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Mandelbrot Set

A fractal is a mathematical set that shows the same patterns at any scale. The Mandelbrot set is one of the most popular, and it was studied by the mathematician Benoit Mandelbrot. This set is closely related with the Julia set, which shows the same shapes.

The Mandelbrot and Julia set are sets of complex numbers. These numbers have the property that if a mathematical function is iterated on them, the result remains bounded (it doesn't trend to infinity). In the frontier of these sets, geometric shapes are generated recursively at every scale.

Using the library three.js (based on WebGL) I have implemented a viewer of the Mandelbrot and Julia sets. These viewers allow the user to do zoom in the sets and see the geometric shapes in the frontier. The zoom is limited to some value because it is not possible to iterate infinitely the function on the GPU and the precision of the floating point variables have a limit.


Images


Demos

Mandelbrot Set Viewer
Viewer of the Mandelbrot Set.
Julia Set Viewer
Viewer of the Julia Set.


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