty rect; putImageData with dirty rect args supported. Yes: putImageData(imageData, dx, dy, dirtyX, dirtyY, dirtyWidth, dirtyHeight).

Handle resize during render: cancel job, restart.

Let me write it.

Also need maxIter formula: iterations = clamp(round(80 + 40*log2(1/uPP / uPP0 ... )). Define zoom factor z = uPP0/uPP (uPP0 initial = 2.0/Wpx). iter = min(2000, 100 + 120*Math.log2(Math.max(1,z))). Also slider multiplies.

Coarse pass: iter = min(target, 160) maybe with 0.5x resolution? Simpler: coarse pass at half resolution (scale pixels 2x) then full. That's more work to implement. I'll do coarse = same resolution with fewer iterations, quick preview.

Actually a nicer progressive: render coarse pass at lower iterations over the whole image quickly, then final pass. Good enough.

Let me write final code.

Escape function with period check: use cardioid & period-2 bulb check for interior detection (fast) — gives "distinct color for points treated as inside the set" and speed. But then those points get smooth boundary? Keep simple: only maxIter → interior.

Include cardioid test: q=(x-0.25)^2+y^2, if q(q+x-0.25) <= 0.25*y^2 → interior. And period-2 bulb: (x+1)^2+y^2 <= 1/16 → interior. That speeds up a lot for initial view.

Write now.

Bug: in frame(), the img imagedata is never updated with j.data before putImageData — I create img with createImageData(W,H) but write into separate j.data array. putImageData of img shows blank. I set j.img.data.set(j.data) only at the end. Need to fix: write directly into j.img.data. Let me just use j.img.data as the buffer. Remove j.data.

Also the initial row push: putImageData with dirty rect works.

Let me fix: in makeJob, data: null; use img.data. In renderRows use j.img.data.

Also note j.img.data is Uint8ClampedArray — fine.

Also bailout 1024 with logBa=log(2): smooth formula uses log(log(mag)/log(2)) which is valid only when bailout is 2. For large bailout, standard smooth formula: mu = i + 1 - log(log(|z|)/log(R))/log(2)? Actually for bailout R, mu = i + 1 - log2(log(|z|)/log(R)). Using R=1024, log(R) = 6.93. My formula uses logBa = log(2) inside denominator of log → wrong. Use mu = i + 1 - Math.log(Math.log(mag)/Math.log(1024))/Math.log(2). That maps continuous. But color mapping then distribution: mu ranges near maxIter. Fine, but with R=1024 the escape values near boundary need higher iterations. Simpler & safer: bailout = 4 with logBa = log(4)? For smooth coloring with bailout 2: mu = i + 1 - log2(log|z|/log2). Let's use bailout R=2^16? hmm.

Standard approach: escape when |z| > 2 but compute smooth via |z| at escape (just above 2) → log(log|z|/log2) small; mu ≈ i+1 - small. Fine. Use bailout exactly 2: check zr2+zi2 > 4.

Then smooth: mag ~ just above 2, log(mag) slightly > log2, log(log(mag)/log2) slightly >0 → mu slightly less than i+1. Good.

But with bailout 2, banding is fine with smooth coloring. I'll use bailout 4 to reduce "aliasing" artifacts? With R=4, log(mag)/log(4) ranges up to ... it still works: mu = i + 1 - log2(log(mag)/log(4)). Let me use R=4 and correct formula.

Actually mu should be normalized: mu in [0,1] roughly i/maxIter with the smooth correction. For R=4: at escape mag in (4, ...) unbounded? No—first escape means mag just above 4, log(mag) just above log4, ratio just above 1, log just above 0 → correction ~0. mu ≈ i+1. Good.

I'll set R=4, logR = Math.log(4).

Let me rewrite those bits.

Also "keep controls responsive during rendering" — the frame budget 11ms is ok.

Another issue: during pan, startRender resets job each pointermove — fine.

Also progress: on startRender I set prog width 0. OK.

Fix renderRows andframe.

Partial render (in progress). Also the palette shows mostly yellow — because mu mapping: for escaped points near i small → t small → cosine palette at t=0 gives r=0.5+0.5cos(0)=1, g=0.5+0.5cos(0.16*2π)=0.5+0.5*cos(1.005)=0.5+0.27=0.77? Hmm yellow-ish. Actually t=0 → r=1,g=0.77,b=0.5+0.5cos(2.01)=0.5-0.21=0.29 → orange. But we see pale yellow everywhere, meaning t values map oddly, maybe t is near 0 for many points? Actually the exterior far away escapes at i=1, so mu≈1 → t≈0.92 → colors change. But everything is uniform yellow, suggesting mu maps same. Let's check: far from set escapes at i=1, mag ~ |z| large, log(log(mag)/logR) large → mu = 2 - something. If mag=100, log(100)=4.6, /1.386=3.3, log=1.2, /log2=1.73 → mu=2-1.73=0.27. So mu varies. But most exterior points at this zoom escape at i=1 with mag maybe 2-10 → mu smallish. Hmm, everything yellow means t constant-ish.

Wait, the picture shows the outside uniformly yellow and the set black. With smooth coloring, the exterior bands should be visible. Actually with 100 iterations and only visible early escape the pattern should show bands. Uniform yellow suggests the palette's t ≈ 0 or similar across... Hmm, cos palette at t=0: r=1, g=0.5+0.5cos(1.005)=0.77, b=0.29 → that's yellow-orange (255,196,74). The image shows pale yellow (230,230,180?) like. Hmm.

Maybe issue: the visible yellow region is only the top part that got rendered; maybe that's the raw buffer uninitialized? No.

Also note the render is progressive from top; but the image shows top rows rendered in yellow and the rest black — but black region includes the set interior, which is black too... The bottom half is entirely black (not yet rendered). OK.

So exterior color: let me compute more carefully. The rendered top rows are exterior far from the set, e.g. zx ~ -2 to 1, zy ~ 1 (top). Escape iteration: for |z|>2 escapes at i=1, mag = |z| ~ 2-3. log(mag)≈0.9, /logR(1.386)=0.65, log(0.65)=-0.43, /log2=-0.62 → mu = 2 - (-0.62) = 2.62, clamped to 1 → t = 0.92 → cos palette: r=0.5+0.5cos(2π*0.92)=0.5+0.5*cos(5.78)=0.5+0.47=0.97; g: 0.5+0.5cos(2π(0.92+0.16))=0.5+0.5cos(6.78)=0.5+0.44=0.94; b: 0.5+0.5cos(2π(1.24))=0.5+0.5cos(7.79)=0.5+0.04=0.54 → pale yellow. Yes! That's the problem: saturation clipping, everything far escapes → mu clamped at 1 → uniform color.

Fix: don't clamp mu at 1 by iter; instead normalize mu by maxIter? Standard: use mu = (i + 1 - log2(log|z|/logR)) / maxIter, but the correction term makes it exceed 1 for far points. Better: use the fractional part based on log-log mapping: t = log(mu)/log(maxIter) style which gives nice gradients for exterior.

Common approach: normalized "smooth" value = sqrt(i/maxIter) or use log scale. Let's use t = Math.log(1+mu)/Math.log(1+maxIter) → smooth, no clipping, far points map to log values. But then bands near boundary compressed. Alternative classic: use t = mu/maxIter where mu only counts iterations (i + frac). Since far points escape at i=1, t≈1/maxIter ≈ 0.01 → all far exterior near same color again.

Best: use a periodic palette on the fractional part plus overall intensity? A common good look: color = palette(0.5 + 0.5*cos) applied to t = log(mu)/log(maxIter)... Let's think: we want the exterior to show visible structure (bands) around boundary, and far exterior to be uniform-ish but not clipping to the same extreme.

Approach: compute continuous escape value mu (unclamped, can be >1). Then use t = log(mu) / log(maxIter+1) mapped, giving exterior gradient from boundary (mu small → dark) to far (mu large → bright). That creates a nice glow but bands won't be visible as stripes.

Alternative: use both: bands via sin of mu scaled. Common: t = mu/maxIter for interior-adjacent, plus palette repeating every N iterations to show bands.

I think a good practical approach: color using t = (i + frac)/maxIter for points that escape with i small relative? Hmm.

Simplest robust: use logarithm of escape count: t = Math.log(mu) / Math.log(maxIter) clamped 0..1, then pal(t). For far points mu is bounded: mu ≈ 2 - log2(log|z|/logR) ~ 2.6 → t = log(2.6)/log(100)=0.97/4.6=0.21 → mid-palette, and closer points have mu small (e.g. mu=1.1 near boundary?) Actually near boundary escape takes many iterations, so mu near boundary is large (e.g. 50-99). Hmm inverse: near boundary → many iterations → mu large → t near 1 (bright). Far → mu small → t small (dark). Bands: mu varies continuously giving smooth gradient across the exterior. That's nice and shows detail.

But the number of bands visible is limited since mu max = maxIter, log compresses. It'll look like a smooth gradient, acceptable "smooth escape-time color gradient".

Better: use a hybrid: t = log(mu)/log(maxIter) gives gradient, and to add banding we can use palette with multiple oscillations: pal(t*3). Let's make palette period: r = 0.5+0.5cos(2π(t*4 + d)) etc. That yields banding stripes in the log gradient. 

Let me define:
- mu continuous (unclamped, min 0.1)
- t = log(mu)/log(maxIter+1), clamp 0..1
- palette: cos with frequencies (3,3,3) and phase offsets → colorful bands.

Also interior: distinct dark color, fine.

Additionally, at high zoom, mu near boundary ~ maxIter → t near 1.

Let me also make color mapping nicer: use three colors interpolation.

Implement pal(t):
r = 0.5+0.5*cos(6.283*(3*t + 0.0))
g = 0.5+0.5*cos(6.283*(3*t + 0.33))
b = 0.5+0.5*cos(6.283*(3*t + 0.67))
This gives rainbow-ish bands.

I'll test.

Also the exterior far away all same → fine.

Let me apply changes and re-check.

Also note the initial iterations was 100 (targetIter min with boost). Slider says 180 → iterBoost=1, target = 100+130*log2(1)=100. Fine.

Also I should double-check "smooth escape-time color gradient" - ok.

Let me edit pal and tcomputation.

Colors now varied. But rainbow banding is heavy; acceptable though a bit garish. Also render is slow — 100 iterations, 1200x800 at DPR1... it took over a frame. Let's see final result screenshot after waiting.

Note the "smooth" log mapping means the exterior bands look rainbow-wide. Acceptable but maybe tone down PAL_FREQ to 2 and make gradient less saturated. Let's check full renderfirst.

The full set is shown: main cardioid, period-2 bulb, lobes. But the interior is entirely black (interior of cardioid is one solid blob) — that's fine but the "inside the set" color is very dark, and the cardioid looks like a black circle. Actually the main cardioid interior should be solid — it is.

Concern: the smooth gradient — the exterior looks like broad rainbow bands, quite garish but that's the palette. However the bands look "blocky" (aliased) near the boundary — there's aliasing because bailout 4 and only 100 iterations with no anti-aliasing; also the bands look stepped. Hmm, the band edges look jagged/pixelated which is normal for escape-time at low res, but smoothness should be OK.

Actually the coloring shows stripes of pure red/green/blue — the squared palette with freq 3 gives harsh saturation. Let me soften: use freq 2 and mix in a base gradient. Also increase initial iterations to ~250 for smoother.

Also the interior of the cardioid is black — maybe give it a distinct dark blue/near-black color (already 6,8,22). Looks black on screen; fine but let's brighten a bit to (12,14,34) so it's visibly distinct.

Also I notice there's no visible detail difference between exterior regions with fractal filaments? The exterior shows some.

Let me improve palette: combine a smooth cyclic palette with lower saturation:
r = 0.5+0.5cos(TAU*(f*t + 0.0)), and then blend with a warm-to-cool gradient. Simplest: reduce freq to 2 and apply gamma 0.85.

Let me set PAL_FREQ = 2.0 and sqrt instead of square.

Also add progressive refinement: after finishing the main pass, run a second pass with more iterations? The requirement says "Use sufficient iterations to reveal new detail as the user zooms" — targetIter scales with zoom, fine.

Also "keep controls responsive during rendering" — yes chunked.

One issue: during pan, startRender is called on every pointermove, restarting; fine.

Another: rendering at DPR 2 on a large screen could be slow; but chunked.

Let me also double check zoom-to-cursor correctness and reset. Test with browser: wheel at some point.

Also potential bug: in resize(), if view.upp truthy we set view.upp = 2.0/H which keeps vertical span 2.0 — fine.

Let's tweak palette and interiorcolor, then test zoom.

Now test zoom behavior. Use browser wheel? The browser tool has scroll action with delta. Let me check: `scroll` with x,y,delta. Also `click`. Wheel via scroll event → our wheel handler with deltaY. Let's reload then scroll at a specific cursor position over a boundary point, e.g. the cusp at (-0.75, 0) which is on screen around x = ? Complex mapping: x = cx + (px - W/2)*upp. Internal W = 1200 (DPR 1 in browser? devicePixelRatio likely 1). upp = 2.0/800 = 0.0025. cx=-0.5. For zx=-0.75: px = (-0.75+0.5)/0.0025 + 600 = -100+600 = 500. zy=0 → py=400. So scroll at (500,400) — that's the cusp (a boundary point, recognizable).

Then check HUD center and zoom, and that the point under cursor stays (-0.75,0): after zoom, center should satisfy: zx = cx + (500-600)*upp = -0.75.

Let me do it.

The scroll zoomed OUT (zoom 0.62×) and panned weirdly to center 0.4241, 0.6161. That's wrong: scroll delta -600 should zoom in (deltaY negative = scroll up = zoom in). Our factor = exp(delta*0.0016) → delta=-600 clamped to -300 → factor = exp(-0.48)=0.62 → newUpp = upp/0.62 = bigger → zoom out. Sign convention: I divided: newUpp = view.upp / factor. factor<1 → newUpp larger → zoom out. So negative delta (scroll up) → zoom out. Should be: scroll up (negative deltaY) = zoom in. So factor = exp(-delta*0.0016)? Let's define zoom in for deltaY<0. Use factor = Math.exp(-delta*0.0016); then newUpp = upp/factor; delta<0 → factor>1 → newUpp smaller → zoom in ✓.

But also the center moved to 0.4241,0.6161 — because the "point under cursor" invariant should hold regardless of zoom direction: the center should update so that zx under cursor stays. Here the zoom-out kept (500,400)'s complex coordinate fixed, which was correct behaviorally. With zoom out, the point under cursor is still the same complex point — the center changed accordingly. Actually correct: center = zx - dx*newUpp. So the center changed, that's fine. But the whole set appears shifted... looks plausible.

But note the browser's scroll action may have generated multiple wheel events with deltaY positive/negative? Anyway.

Also possible issue: the browser tool's scroll might set deltaY with different sign convention. Let's just fix the sign so that scrolling up zooms in (standard).

Also, the clamp of delta to ±300 limits zoom per event: exp(300*0.0016)=1.62 per event. Fine.

Additionally, with zoom out beyond home, zoomFactor < 1 → targetIter lower bound 60. Fine.

Also the render during scroll: we re-render on every wheel event — fine.

Let me also consider: after zoom-out the view shows more; initial framing requirement is about reset.

Fix sign.

Rendering is progressive; the top part rendered. Note the initial render took a while (100 iterations at 1200x800). Let's wait and screenshot.

Concern: The render speed — 1200x800 * 100 iterations in JS ≈ maybe 200ms-1s. Fine.

Let's screenshot after a moment, then do zoom test.

Full view shows the complete set. Good. Colors are garish rainbow but that's a procedural palette; acceptable. Maybe soften later.

Now test zoom at the cusp (-0.75, 0) → screen x = 500? Let's verify mapping: complex x = cx + (px - W/2)*upp, W=1200, upp=2/800=0.0025. px=500 → -0.5 + (500-600)*0.0025 = -0.5-0.25 = -0.75 ✓. The cusp is at screen x=500,y=400. In screenshot, the cusp (notch between cardioid and left bulb) is at ~x=497,y=395 ✓.

Now scroll (delta -600) at (500,400) → should zoom in keeping (-0.75,0) under cursor.

Note: browser tool scroll might dispatch wheel events with deltaY negative? Let's see what happens.

Zoom 1.90× and center changed to (-1.2091, -0.4727). Check invariant: point under cursor should remain -0.75+0i. Complex at cursor = cx + (500-600)*upp. upp = span/W = 1.5819/1200 = 0.0013183. → -1.2091 + (-100)(0.0013183) = -1.2091 - 0.1318 = -1.3409. That's not -0.75! So invariant broken — the zoom centered somewhere else, and the view drifted.

Wait — maybe the browser's scroll event has an offset position different, or scroll happened at a different position. Also the center's y is -0.4727, weird: the cursor y=400 = H/2 → dy=0 → cy should stay 0 (since cursor point had zy=0). But cy=-0.4727. So something's off — likely the browser tool dispatches wheel events at the mouse's last position or without coordinates, and also perhaps the pointerdown/pointermove happened.

Hmm, maybe the browser tool's scroll sends a wheel event at (0,0)? Then dx = -600, dy = -400: zx = -0.5-600*0.0025 = -2.0, zy = 0-400*0.0025 = -1.0. Then after zoom newUpp=0.0025/1.9... let's verify: factor = exp(-delta*0.0016) with delta=-500 → factor=exp(0.8)=2.226, but zoom shows 1.90 → maybe multiple events or delta clamping. Anyway with cursor at (0,0): cx_new = zx - dx*newUpp = -2.0 - (-600)(0.0013183)= -2.0+0.791 = -1.209 ✓ matches! cy_new = -1.0 - (-400)(0.0013183) = -1.0+0.527 = -0.4727 ✓ matches.

So the browser tool dispatches wheel at (0,0) top-left, not at x,y. So the invariant math is consistent — the tool just doesn't honor x,y for wheel. Hmm, but maybe scroll action uses x,y as the mouse position? Apparently not, or the mouse was at 0,0.

Let me instead dispatch wheel events via JS evaluate? The browser tool doesn't have an evaluate action. But I can verify using keyboard? Alternative: use drag (click + drag) which uses coordinates properly — pointer events at specified coords seem handled (click action has x,y).

To test wheel-to-cursor properly, I can use the "motion" or "key" action? Maybe the browser tool's scroll does support x,y but the mouse needs to be moved there first via click? A click at (500,400) would move the mouse. But click also triggers pan (pointerdown/up with no move) — harmless.

Let's: click at (500,400) first, then scroll, then check invariant.

Also note that the earlier scroll (before sign fix) behaved similarly, so coordinates were ignored then too.

Let's try: click at 500,400, then scroll delta -500 at 500,400.

Also worth adding: mouse position tooltip showing complex coords under cursor — nice and helps verification. Let me add a cursor readout in HUD (updates on pointermove). Good idea.

Also potential issue: pointermove over HUD elements still updates canvas? Fine.

Let me add the coords readout and also a "rendering" indicator already there.

Implement: on pointermove (always, not just dragging), update #cursor element with complex coords. But note our pointermove handler returns early if !dragging; restructure.

Also I should double check the 'R' key.

Let me edit the file to add cursor coords display.

Cursor readout shows -2.0,-1.0 → confirms the mouse is at (0,0) top-left. Now click at (500,400) to move the mouse there, then scroll.

Note the tool's scroll might scroll relative to current mouse position. Let's click first.

Cursor at (-0.75, 0) — the cusp. Now scroll with mouse at that position.

Note: the click also triggers pointerdown/up which we treat as drag start/end — no movement so fine.

Now scroll delta -500 at (500,400).

The zoom is centered on the cusp: cursor still (-0.75, 0) ✓ and the cusp notch is at screen (500,400) ✓. The set is bigger. Detail renders (220 iterations).

Now zoom deeper a few more times to check detail and cursor stability. Let me scroll again with the mouse still at 500,400 (mouse hasn't moved).

Note: after scroll, the "cursor" readout is stale (-0.75,0) but it's still correct since mouse hasn't moved.

Let me do two more scrolls and check the cusp stays at 500,400 and more detail appears.

Zoomed into the cusp: the cusp point is at (500,400) ✓ (the notch apex). Detail is emerging, iterations 340. Good.

However the color palette at deep zoom: the exterior far away is uniform yellow-green. That's because log-scaling compresses. Near the boundary, magenta/cyan. Acceptable, though the "far exterior" flatness looks a bit plain. Could improve by mixing in the raw iteration fraction to give banding. Let's improve palette mapping: use t = log(mu)/log(maxIter) but also add periodic bands based on mu directly: add a modulation sin(mu * something) to give the classic bands. Let's do: t2 = t + 0.06*Math.sin(mu*0.9) — subtle bands.

Actually the "smooth escape-time color gradient" is satisfied. But visual quality would improve with classic bands. Let's implement a hybrid:

value = smooth normalized via log → t.
color = cosine palette with freq based on t.

To get classic bands: use v = mu (continuous iteration count); band = fract(v) mapped through palette, plus brightness from log scale. Combine: color = palette(0.5 + 0.5*cos?) hmm.

Simplest classic approach that still shows smooth gradient: t = mu/maxIter for coloring with a cyclic palette where the cycle repeats every 1 unit of mu... too high frequency at deep zoom (mu values large).

Alternative widely-used: color by t = log(mu)/log(maxIter) but palette with frequency f=6 gives several bands across the gradient — the current f=2 gives 2 bands. Increase to f=4 or 6 to get more banding visible along the gradient. Let's set PAL_FREQ = 5.

Hmm, but with the log mapping, the whole exterior gradient spans t 0..1 so freq 5 → 5 color cycles across the exterior: nice.

Let's set PAL_FREQ = 5 and see.

Also I want the interior to be more distinguishable — dark navy is fine.

Another improvement: the initial view has a huge flat gradient far field; with freq 5 there will be more structure.

Let me change and re-render at reset.

Also test pan and reset afterwards.

Colors are nicer now with more banding. Render in progress.

Now let's test pan (drag) and reset. Drag from (600,400) to (400,300). Then check center changed accordingly: dx=-200 → cx -= (-200)*upp → cx = -0.5 + 200*0.0025 = 0.0; dy=-100 → cy = 0 + 100*0.0025 = 0.25.

Wait sign: view.cx -= dx*upp → cx = -0.5 - (-200)(0.0025) = -0.5+0.5 = 0.0 ✓ (image moves left with mouse, correct).

Let's do drag.

Pan works: center moved to (-1.0, -0.25) as expected (drag right by 200 → content moved right → center moved left) ✓.

Now click Reset view and verify back to center (-0.5, 0), span 3.0, zoom 1.0.

Reset works: HUD back to center -0.5,0, span 3.0, zoom 1.0. The image is still rendering progressively (top rows shown, rest stale from panned view). Once done it should match initial framing.

One issue: during progressive rendering, stale pixels of the previous view remain in unrendered areas — visually confusing but acceptable; better to clear canvas to background color at start of render. But then blank regions show. Alternative: render progressively but keep old image until done (current behaviour = stale). Hmm — current: at start of job, the canvas still shows old frame; new rows overwrite from top. So mixed old/new. It's ok-ish but cleaner: dim the canvas during render? I'll leave as-is but clear to a dark background when the view changes drastically? Simplest: at start of render, don't clear; final result correct. The mixing may look odd (as seen). Let me improve: draw the previous frame scaled/translated? Too complex.

Alternative: render the job into the ImageData and blit only at end — but then no progressive feedback. Compromise: draw old image, then progressively overwrite; the visual mixing is common in progressive renderers.

I think it's fine, but I can reduce weirdness by clearing the canvas to the background color at job start so unrendered area is neutral dark rather than stale fractal. Actually the stale region shows a wrong framing which might confuse verification. But since it's temporary (render takes <1s), fine. I'll add a subtle approach: on start, fill canvas with #05060c so the user sees the new framing appear progressively (rows of the correct new view). That's cleaner. But then during pan you see the image re-appear from top which is standard.

Let's do that: at startRender, ctx.fillRect with background. Hmm, but this makes the render appear "empty" briefly. Many viewers do that. I'll do it — it avoids showing wrong content.

Actually, better: keep the old frame until the new one is ready? That prevents flicker but shows stale framing. Progressive top-down with blank fill is fine.

Wait, there's a subtlety: the previous frame at the same zoom is usually almost identical, so stale content is nearly identical → minimal artifact. In the reset case, the stale content is a panned view — different. I'll go with the blank fill (dark) — clearer that it's recomputing.

Let me add fill at start.

Also, the "rendering N iterations…" chip in the middle of the canvas is a bit intrusive; move it to bottom-left? It's centered. I'd rather position it bottom-left above the progress bar. Let's move .busy to align-items:flex-end; justify-content:flex-start; padding bottom-left.

Also potential responsiveness issue: the render loop hogs with 11ms per frame → fine.

Another improvement: progressive refinement with more iterations after the first pass completes (to reveal extra detail). The target iteration already scales with zoom. But requirement "Use sufficient iterations to reveal new detail as the user zooms" — satisfied.

However there's a subtle problem: at deep zoom, targetIter = 100+130*log2(zoom) → at zoom 1000, iter ≈ 1400. Fine, but rendering at 1400 iterations for 960k pixels might take several seconds. The chunked approach keeps UI responsive. Also slider multiplies.

Let me also make the initial render quicker: base 100 iterations fine.

Now, one more: the mouse wheel over the canvas — the global window wheel preventDefault might block scrolling but there's nothing to scroll. Good.

Also pinch/trackpad: wheel with ctrlKey → browser zoom; we preventDefault so fine.

Let me apply the fill + move busy chip, then final check with console errors and a final screenshot at full render.

Also add title attr? no.

One more requirement: "Prevent wheel navigation from scrolling the surrounding page." Body overflow hidden + preventDefault ✓.

Let me makethe edits.

Progressive top-down rendering works. The busy chip is bottom-left now.

Concern: the initial render is slow-ish (~2s for 100 iterations at 1200x800?). Let's check how long. The screenshot after reload shows only ~360 rows done. Each frame ~11ms of compute; so 960 rows/24-row bands = 40 bands; at ~60fps → ~0.7s minimum plus compute. It took maybe 1s. OK.

Hmm, but rendering only 24 rows per band then looping while <11ms — it should render many bands per frame. Fine.

Now let me wait and take a final screenshot to see the full initial framing, plus check console for errors.

Also potential improvement for perceived quality: supersampling for antialiasing. Not required.

Let's take a final screenshot after rendercompletes.

Initial framing shows complete cardioid + lobes ✓. Console clean.

The palette is very saturated/rainbow. Slightly tasteful would be nice, but it's procedural and shows detail. Maybe reduce saturation a bit for a nicer look: mix palette with a dark base so it looks less neon. Let's soften: blend the cosine color with a blue-violet gradient.

Quick change in pal: r = 0.5+0.5cos(...), then out = 255*(0.15 + 0.85*r^1.3)? Current uses sqrt which brightens. Let's use r^1.4 to darken midtones and add a slight blue tint in dark regions. I'll adjust: out[o] = 255*Math.pow(r,1.35)*0.95.

Let's do that quickly and re-check appearance. Also consider a "distance estimate" coloring for extra depth — skip, time budget.

Then final verification: zoom deep check with detail, and reset comparison. I've done most.

One more thing: check that the iterations slider works (click on slider). Maybe test by pressing arrow key on slider? Use click at slider position.

Let me apply palette tweak, reload, screenshot, then test slider, then zoom deeper to seedetail.

Colors look nicer. Now let's do a deep zoom test to confirm detail renders and cursor anchoring persists. Click at the cusp (500,400) to place mouse, then scroll several times.

Note: after clicking, mouse stays there. Let's do click then 3 scrolls.

Zoom-to-cursor works: the cusp notch (between cardioid and bulb) is at x=500, y=400 ✓ (visible notch at ~(500,400) — yes the cusp point at the tip of the "V" between left bulb and cardioid is right at 500,400).

Now deeper zoom twice more to verify detail and anchoring, then reset.

The cusp is at (500,400) ✓ — the sharp point of the cusp sits exactly at the cursor position (500,400). Excellent zoom-to-cursor anchoring.

But there's a problem: the entire exterior beyond the boundary is a flat dark navy — because of the log mapping, the far exterior (which escapes quickly) is very dark, while near-boundary is bright. Actually here the interior is dark navy (that's the set, since the cusp region is interior) — right, the interior of the set is the big dark area, so it's correct: the dark region IS the set interior. The colored region is the exterior near the cusp. So the flat dark = inside set ✓. Good.

Also visible aliasing/noise along the boundary (speckles). Could improve with more iterations or supersampling. 340 iterations gives speckle noise typical of escape-time at pixel level. It's acceptable but a bit noisy. Could add 2x supersampling when zoomed? Costly. Alternative: increase iterations slightly and use bailout 4 (already). The speckles come from points that escape at nearly maxIter. Standard artifact. Acceptable.

Now check Reset view returns to initial framing identical to initial screenshot. Click reset.

Reset restores initial framing (identical to initial view) ✓.

Remaining: the interior is a huge dark region — a bit plain but "distinct color for points inside the set" ✓.

One more improvement worth doing: the initial view has the interior fully flat; adding a subtle gradient inside (e.g. based on distance) would be nicer, but requirement says distinct color for inside. Fine.

Also note that the interior of the cardioid is flat dark, which visually is fine.

Final check: the iteration slider. Let me test by clicking on the slider track to increase iterations, verifying the render changes. The slider spans x 355-485 approx at y=25. Click at 430,25 → value ~ (430-355)/130 = 0.577 → 60+0.577*1140 = 718.

Actually the range input's thumb position: min 60 at x=355, max 1200 at x=485 (track width 130). Click at 420 → value ≈ 60 + (65/130)*1140 = 630.

Let me test and verify iter readout changes and render updates.

Note clicking on the slider is on the HUD (pointer-events auto) so it won't pan the canvas ✓ (HUD is above the stage).

But careful: our stage pointerdown listener is on #stage; HUD is a sibling overlay, so clicks on HUD don't hit stage ✓.

Slider works: 600 → target 333 iterations. Detail is finer.

Everything works. One last thing: page-scroll prevention. The page has overflow hidden and preventDefault on wheel. Verified implicitly (no scroll).

Also the render takes a while at 333 iterations; but the UI stayed responsive (we could click during render). Good.

Final: maybe reset the slider default back to 180 in the file (it is 180 by default; my click changed runtime only).

Also, one issue: at the very end the render loop leaves prog bar width 100% then resets to 0 via setTimeout — fine.

Let me double-check there's no leftover "inMax" unused var etc. Fine.

Let me do a final full screenshot after the render completes to confirm no console errors, and check file size.

Also I should double check that zoom in + reset restores exact initial framing — verified via HUD (span 3.0000, center -0.5,0, zoom 1.0) and identical screenshot ✓.

Also verify the interior detection & that "inside the set" uses a distinct color ✓ (dark navy).

Done. Final report.

One last consideration: performance at deep zoom with high iterations — the chunked loop keeps UI responsive; verified.

Let me take a final screenshot to confirm complete render and no errors.

Everything renders correctly. Console clean. Done.

Final answer: report what waschecked.