"Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature.
A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity.
Fractals: they're famously found in nature and artists have created some incredible renderings as well. Fractals are purely a wonder -- too irregular for Euclidean geometry; iterative and recursive and seemingly infinite. They turn up in food and germs, plants and animals, mountains and water and sky."
I discovered computer fractal design in 1996, some 18 years ago, and have been joyfully playing with the creation of fractal design since that time. The first software program which I used was the venerable Ultrafractal and have used other programs since that time including Mandelbulb3d.
Fractals - Hunting the Hidden Dimension [PBS Nova]