Bill Gosperborn 1943
Flowsnake curve
American mathematician and early hacker whose flowsnake curve fills a hexagonal territory with one continuous, non-crossing line.
Gosper Curve
A single line that fills a hexagon and never crosses itself. Far away it is a texture; up close it is one continuous path you can follow end to end.
About this pattern
Bill Gosper, 1970s
The flowsnake is a Lindenmayer system on two letters, A → A-B--B+A++AA+B- and B → +A-BB--B-A++A+B, with sixty-degree turns. Each order replaces every segment with seven, so the curve grows 7ⁿ steps long while its hexagonal territory stays the same size. The boundary it encloses is itself fractal: the Gosper island.
Behind the mathematics