Fractal Explorer: GPU Edition

This project lets you zoom into, modify, and explore several fractal formulas in the browser. The standard renderer is fast and interactive, but it still hits floating point precision limits at relatively shallow zoom depths. An experimental deep zoom path is now wired in on top of ShaderPad and GMP-WASM.

This project is just for fun and learning. Pull requests are welcome as long as the app stays performant and fun to explore.

Features

• Julia, Mandelbrot, Burning Ship, and Mandala formulas, each at any integer exponent from 2 to 16
• Arbitrary-depth zoom via perturbation theory
• Keyboard, mouse, and touch controls
• Animated palettes, stripe-average coloring, slope shading, distance-estimate anti-aliasing
• URL hash persistence for shareable views
• PNG frame export
• Works offline as a PWA

How it works

Rendering is a two-pass pipeline: an iteration pass writes a per-pixel metric (smooth escape time, stripe value, packed visual data, coverage) to an RGBA32F framebuffer, and a display pass maps it through the palette, lighting, and an ACES tone map. Palette animation and visual toggles only re-run the cheap display pass.

Past the deep-zoom threshold the iteration pass switches to perturbation: gmp-wasm computes a high-precision reference orbit (uploaded as a texture), and the shader iterates only each pixel's tiny delta from it, carried in mantissa/exponent form so it survives any depth.

• Quadratic Mandelbrot and Julia take the fast path: Newton-on-period reference search plus hierarchical bivariate linear approximation (BLA), which skips up to 2048 iterations at a time under a rigorous validity bound.
• Burning Ship and Mandala perturb their |z| folds exactly (diffabs, correct across fold crossings); exponents above 2 use the binomial expansion of (Z + δ)ᴺ − Zᴺ. These variants use grid-sampled references and scalar perturbation, with Brent cycle detection so interior pixels exit early.
• The fractal type and exponent are baked into the generated shader source — fully unrolled, branch-free inner loops with literal coefficients. Changing either recreates the renderer (ShaderPad recreation on a shared canvas is nearly free).
• While you zoom or pan, the display pass reprojects the last finished metric frame (with bilinear color blending) and fresh iteration passes are scheduled only as the view outgrows it, so interaction stays continuous even when one iteration pass takes seconds.

Controls

Keyboard

• Z / Shift+Z: zoom in / out
• Arrow keys: pan (Shift for larger steps)
• F / E: change fractal type / exponent
• R / I: change the constant's real / imaginary component (Julia and Mandala)
• C / G: change palette / color density
• A: toggle stripe-average coloring
• N, L, K, J: slope shading toggle, light angle, height, intensity
• Q: change escape radius
• D: change render density
• S: change animation speed; Space pauses; Shift+Space reverses
• O / X: return to origin / reset everything
• Enter: export the current frame as PNG
• P: toggle the profiler overlay
• ?: show help
• Hold Shift with any stepped control above to reverse or shrink the step

Mouse / Touch

• Click / tap: set the image center
• Scroll / swipe: zoom
• Multi-finger swipe: change palette and tweak parameters

Architecture

• src/main.js — application state, URL persistence, inputs, renderer lifecycle, zoom-preview scheduling
• src/standardShader.js / src/perturbationShader.js — generators for the iteration pass (standard float and deep perturbation variants)
• src/deepDisplayShader.js — display/compositor pass
• src/shaderCommon.js — GLSL shared by all passes (metric packing, coloring math)
• src/deepZoom.js / src/gmpUtils.js — reference-orbit search and high-precision arithmetic
• src/deepZoomTables.js — BLA hierarchy and orbit prefix tables

Development

git clone git@github.com:rileyjshaw/fractal.git
cd fractal
npm install
npm run dev   # local dev server
npm test      # unit tests (perturbation math, shader structure, GMP orbits)
npm run build # production build

Built with

• ShaderPad — fullscreen WebGL2 rendering, uniforms, textures, framebuffers
• gmp-wasm — arbitrary-precision reference orbits (MPFR)
• tween.js — camera easing
• tinykeys — keyboard shortcuts
• Vite — dev server and bundling

Limitations

• Variants without BLA (Burning Ship, Mandala, and exponents above 2) run every iteration scalar, so they render slower than quadratic Mandelbrot/Julia at equal depth; per-iteration cost also grows with the exponent.
• Reference-orbit computation runs on the main thread and can take seconds at extreme depth.
• Pan/center state ultimately derives from JS doubles; true arbitrary-depth navigation needs a high-range view state.

License

GNU General Public License v3.0