A Tool to Explore the Mandelbrot Set

The title picture of this website was made using this high school project from back in the mid-2000s, when Delphi and Turbo Pascal were my first entry into the world of coding.

Of course, given it’s age, I would approach the codebase completely different today. Furthermore, techniques on fast processing and parallelism could make exploring this fascinating mathematical object a lot smoother; and some bugs would need to be ironed out. However, it was fun to code the algorithms and the way the user interfaces with them, and it is a fond memory to this day.

It includes a fully customizable color palette, exportable pictures and iteration data, as well as the option to “record” zoom sequences by interpolating between fully computed pictures.

What intrigued me back then was the sheer complexity generated by such a simple rule; how these intricate patterns could be generated from just the dynamics of iterating the equation f(z) = z^2 +c over the plane of complex numbers, starting with z=0. In retrospect, it is a funny coincidence that the complex numbers became a focus during my maths studies much later in life!

Below are some additional pictures that were generated using this software.