Mandelbrot Set

2023년 12월 1일

The Mandelbrot set represents a set of complex numbers with distinctive and very well known intricate geometric properties. Here I have attempted to implement it in Pinescript leveraging tables.

The defining formula for the set is:

Pine Script®

If, after a certain number of iterations, the magnitude of the complex number remains bounded (does not diverge to infinity), the point is considered part of the Mandelbrot set.

The Mandelbrot set exhibits intricate and infinitely detailed fractal patterns, characterized by self-similarity at different scales. Due to limitations in Pinescript and the number of possible table cells (Pinescript is not designed for this at all and this is merely a showcase of how flexible & great Pinescript can be it is) the resolution over this set is low.

Users can zoom in and out of the set via the provided inputs.

The values in each cell represent the number of iterations required for the corresponding point in the Mandelbrot set to escape a certain threshold.