http://jrf.io/categories/math/Recent content in Math on Jeffrey R. FetzerHugo -- 0.147.0en-usTue, 12 May 2026 20:00:00 -0600http://jrf.io/posts/manimations/Tue, 12 May 2026 20:00:00 -0600http://jrf.io/posts/manimations/<p>A collection of mathematical animations built with <a href="https://www.manim.community/">Manim</a>. Each one visualizes a concept from fractal geometry or dynamical systems.</p> <h3 id="box-counting-dimension">Box-Counting Dimension</h3> <p>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:</p> $$d = \lim_{r \to 0} \frac{\log N(r)}{\log(1/r)}$$<p>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.</p>