Visualizing the Mandelbrot Set using WebGL

Can’t call myself a math nerd without doing this right?

Click/double-click on the canvas to zoom in/out!

Today I thought I’d work on a really quick vizualization of the mandelbrot set. It’s one of the most iconic images when it comes to showing of beautiful structures in math. The mandelbrot set is defined as follows:

\[ \{c \text{ } \forall c \in C\text{ if }F_n\text{ is bounded as } n\rightarrow \infty \} \] where \(F_{n + 1}(c) = F_n^2(c) + c\) with \(F_0(c) = 0\), \(C\) is all complex numbers.

In the program above, “divergence” of the sequence \(F\) is approximated by whether the computation for one element of the sequence ever exceeds the maximum value for a 32-bit float. That was sufficient to get the iconic mandelbrot shape.

The colors visualize how quickly the series diverges. You can see the source code for this project here:

Written on August 19, 2020