Mandelbrot explorer · deepseek-v4-flash-0731

Let me build a Mandelbrot set explorer. I'll write it as a self-contained index.html file.

Let me plan the implementation:
- Full screen canvas
- Mandelbrot set with smooth escape-time coloring
- Pan with drag
- Mouse-wheel zoom centered on cursor point
- Reset view
- Recompute after navigation
- Iterations scale with zoom
- Responsive rendering (async chunked rendering to keep controls responsive)

Let me write the code.

Complex plane conversion: for each pixel (px, py), map to complex coordinates. Given view bounds (xMin, xMax, yMin, yMax).

Rendering async in chunks (rows) so UI stays responsive. Use requestAnimationFrame based rendering.

Let me write it.

I left a leftover dead function `renderRowComplex` in the code. Let me remove it. Let me check the code cleanup. There's a stray function renderRowComplex that's unused and has a placeholder that doesn't do anything meaningful. I'll remove it for cleanliness.

Let me also verify the smooth coloring and that it looks good. Let me remove the dead function.

There's an error: "Cannot read properties of null (reading 'width')". This is in ensureOffscreen or drawToScreen where offImg is null. On the first resize(), drawToScreen() is called before offImg exists (offImg is null initially). Let me fix - in drawToScreen check if offImg exists, and in resize the initial drawToScreen call references offImg.width which is null.

Let me fix drawToScreen to guard against null offImg.

No console errors now. Initial render shows iters 300, center -0.62. Let me wait for render to finish and take a screenshot. The stats say "Rendering… it=300". Let me wait and screenshot.

Render done. Let me screenshot to see the image. The tool says "model does not support images" for images but let me try screenshot which returns images field empty. Hmm, the screenshot returned no image. Let me try to test the interactions programmatically.

Let me verify zoom behavior. Let me test wheel zoom at a point and check the view center and the point under cursor stays fixed.

Let me inspect more carefully. Let me use the browser tool to do a wheel scroll. But the browser tool doesn't have a wheel action. It has scroll though. Let me use scroll to simulate wheel.

Actually, I need to verify the zoom centers on cursor. Let me compute manually instead and add a test via console evaluation through the browser. But I can't run JS directly with the browser tool. 

Let me think about checking behavior. I could temporarily add debug output. But better to reason.

Actually let me test pan and reset using the browser. Mouse drag — I can use drag action. Reset via button click.

Let me verify the wheel handler works. The scroll action in browser sends wheel events? Let me try.

First, let me test that wheel prevents page scroll - since page doesn't scroll anyway (overflow hidden), it's fine.

Let me do a drag to pan, then check stats changed, then click reset and check stats back to initial.

Let me do drag.

Pan worked: dragging right 100px and down 50px moved center from -0.62 to -1.74 (dx positive reduces cx: -0.62 - 100*0.0028 = -0.62 - 0.28 = -0.90... wait gets -1.74). Hmm -0.62 - 100*0.0028 = -0.9 not -1.74. Let me check: -0.62 - 0.28 = -0.90. But result is -1.74. That's 0.84 difference = 300px. Hmm maybe multiple mousemove events fired. Actually probably drag triggered multiple moves. Regardless it panned. cy: 0 - 50*0.0028 = -0.14 ✓.

Now click Reset.

Hmm, the click at (30,30) hit the reset button area but the stats still show center -1.74? Wait maybe the rendering hasn't updated stats yet, or the click missed the button. Let me check where the button is. #ui is at top:12 left:12. The button "Reset view" is around y=12-30, x=12-100. Click at 30,30 should hit it. But center still -1.74. Maybe render hasn't completed (still Rendering). Let me wait and re-check DOM.

Actually the drag changed center to -1.74, reset should have set it back to -0.62. The status still shows "Rendering…" meaning reset triggered a new render. But center showing -1.74 means the click didn't reset, OR the drag rendernoids happened. Let me wait and inspect. Actually click may have landed but the mouseup... Let me re-inspect after a moment.

The scroll action didn't seem to change things. wheelDelta param maybe not supported. Let me check the scroll tool params - it takes delta, not wheelDelta. Let me retry with the scroll action using delta and a position.

The scroll action doesn't seem to trigger wheel handling, possibly it triggers at a different coordinate or not on the canvas. The view is unchanged. Perhaps the scroll tool scrolls the page rather than dispatching wheel at x,y. Since I can't reliably test wheel zoom via the browser tool, let me verify the wheel math separately by reasoning.

Actually, let me try to verify the wheel handler by temporarily injecting a test. Instead, let me reason about correctness:

The wheel handler computes:
- pt = complex point under cursor using old view.scale
- newScale = scale * factor
- newCx = pt.re - (px - W/2)*newScale  → this keeps the complex point at pixel px constant. Good.
- newCy similarly.

This is correct math for centered zoom.

Iterations scale with zoom: newIter goes up as scale decreases (since scale^0.45 decreases → but 20000*scale^0.45? No: smaller scale → smaller exponent value → smaller newIter!). Wait that's wrong. scale^0.45 for smaller scale is smaller. So newIter = 20000*scale^0.45 would decrease as we zoom in. That's backwards.

Let me reconsider. I want MORE iterations as we zoom deeper. As scale decreases (zoom in), we want newIter to increase. So newIter should be proportional to 1/scale^0.45. Let me fix: newIter = 20000 * Math.pow(INITIAL/scale... ) hmm. Actually define zoom factor = INITIAL_VIEW.scale / view.scale. As zoom increases, scale decreases, zoom factor increases. 

newIter = clamp(base * pow(zoom, 0.45)). Let me recompute. At zoom=1, newIter should be ~300. So base*1 = 300 → base=300. Hmm my current code gives 20000*0.0028^0.45 = 20000 * (0.0028^0.45). 0.0028^0.45 = exp(0.45*ln0.0028)=exp(0.45*-5.878)=exp(-2.645)=0.071. So 20000*0.071=1420, then clamped to 300 (since scale<0.0004 false at 0.0028, so still 1420 then min 300→300). OK at initial gets 300 via the overview clamp.

As we zoom in, scale drops below 0.0004, removing the overview clamp. Then newIter=20000*scale^0.45 keeps DECREASING as scale decreases. That's wrong — zooming deep would give fewer iterations. E.g. scale=1e-6: 0.45*ln1e-6=0.45*-13.8=-6.2, exp=-6.2/... 1e-6^0.45 = 1e-2.7=0.002. 20000*0.002=40. Way too few.

I need to fix: more iterations as zoom depth increases. Let me redefine based on zoom factor = initial scale / current scale.

newIter = clamp( base * Math.pow(zoomFactor, 0.5), min, max )

At zoom=1 → base. Let's pick base=250. At deep zoom 1e6, pow(1e6,0.5)=1000, *250=250000 → capped at 4000.

Let me set: 
var zoom = INITIAL_VIEW.scale / view.scale;
var newIter = Math.round(250 * Math.pow(zoom, 0.5));
newIter = Math.max(80, Math.min(4000, newIter));

That gives increasing iterations with depth. Good.

Let me apply this fix.

Now iters 250 at zoom 1. Let me verify the wheel handler by injecting a wheel event via the browser's JS? The browser tool doesn't run arbitrary JS. But I can test wheel math by reasoning, which is correct.

Let me verify zoom produces more iterations. I'll simulate by temporarily... Actually, I can use the scroll action differently. Let me check if scroll at a position dispatches wheel to canvas. The result showed no change. Perhaps scroll uses delta for vertical page scroll (Cocoa). Let me check if there's a way to send wheel to the canvas element.

Alternatively I can add a hidden test by editing that dispatches a WheelEvent. But that's modifying production code. I could temporarily add a debug hook: a keyboard shortcut that zooms. Actually I already have R for reset. Let me add a temporary diagnostic that on a key like 'z' dispatches a synthetic wheel event at center. But better to keep production clean.

Let me just verify the wheel handler works via the scroll tool with proper coordinates. The issue might be the scroll action scrolls an ancestor. Since overflow hidden and fixed canvas, maybe it dispatches to top. Let me try scrolling directly and see if 'Rendering' appears (indicating a re-render triggered).

Let me try scroll with delta small.

The scroll (without position) did trigger wheel on the canvas! Scroll down (delta negative?) resulted in zoom OUT: zoom ×0.8, width increased to 4.2, center changed to -0.2, 0.28. Wait, that center change is odd. Actually the default position is likely center (0,0? or 600,400). delta -240... the sign: my handler: if e.deltaY > 0 zoom out (factor=1/1.25). delta here negative → factor 1.25 zoom in. But we got zoom out (0.8). Hmm so deltaY sign was positive. Anyway left/right.

The center changed to (-0.2, 0.28) which means the zoom was centered around a point offset from screen center. That indicates the wheel was dispatched at some position (maybe center 600,400) — centered at (-0.2, 0.28) complex point. Since zoom out by 1.25, if centered at (600,400): screen center is (600,400)=complex (-0.62,0). Zoom out about that point: cx stays -0.62. But we got -0.2. So the point was at a different location.

Hmm, actually maybe the wheel was dispatched at the mouse's last position (300,300 from earlier scroll attempts). Let me not overanalyze. The important thing: zoom changes iterations (224) and re-renders. And iterations increase with deeper zoom.

Let me test zooming IN (to get more iterations) by scrolling up at a point. Let me zoom in and verify iterations increase and point under cursor stays fixed.

Let me position at some boundary point. Let me just do scroll with delta +420 (zoom in). With no position, it defaults somewhere. Let me check result.

Hmm interesting: after delta +420 at default position, it reset to zoom ×1.0 center -0.62, 2.2e-16. That means the scroll action with delta 420 produced deltaY < 0? No... Actually wait, delta +420 after the previous zoom-out state (scale larger). Zooming in by factor would reduce scale. The result back to ×1.0 exactly... coincidence? 

Actually the default scroll position might be the last used (300,300), and the deltas seem to be interpreted oddly. The multiple scroll calls each have delta. It's hard to control precise zoom level via this tool.

Given delta +420 gave zoom ×1.0 exactly back from 0.8... 0.8 * 1.25 = 1.0. Yes! So delta +420 caused zoom-in factor 1.25, returning to ×1.0. But wait, that means the previous 0.8 was reached from initial 1.0 via 1/1.25. And now +420... the sign correlation: earlier delta -240 → zoom out (0.8). Now delta +420 → zoom in. So mapping: negative delta → out? That's odd but deltaY interpretation. Actually there may have been multiple wheel events. Anyway zooming in increased iterations from 224 back to 250. Good—iterations scale with depth.

Now I need to verify that while zooming into a boundary point, the point under cursor stays near cursor and detail is rendered. The wheel centered at (300,300) both times, so the fixed point is being held. Let me zoom in more to increase iterations significantly and confirm detail. Let me do several more scrolls to zoom in deep, then check iterations high and center.

Let me do a couple more large deltas to zoom in substantially.

Now zoom ×1.2, iters 280 (still zooming in, center changed to near a boundary at -0.956, -0.224). Let me continue zooming in significantly to get more iterations.

delta must be <= 1600. The oversized deltas were rejected. So I'm stuck at ×1.2. Let me do repeated 1600 scrolls to zoom in deep. Let me chain several 1600 scrolls. Each 1600 delta scroll seems to produce one factor-1.25(ish) zoom? Earlier delta 840 gave zoom ×1.2. So scaling: roughly each scroll step is per-event, and the total delta may be split into events. delta 840 → single event factor. Let me just do many 1600 scrolls and check.

Let me do a series.

Excellent! Each scroll zooms in ×1.25, iterations grow: 313→349→391→437→488→546. So the iteration formula scales correctly with zoom depth. The rendering recomputes each navigation (fractal recomputed, not scaled image). The center is tracking along a boundary region.

Now let me verify zoom-in centered on cursor keeps point under cursor fixed. The scroll dispatches at a fixed point (300,300 presumably), and the center shifts accordingly while the point under the cursor remains the same complex point. I verified the center changes during zoom which means it's staying anchored.

Let me now verify the point-under-cursor invariance numerically. I can compute: the complex point at the scroll position before and after. But I don't know exact scroll position. Instead let me trust the math. The wheel handler correctly keeps pt fixed.

Let me now do one more important verification — that a recognizable boundary point stays near the cursor while zooming. Since each scroll is centered at the same pixel location (the default position), the complex point at that pixel remains constant across zooms. That's exactly the requirement. So comparing successive states is the check.

Let me verify by checking that recomputing: at scroll position p, complex coordinate should be same before/after. I have before zoom 1.2 center (-0.956, -0.224), width 2.688, scale = width/1200 = 0.00224. After zoom 1.6: center (-1.2248,-0.4032), width 2.15, scale 0.001792. 

Let me find pixel p such that complex value is equal:
Before: re = -0.956 + (px-600)*0.00224 ; im = -0.224 + (py-400)*0.00224
After: re = -1.2248 + (px-600)*0.001792 ; im = -0.4032 + (py-400)*0.001792

Set equal:
-0.956 + (px-600)*0.00224 = -1.2248 + (px-600)*0.001792
=> (px-600)*(0.00224-0.001792) = -1.2248+0.956 = -0.2688
=> (px-600)*0.000448 = -0.2688
=> px-600 = -600
=> px=0.

Hmm px=0. That's a weird location (left edge). im:
-0.224 + (py-400)*0.00224 = -0.4032 + (py-400)*0.001792
=> (py-400)*0.000448 = -0.4032+0.224 = -0.1792
=> py-400 = -400
=> py=0.

So the fixed zoom point is (0,0). Interesting — the browser's scroll default position must be (0,0) (top-left). So it zoomed anchored at pixel (0,0). At (0,0): before re = -0.956 + (-600)*0.00224 = -0.956-1.344 = -2.3. After re=-1.2248 + (-600)*0.001792 = -1.2248-1.0752=-2.3. ✓ Same. im before: -0.224 + (-400)*0.00224 = -0.224-0.896=-1.12; after: -0.4032 + (-400)*0.001792 = -0.4032-0.7168=-1.12. ✓ 

So the zoom point under the cursor is held perfectly fixed across zooms. The requirement "stays near the cursor while additional detail is rendered" is verified. And iterations increased (313→546), confirming recomputation of new detail rather than image scaling.

Now let me test Reset returns to initial framing from a deep zoom. And confirm wheel doesn't scroll page (page has overflow hidden, can't scroll anyway).

Let me click reset.

Reset restored initial framing (center -0.62, 0; width 3.36; zoom ×1.0; iters 250). 

Let me verify the responsiveness / async rendering works and check the initial cardioid renders. Let me reset once more and take a screenshot to actually see the fractal. The screenshot tool returns images field empty ("model does not support images"). So I can't visually confirm, but the DOM shows render is "Done".

Let me verify the cardioid is present by checking. I can't see the image. But the render completed without errors, and math is standard.

Let me also double check the inside-set color distinct and palette. Those are set.

One thing to verify: keyboard 'r' reset. And that wheel prevents page scroll — page is overflow:hidden so it can't scroll anyway, and I call e.preventDefault().

Let me take a screenshot for the record and confirm no console errors.

Actually the browser screenshot doesn't support images in this model. Let me rely on DOM.

Let me do a final review of the file for any remaining issues. Let me re-read the relevant parts.

Let me verify the wheel handler position computation uses clientX relative to rect - since canvas is at 0,0 full screen, rect.left=0. Fine.

One concern: during drag I call scheduleRender on every mousemove, which spawns many renders that get superseded by token. That's fine but could be noisy; acceptable.

Also renderScale downscales for big screens >1.4M pixels. At 1200x800 default (probably rendered at some size), renderScale=1. Fine.

Let me confirm screenshots work to visually check. Let me take a screenshot and reset.

Let me do a quick final screenshot after reset.

The screenshot tool can't display images in this model, but render is "Done" with no errors, and I've verified all interactive behavior via the countdown.

Let me do a final syntactic check of the file by reading the whole thing quickly to ensure cleanliness and no leftover dead code.

There's a leftover unused line: `var buf = new Float64Array(w * 2); // working row buffer (real, imag pairs not needed)` which is never used. Let me remove it for cleanliness.

Everything works. The only console message is the harmless iframe sandbox warning (from the harness, not my code). No errors. index.html exists and is self-contained (no external refs confirmed).

Let me confirm the final file exists and I'm done. The verification:
- Initial render with complete cardioid framing (center -0.62, width 3.36 covering cardioid+bulbs)
- Pan drag works (center shifted)
- Reset restores initial bounds exactly
- Wheel zoom-in centered on cursor keeps complex point fixed (verified numerically: fixed point invariant across zooms)
- Iterations scale with depth (250→546) proving recomputation of new detail, not image scaling
- Rendering is async/chunked; status shows "Rendering…" then "Done"
- Wheel handler calls preventDefault so no page scroll (page also overflow:hidden)

Unverified: visual appearance (browser image display unsupported in this session), and exact zoom-out behavior / keyboard 'r'. But zoom-out logic mirrors zoom-in and is symmetric; keyboard handler uses same resetView function tested via button.

I'm confident. Done.