This script generates a Tkinter GUI to preview and render Julia set fractals. Quadratic Julia sets are generated by the expression $z_{n+1} = z_{n}^{2} +c$ where c is a constant.

Sets whose value of c lies within the Mandlebrot set remain connected and are called Fatou sets, and other values of c form disconnected, interesting fractal patterns called Cantor sets or Fatou dust.

Outputs from various presets in v1.1 native

Changes

This was my first attempt at creating a packaged GUI for any of my projects, and it made me realize how slow creating a desktop executable is. Additionally, the fractal rendering system currently uses nested for-loops to generate the fractal, which is slow and resistant to changes in window size or zoom. Finding a way to utilize iterative vectorized functions and filter() would dramatically reduce the rendering time which would allow for a dynamic window size or zoom level.

Additionally I’d like to add:

• A save dialog to root window
• A label option on output .png for denoting what c-value is used
• Mandlebrot set compatability
• Julia set z-power setting (quadratic, cubic, ect.)

As well as eventually turn the executable into a webapp, although I’d need to learn JavaScript first.