Fractals

A WebAssembly accelerated online viewer for the Julia and Mandelbrot Sets

362 words • 3 mins

The Mandelbrot Set
Image of the Mandelbrot Set

Algebraic fractals, like those of the Julia and the Mandelbrot Sets, are rich with interesting textures and designs. They are mathematical curiosities: out of such simple equations arises great complexity and beauty.

Demo

Link to the demo of the WebAssembly-accelerated fractal viewer.

Key features

  • Progressive Refinement - The viewer starts with a pixelated image and iteratively increases the resolution of the output. This UX consideration gives the user immediate feedback
  • Gesture support - Uses touch APIs to support pinching in and out to zoom and dragging to move the image around
  • Adaptive throttling - adapts to your computer’s hardware and/or workload to maintain responsiveness while rendering as many pixels as it can
  • Performance - Key code is run on WebAssembly for better performance, plus optimizations to escape iterations early to avoid doing unnecessary work

Limitations

  • Arbitrary precision arithmetic is not yet supported

Controls

  • Mouse
    • Scroll with your mouse in order to zoom in and out
    • Click and drag to pan around
  • Touch
    • Use pinch gestures to zoom in and out
    • Touch and drag to pan around

Coordinates of interest in the Mandelbrot set

  • x: -0.761574 y: -0.0847596 zoom: 0.0000192
  • x: -1.04180483110546 y: 0.346342664848392 zoom: 0.008
  • x: -0.751095959125087 y: -0.116817186889238 zoom: 0.009
  • x: -0.812223315621338 y: -0.185453926110785 zoom: 0.0008
  • x: -0.5659231995767843 y: 0.6389989720095453 zoom: 0.000194

Example images

View images
Image of the Mandelbrot Set
A close up of a minibrot (a tiny version of the Mandelbrot set)
Image of the Mandelbrot Set
A close up of a minibrot embedded inside of white snowflake-like patterns
Image of the Mandelbrot Set
A series of spirals that look like galaxies surrounds a minibrot
Image of the Mandelbrot Set
A far away look at a minibrot surrounded by intricate patterns of white, yellow, and blue
Image of the Mandelbrot Set
A minibrot is surrounding by four spikes in an interesting configuration
Image of the Mandelbrot Set
A minibrot is surrounded by white intricate patterns
Image of the Mandelbrot Set
A minibrot with many spikes coming out of it
Image of the Mandelbrot Set
A bunch of minibrots are shown near white intricate swirls and line patterns
Image of the Mandelbrot Set
A minibrot is shown at the center of a very geometric, gem-like orange background
Image of the Mandelbrot Set
A minibrot is shown at the center of a white intricate pattern of swirls that, in aggregate, looks like a snowflake
Image of the Mandelbrot Set
A close up of a minibrot surrounded by a white intricate pattern against a dark blue background
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