A visual experiment exploring Mandelbrot set variants generated by changing the starting value z₀ ≠ 0.
This repository contains Python scripts that investigate how the Mandelbrot set behaves when the iteration starts from different complex values z₀ instead of the usual z₀ = 0. Each script offers a different angle on this meta-structure of Mandelbrots.
Make sure you have Python 3 installed. Then install the required packages:
pip install numpy matplotlib tqdm🔹 Generates a large grid of actual mini Mandelbrot sets — one for each z₀ value.
- Each tile in the grid is a full Mandelbrot set, computed starting from a specific
z₀. - This gives an intuitive view of how the familiar shape warps, splits, or collapses as z₀ varies.
- Parameters like grid size and panel resolution are configurable.
📄 Output: meta_mandelbrot.png
🔹 Computes a single meta-level image: each pixel represents a unique z₀, and its color indicates how stable the corresponding Mandelbrot set is.
- Instead of showing each set visually, it uses a scoring method.
- The score represents the fraction of c-values in the complex plane for which the orbit remains bounded (i.e. in the Mandelbrot set).
- The result is a scalar map of "Mandelbrot stability" across the z₀-plane.
📄 Output: meta_mandelbrot_with_axes.png
🔹 Similar to
meta_mandelbrot.py, but focuses on visual clarity of how individual Mandelbrot sets differ with z₀.
- It uses a smaller number of z₀ values but much higher resolution per tile.
- Useful to closely observe how the standard Mandelbrot structure morphs as z₀ changes.
- This script is for exploratory understanding, not to generate the meta-structure.
📄 Output: meta_mandelbrot_panels.png
This project explores a kind of meta-space of Mandelbrot sets — each point in the z₀-plane gives rise to a new variant of the set. By rendering them either directly or via stability scores, we can start to understand how the structure behaves globally.
Inspired by fractals, complex dynamics, and a lot of curiosity.
If you're into fractals, complex systems, or just weird math structures — feel free to open an issue, suggest ideas, or extend the exploration. Email: modcrafter72@gmail.com