Box counting in Cython
A Cython extension that estimates the fractal dimension of a point set by counting occupied cells, without building the whole grid. I wrote it on my own in one month, between November and December 2022.
Stack: Python, Cython, C, NumPy, SciPy, Matplotlib.
The problem
To measure the dimension of an attractor with box counting you count how many cells of side ε contain at least one point. With many points or many dimensions the full grid takes too much memory. I used a tree that branches only where there are points.
How it works
- 01
The tree
A recursive N-ary tree written in C inside Cython: each level halves the cell side and only occupied branches are created. The tree memory is freed by hand with free().
- 02
The fit
occupation counts the cells at each level; fit_show does the linear fit with SciPy and shows the plots.
- 03
Tests
On the Hénon and Lorenz attractors, with figures saved in the repository.
What I did
All the code, 19 commits, about 530 lines of Cython and Python.
Limits
One-line README, no documentation, test scripts run by hand. I did not measure how much faster it is than a grid, so I claim nothing.