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The Colours of Infinity (1995)
This is the very best explanation of fractals ever presented
"Colors of Infinity" is the very best explanation of fractals in general and the Mandelbrot set in particular ever presented. Arthur C. Clarke's soft-spoken style sets the "common man" at ease, and his pinpoint commentary makes the concept of fractals easy to understand. One need not be a stellar mathematician to grasp the concepts and why they are profound. The experts are trotted out, and they, too, explain fractal geometry in ways that are accessible to everyman.
Fractals are part of our lives, and math informs everything that exists, whether natural or man-made. When I saw this on TV several years ago, it reminded me of the Douglas Adams (of "Hitchhiker's Guide" fame) book "Dirk Gently's Holistic Detective Agency." In the novel, a software engineer tries to create a program that sets the flapping of a bird's wings to music using mathematical equations. That is exactly what fractals seem to do; they describe events in nature in mathematical ways, and the section of "Colors" which discusses this is eye-opening.
Whether you think you would be interested or not, give this show a viewing. You will be glad you did.