This repository contains my personal collection of Python scripts for generating and visualizing fractals. Fractals are fascinating mathematical structures that exhibit self-similarity at different scales.
Mandelbrot fractals showcase the iterative behavior of complex numbers within a specific mathematical formula known as the Mandelbrot set. As points in the complex plane undergo repeated evaluation, the fractals unveil intricate, self-replicating patterns. Notably, these patterns exhibit a fascinating blend of chaotic and orderly regions, with intricate structures manifesting at various levels of zoom.
"It's a butt" - Maria
source: https://en.wikipedia.org/wiki/Mandelbrot_set
The Buddhabrot is a visualization technique used in the field of fractal art, particularly associated with the Mandelbrot set. The Mandelbrot set is a set of complex numbers defined by iterating a simple mathematical formula. The Buddhabrot technique is a way of rendering the orbits of points in the complex plane that escape the set.
"It's a woman sitting on a chair" - Maria
source: https://en.wikipedia.org/wiki/Buddhabrot
Newton fractals are a type of fractal generated through iterative processes applied to complex equations. These fractals illustrate the roots or solutions of equations by examining the convergence or divergence of points under iteration. Each color or shade in the fractal corresponds to the root that a particular point converges towards.
"It's the Duolingo owl" - Maria
source: https://en.wikipedia.org/wiki/Newton_fractal
Lyapunov fractals are generated through the analysis of chaotic behavior in iterated mathematical functions. The fractals depict the stability of trajectories by computing Lyapunov exponents, representing the rate of divergence or convergence of nearby points. Lyapunov fractals are generated by the script using Numba with CUDA, allowing for efficient parallel computation of Lyapunov exponents.
"It's a ship on fire" - Maria
"It's just fire" - Maria
"It's a bug" - Maria
"It's NSFW" - Maria
source: https://en.wikipedia.org/wiki/Lyapunov_fractal
A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems. The dragon curve is probably most commonly thought of as the shape that is generated from repeatedly folding a strip of paper in half, although there are other curves that are called dragon curves that are generated differently.
"It's a gym bro flexing" - Maria
source: https://en.wikipedia.org/wiki/Dragon_curve
To run the fractal scripts, you'll need to have Python installed on your machine. Additionally, you might want to install any dependencies specific to certain scripts. You can install the required dependencies using the following command:
pip install -r requirements.txt
Each fractal script is located in its own directory and may have its own set of parameters. You can run a script using the following command:
python script_name.py
This project is licensed under the MIT License - see the LICENSE file for details.