Mandelbrot explorer · kimi-k3.1-pro

I need build index.html self-contained full-screen Mandelbrot explorer. Should have actual functionality quality. Should use tools. Should inspect cwd.

Should implement robust performant responsive rendering. Fullscreen canvas, controls overlay nice design. Should have initial full cardioid and lobes e.g center -0.55,0 width 3.35 at aspect 1.5 height 2.23, actual viewport 1200x800. Full set x [-2.25,1.15] y [-1.117,1.117]. Great.

Rendering: progressive chunked, avoid blocking. Could use tile bands via requestAnimationFrame/setTimeout. High DPR but cap at perhaps 1.5 and adaptive max pixels 1.5m. Should have actual canvas 2d compute per pixel JS. Iterations increasing based zoom base 120 up to 1500 perhaps. Progressive passes coarse preview 4x then 2x then full resolution recompute actual not static scaling. Requirement recompute after navigation rather than static image. Can have render scheduler progressive tile imageData. Each pass recompute. Could optimize using typed arrays, escape smoothing log(log|z|)/log2. Use periodicity? basic optimized. Should have controls responsive during render. requestIdleCallback? requestAnimationFrame each row chunk with time budget ~10ms. Should handle events invalidate token. Full resolution might take at 1200*800 * 150 ~144m operations could be 300ms-1sec chunking. I can progressive rendering coarse pixel resolution 4,2,1, each true recompute. Draw preview tiles as rectangles or imageData scaled. Requirement not scaling static image means okay progressive compute but no scaling old. I can create offscreen ImageData per pass and putImageData? Should progressive visible. Simplest offscreen document.createElement canvas internal equal display resolution? draw pass at coarse resolution with putImageData onto main scaled could be interpreted static scaling but it's progressive computed image each pass. Fine. Better direct fillRect coarse cells, then final pixel ImageData per horizontal rows. On navigation clear, render coarse blocks immediately (4 or 6 css px), then refine full image. No scaling static old. Canvas internal render dims capped DPR, fillRect size mapping.

Use pointer drag. Should pointer capture. On pointerdown start, set dragging, pause rendering? Render cancellation. pointermove update view center by delta complex. Can pan live with canvas transform to feedback (static scaling transient) then recompute after pointerup. Requirement recompute after nav. Better translate displayed previous canvas during drag and restart progressive render after 80ms/once pointerup. I can draw current canvas itself shifted via offscreen snapshot. Should avoidputImageData. Could maintain offscreen last canvas as display. On pan each move, update center and render scheduling perhaps progressive. Simpler update view and schedule render after 70ms debounce; during dragging transform main canvas style translate? But style full-screen causes background; no. Could have persistent canvas source and drawImage(source, dx,dy) every move; source holds last render. Then schedule new. Main visible updates. On render start copy? Should source managed after each pass. Alternative main canvas displayed, pointer drag: get snapshot on pointerdown to offscreen, each pointermove clear and drawImage(snapshot, dx*dpr,...), update center. On pointerup schedule compute fresh. Fine. Wheel: prevent default {passive:false}, zoom factor exp(-deltaY*0.0015) clamp; center cursor invariant:
mouse complex before = center + ((x - width/2)/width)*span etc. scale span*=factor; newCenter=before - normalized * newSpan. schedule immediately cancel and progressive. Cursor stays exact. update overlays coordinates readout perhaps. Reset restores. Keyboard + -, R perhaps accessibility. Add help. Full screen no scroll.

Should color smooth gradient visually appealing. Palette based t = smooth iteration; use cosine palette. Inside near black #070b14. Smooth escape coloring: if escape iter < max and finite zn, logZn = log(zx^2+zy^2)/2, nu = log(logZn / log2)/log2? Standard nu = i +1 - log(log|z|)/log2. logAbs = .5 log(z2); nu = i+1 - log(logAbs)/ln2. Then color via t = (nu perhaps plus offset) / something. Use cyclic palette and avoid aliasing. Could use multi stops with interpolated smooth gradient. Procedural cosine:
t = 0.015*nu + perhaps zoom offset; color = 0.5+0.5 cos(2π(t + offsets)). Standard can produce nice. Should have full main black. Better mapping noncyclic gradient with smooth interpolation from deep navy to cyan/gold/ivory; sqrt or log. Color based s = log(1+nu)/log(1+maxIter)? At initial most escape low -> low colors, boundary high. use palette periodic with fractional nu and smooth. E.g const v = Math.log(nu+1)*0.65; r=... Could be bland.

Use lookup LUT of 2048 based iteration but max changes; color based log1p(nu)*0.55 and cosine. Since max increasing reveals detail. At initial render iterations dynamic 180. For outside very fast nu 2 etc t .6. Colors. Known palette: r=0.5+0.5*cos(3 + t*0.15 + 0), etc using t nu (not normalized), leads cycles. Use t = Math.log2(nu+1)*0.85; cosine. Inside #05070d. t low around 1.3. Choose phases resulting nice. Could manually color stops based u = (log(nu+1)/log(maxIter+1))^(0.35) then gradient; would zoom-dependent color, fine. Most outside low u. Palette [0:#08101f,0.18:#172c63,0.38:#126e82,0.58:#29c5b5,0.74:#f4d35e,0.88:#ee6c4d,1:#fff4d6]. But boundary max points appear white. At deep max dynamic yields consistent relative. Smooth escape. Should efficient LUT per render of perhaps maxIter+2? Smooth nu indexing by floor perhaps LUT 1024 from u continuous. Precompute 1024. Compute t = pow(log1p(nu)/log1p(iter),0.35), costly pow per escaped pixel. Could t = Math.log(nu+1) * (0.9 / Math.log(iter+1)), then t = Math.sqrt(t) or no. pow perhaps okay but optimize sqrt. Color LUT index floor(t*1023). Smooth coloring still discrete 1024 effectively smooth. Palette. Perhaps log mapping ensures low escapers not all same. At initial outside near 2, iter 180 log 3/log181=.21 sqrt .46 gives teal; huge area teal. Alternative u= Math.log(nu+1)/Math.log(max+1) then *1.7 clamp. at nu2 ->.2*1.7=.34 blue. boundary nu20 ->.58*1.7=.99 light. Good. max dynamic. Fine.

Could use direct RGB formula and LUT based normalized smooth value. Should distinct inside.

Iterations based zoom = initialSpan/viewSpan. base 160; max = min(2000, floor(160 + 90*log2(zoom))) perhaps at 1x 160, 16x 520, 1000x 1056. "sufficient iterations" good. For coarse pass can use same iterations or lower? Same sufficient ensures detail. Progress info status "Rendering · 160 iterations" and progress bar. Controls Reset, zoom out/in perhaps. Display scale and iteration. Fullscreen canvas. Nice UI. Add coordinate cursor tooltip? footer top right. Should have no external fonts. Responsive.

Rendering design in detail:

State:
const canvas, ctx = canvas.getContext('2d',{alpha:false});
let width,height,dpr, renderW,H
view={cx:-0.6,cy:0,span:3.4}; span is width in complex, vertical span = span*height/width.
initial constant center perhaps -0.58? full x center -0.55. span 3.45.
pointer interactions use CSS coords but normalization same.

resize: set canvas width=round(innerWidth*dpr), height, style sizes. DPR cap = min(devicePixelRatio,1.75, sqrt(2_000_000/(w*h)))? Lower bound 1? If huge 4k can dpr<1 fine perhaps. Keep canvas CSS full. ctx no smoothing.
If old view preserve center & span. snapshot invalid. schedule render.

render generation:
let job=null; let raf=0;
function requestRender(immediate=false) {
 if(job) job.cancelled=true; job=null;
 cancel scheduled;
 clearTimeout...
 const id=++renderId;
 status rendering...
 schedule start via setTimeout(..., immediate?0:45)
}
Should handle if pan uses snapshot and render not until up. `cancelRender()` increments generation cancels rAF/timeouts.

Job algorithm progressive passes. Passes block sizes [6,2,1] in device pixels? On DPR, use 6*dpr coarse ~4 css. Full pixel expensive. Could [4,1] enough. First at max(4, floor(dpr*4)) pixel blocks, second full. Optional [8,3,1] progressive. Initial 3 passes compute costs: coarse 1/64 + 1/9 + full = overhead 12%. Good. Render passes with ImageData per pass at ceil(W/block) dims and putImageData to scratch then drawImage scaled. But requirement no static scaling refers navigation not progressive. Yet avoid confusion by fillRect each coarse cell, final imageData. FillRect per coarse cell perhaps 30k calls at initial. Fine. Pass 1 block=8, pass2=3, pass3=1. For coarse each pixel fillRect x,y,b,b. Full pass render row chunk with ImageData of W x rows, putImageData at 0,y. Use ctx.fillStyle each pixel expensive ~W*H/block^2 30k okay. Could use single ImageData W*H and put portions? Should progressive display. allocate full ImageData once final, fill row chunk then `ctx.putImageData(image,0,0,0,y,W,rows)` dirty rectangle, correct (source coordinates? putImageData(imageData, dx,dy, dirtyX,dirtyY,dirtyWidth,dirtyHeight)). Yes. Job state data = ctx.createImageData(W,H), fill final rows; each chunk putImageData(image,0,0,0,y,W,end-y). Nice. For coarse pass could ImageData small and use temporary canvas then draw scaled but fillRect easier.

Time chunk scheduler:
function work(job, deadline?) {
 const start=performance.now();
 if pass coarse:
 while y<H and time<10:
   for x blocks compute...
   y+=block
 ctx fill each cell as compute; fillStyle call each. Could optimize group? okay.
 if complete pass advance to next, y=0, schedule next rAF.
 final:
 create imageData. while y<H && time<12: compute row; after loop put dirty rows.
 progress based passIndex/(n) + etc. final contributes 85%.
 rAF(work) continuous. `requestAnimationFrame` callback work with time 12ms leaves responsive. Each rAF max ~60fps.
 compute pixel function inline for perf. Function sample(px,py) returns RGB perhaps object bad. For coarse use color index to CSS from LUT? Could `sample` return integer packed 0xRRGGBB then fill style `#...` expensive. Could store palette css array and inside. For final write data directly. Duplicate loops coarse and final via a generic render block returning integer color; `(r<<16)|(g<<8)|b`; final extract. LUT array of ints. Color index calc. Inside constant int.

Coordinate pixel mapping: xmin=cx-span/2, ymax=cy+vspan/2. re = xmin+(x+block/2)/W*span for coarse. final use (x+0.5)/W. im = ymax-(y+0.5)/H*vspan.

Optimization cardioid and bulb interior test before iterations:
q=(x-0.25)^2+y^2; if q*(q+(x-0.25)) <=0.25*y^2 or (x+1)^2+y^2<=0.0625 inside. This treats known analytic interior regardless iteration. Fine.
Escape loop:
let zx=0,zy=0,zx2=0,zy2=0,i=0;
while(zx2+zy2<=256 && i<maxIter){ zy=2*zx*zy+ci; zx=zx2-zy2+cr; zx2=zx*zx; zy2=zy*zy; i++; }
if i>= maxIter inside. Use bailout 256 smooth.
Smooth nu = i + 1 - Math.log(Math.log(Math.sqrt(zx2+zy2)))/LN2 = i+1 - Math.log(0.5*Math.log(mag2))/LN2. clamp >=0.
Color from LUT with u = Math.min(0.999, Math.log1p(nu)*colorScale), colorScale=1.65/Math.log1p(maxIter), perhaps sqrt? no. At i 2 max160 u .202*1.65=.333, blue. i20 u .587*1.65=.969 yellow. Great. Deep max1000 low i2 u .159*1.65=.263. fine.
LUT gradient with stops. Include 0 at almost dark. Since far outside all nu2 constant blue. Main set black. Nice.

Perhaps exterior bands too vivid. Add status overlay.

Interaction wheel:
canvas.addEventListener('wheel', e=>{e.preventDefault(); if e.ctrlKey? still zoom; const factor=Math.exp(Math.max(-?)*...). deltaMode line/page normalize. factor=Math.exp(-delta*0.0015) clamp [.2,5] per event. min span 1e-13 perhaps double coords limit around 1e-12. max 8.
const px=e.clientX/width -0.5, py=0.5-e.clientY/height;
const targetRe=cx+px*span; targetIm=cy+py*(span*height/width)
newSpan=clamp
cx=targetRe-px*newSpan; cy=targetIm-py*newSpan*height/width.
requestRender(true perhaps debounce 25)
}, {passive:false})
Zoom under cursor stable. During wheel no visual transform old image until recompute first pass within ~1 frame. fine.

Buttons zoom centered use zoomAt(w/2,h/2,factor).
Reset with animation? immediate restore. Reset button. compare initial framing exact.
Pan pointer:
on down if primary: cancel scheduled job? snapshot canvas to offscreen matching dimensions; dragging object pointer id, last coords, total; canvas.setPointerCapture; class.
on move if dragging:
dx=e.clientX-last; view.cx -= dx/width*span; view.cy += dy/height*vspan. totalDx etc. ctx clear fill bg and drawImage(snapshot,totalDx*dpr,totalDy*dpr). Exposed areas fill dark. update readout.
Perhaps schedule render only after pointerup. Responsive. On pointerup snapshot=null requestRender.
If pointer cancel likewise.
On pointer move not dragging update cursor coords and readout. Pointer leaves set coordinate em dash.
Touch single drag works; pinch not required. Wheel prevent page.
Prevent context? no.

Buttons should not propagate pointer to canvas since overlay separate. keyboard ignore if button? r/+/-; Reset. use event key and no input. `0` reset perhaps.
Status and progress with aria. Initial render info. Zoom display `1×`, at deep scientific. Coordinates use toPrecision. Small HUD bottom left perhaps controls top-left.

Should have screenshots/test. I can write file.

Should inspect bugs. Major coarse palette.indexOf per pixel O(1024) terrible. Should have sample return color and index? I can CSS map by packed int Map. Better paletteCss as object mapping packed to css and inside. `colorCss[INSIDE]='#...'`; sample palette lookup then `colorCss[color]`. Arrays as sparse huge indices perhaps array length 16m memory bad. Object paletteColorCss = Object.create(null) assign [packed]. Then use. Or sample returns index not color and final needs convert. Could make `colorToCss` object. Modify. Also resize initial oldWidth=1 oldHeight=1 triggers. good. RequestRender cancellation serial logic: cancelRender increments, serial = renderSerial, startRender checks equal. fine. start new while old work JS no simultaneous. coarse endY uses job.y+block*3 but time checked per row chunk after 3 rows, may exceed 11 slightly. okay. Final time check per row. coarse fillRect not clear old full canvas beyond eventually. okay.

Major wheel factor: delta positive => factor exp(+)= >1 zoom out correct. Cursor anchor before and view update. Fine.
Pan formula view.cy += stepY * view.span * cssHeight / cssWidth / cssHeight = stepY*view.span/cssWidth correct vertical. Fine.
Reset active drag? reset button impossible while capture but keyboard during drag can weird, not important.
Colors smooth but `palette.indexOf` fix.
Potential iteration "controls responsive" chunk is good.
Could optimize coarse using packed css map.

Now run browser initial inspect screenshot console.

Looks okay initial coarse. Should wait completion browser inspect perhaps.

Initial complete. Colors perhaps too flat green but okay. Should verify wheel boundary point near cursor. Browser scroll x/y delta. Choose recognizable seahorse valley at between main cardioid and circle x around 530? Actual boundary at x530,y400 (c=-0.75). Zoom there repeated. Browser scroll tool likely at x y. Do e.g x531 y399 delta -500.

Screenshot during coarse pass shows stale previous bottom and new top; expected progressive but jarring. At completion check.

At x531,y399 in zoom view it's blank near boundary? I anchored c at (-0.7479, .0014), the neck between main and bulb; after zoom x531 at junction boundary yes x531 y399 looks thin line perhaps. Stays near cursor. Should deeper additional detail and recognizable. Repeat scroll same x531 y399 perhaps zoom around neck boundary.

Why magnification expected 1.72* exp(0.93)=4.36 but result 2.94, perhaps screenshot zoom previous not finished? Actually factor 1.71 =>2.94 yes 1.72*1.71=2.94, exp(.93)=2.53 no 620*0.0015=.93 factor2.535. Browser tool perhaps delta scaling. irrelevant.

Should test reset after pan. Use drag from 600,400 to 750,470.

After drag perhaps panned to exterior mostly because deep neck. Fine. reset click.

Reset exact. Should potential quality issue status DOM percent shows 6 vs 13 due screenshot immediate no matter.

Should deeper check at proper boundary point to verify detail. Could reset complete then choose x530 y390 perhaps. More importantly code performance coarse `colorCss` good.

Should identify any subtle bug: on wheel cursor anchored with browser event client coords relative full viewport yes. Deep detail max 2400. Requirement "smooth escape-time color gradient" yes though palette indexed normalized. Distinct inside. "complete main cardioid and surrounding lobes" yes. "keep controls responsive during rendering" rAF chunks. "Recompute after nav rather than scaling static image" yes recompute. "prevent wheel scrolling surrounding" overflow hidden and prevent. good.

Could improve initial zoom label 1.00x, reset initial exact. done.

But browser test of pointer anchor can inspect readout by moving? Browser move not available except drag/scroll perhaps type? No direct evaluate. I can test mathematically code.

Potential bug resizing vertical maintains horizontal span center same good. Device pixel ratio budget can <0.75 for 8k yields enormous >2.2m but okay.

Potential touch pinch no requirement.

Could optimize sample interior main cardioid formula uses q*(q+xq)<=0.25*ci^2 correct. period bulb correct.
Smooth formula bailout 256 yields mag2 >256, log positive. good.
Colors for very distant low iteration etc.

At max zoom span min1e-13 JS double okay near -0.55 precision 1e-16 gives ~1000 pixels only at 1e-13 enough. min. At zoom max additional wheel `actualFactor=1` no requestRender but still updateReadout not called. zoom label remains previous same, fine.

Status aria-live entire info update percent every frame could chatter screen reader; not key.

Perhaps avoid canvas rendering of old content while new starts, expected progressive. Fine.

One issue initial coarse fill style map color key numeric signed? packed up to 0xfff4d6 = 16774358 less 2^31 positive. INSIDE 329485. good.

Should test completed reset screenshot compare.

Should have final response concise report checks and unverified per instructions. Could mention file. But perhaps need additional deep detail test because claimed additional detail? I only zoom 3x not much. User specifically verify zoom recognizable boundary and stays near cursor while additional detail rendered. I did two zoom at neck 2.94x. Additional detail limited. I can zoom more repeated and inspect. Time budget 15 min plenty. Use repeated scroll same coordinate perhaps after reset anchor again. 3-4 times to 100x. Should inspect at completion.

Interesting scroll didn't trigger? DOM unchanged screenshot. Perhaps pointer coordinates readout — implies mouse wasn't over canvas? Scroll action perhaps only wheel if pointer moves but event perhaps after reset overlay? x530,400 canvas. Earlier worked. Why not? Perhaps tool result immediate before event? inspect.

Perhaps delta limit max 1600 min but scroll -700 should. Earlier -480 worked. Did click reset leave mouse over button and browser scroll x,y ignores? no. Could be browser tool weird wheel only once after click? Try move? No move. click canvas at 530 then scroll would initiate drag pointer down/up and render. Could click then scroll.

Click triggers full re-render unnecessarily but okay. scroll now.

Browser delta normalized weird -700 gives 1.72 same as -480. Fine. Now repeat at same pointer after complete.

Cursor coordinate readout remains -0.75125 exactly (it isn't updating on wheel but complexAt cursor after zoom should same by design) good. Repeat several via multi tool can't sequential dependent but same no need parallel unsafe.

Repeat perhaps c=-0.75125 lies outside neck slight, after zoom point stays at gap, good.

At x530,y400 still exact meeting thin pixel. Additional detail around boundary. Good. Could deeper 8x.

This point exactly on real axis has mostly black at 5x, not pretty. Could target a boundary with visible detail e.g initial around x760,y160 (seahorse top cardioid). Perhaps reset and zoom at upper cardioid x770 y180. Recognizable boundary and remains. I already enough. But quality at neck reveals black because connected interior. Additional boundary visible left/right. Fine.

Should I improve progressive coarse to avoid weird stale horizontal lower third? Not required but polish. On request render could clear canvas dark to avoid old region. Currently coarse overwrites whole over several chunks. Old content persists until overwritten, standard progressive but horizontal seams. Fine.

Potential performance coarse 3 rows per chunk can be long >11, because only check every 3 rows. At coarse 8 and width1200 150*3=450 samples negligible. final each row 1200*160 ~ could be 3ms. Good.

One concern "smooth escape-time color gradient" coarse screenshot jagged but final smooth. yes.

Perhaps verify actual console no errors after interactions inspect says console []. Good.

Could respond now. But need final reset to initial state? User opens app resets initial anyway. Browser state irrelevant file. No.

Perhaps I should run syntax check? Browser done.

Could mention unverified touch/high-DPI/extreme zoom. Respond with 2 bullets checks and unverified. Keep it brief.