L-System Discovered 1973 (Bill Gosper) Dimension log 7 / log √7 = 2

The Gosper Curve

A \to A{-}B{-}{-}B{+}A{+}{+}AA{+}B{-}, \quad B \to {+}A{-}BB{-}{-}B{-}A{+}{+}A{+}B

★Cool Fact

Also called the “flowsnake.” Like Peano and Hilbert, it’s a space-filling L-system curve with similarity dimension exactly 2 — but built on a hexagonal grid instead of a square one, giving it a completely different silhouette from either.

iterations 3

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Read the full chapter on L-Systems: a Grammar for Growth →