“You certainly know fractals, the most famous of which is the Mandelbrot set.
Here is a program to play with on ESP32. I chose the ESP32 because I think it will do the calculations faster than a standard Arduino (higher clock frequency: 240 MHz): about a second to a second and a half for calculation and display.
The code displays on a 480 x 320 TFT touch screen. It calculates Mandelbrot and Julia sets for several parameter values, and allows you to zoom in on areas of interest to see the fractal aspect (i.e. the presence of the same structures at each scale change). The zoom level is limited due to the limited accuracy of the calculations, but a half a dozen zooms can be made before the image degrades.
Get ready to explore the magic world of fractals…”