The Mandelbrot Set is a single equation that, run through a computer millions of times, produces patterns that never stop revealing new detail no matter how far you zoom in. Arthur C. Clarke hosts this look at fractal geometry, tracing the set back to Benoit Mandelbrot's 1980 discovery, when cheap computing power finally let mathematicians see what their equations actually looked like. Clarke walks through how Mandelbrot's simple formula, repeated over and over, generates the coastlines, seahorse tails, and spiraling branches that give the set its name in popular science circles, and the film leans on then-state-of-the-art computer animation to render the zooms rather than just describing them. Mathematicians and physicists appear to explain why this geometry keeps turning up in clouds, coastlines, and blood vessels, arguing that fractals describe the natural world's irregular shapes better than Euclid's circles and lines ever could. The animation sequences, cycling through color-coded zooms into the set's boundary, are the film's real showpiece, built to demonstrate infinity as something you can watch rather than just calculate.