Every picture here comes from one line of math, repeated. Here's how it works, mostly in pictures.
z → z² + c
Each picture is the white box in the one before: 800,000× deeper, and new shapes keep appearing, including tiny copies of the whole set (last picture). Nobody designed them; they all come from the rule.
Fix c at one point and vary the start instead: you get a Julia set. Each ring marks a point, and the matching frame shows its Julia set. To try it, choose Julia while zoomed into a spot you like.
The bottom row isn't drawn pixel by pixel: millions of points are thrown and the picture is where they land. All of these are in the Fractal menu.
A second graphics card invents and tests new formulas around the clock: polynomials, divisions, sin/exp, formulas with memory, and Newton-style ones. The best 200 (40 of each kind) appear in the Discover tab; click one to explore it.
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