Manimations: Animated Math with Manim
A collection of mathematical animations built with Manim. Each one visualizes a concept from fractal geometry or dynamical systems. Box-Counting Dimension Estimates the fractal dimension of a binary image by overlaying grids at progressively finer scales and counting how many cells contain structure. The box-counting dimension is the slope of the log-log regression: $$d = \lim_{r \to 0} \frac{\log N(r)}{\log(1/r)}$$where $N(r)$ is the number of boxes of size $r$ that intersect the fractal. The animation sweeps through grid sizes from 4 to 128, plotting each $(log(1/r),\ \log N(r))$ point in real time and fitting the line at the end. ...