Interactive Lab / The Koch Snowflake

Iterated Function System Discovered 1904 Dimension log 4 / log 3 ≈ 1.262

The Koch Snowflake

F→F−F++F−F,angle 60∘F \to F{-}F{+}{+}F{-}F, \qquad \text{angle } 60^\circ
★Cool Fact
The Koch curve is continuous everywhere but has no well-defined tangent anywhere — at every scale it turns another corner. Its perimeter is infinite, but it encloses a finite area. It’s also secretly an L-system — this page’s drawing is generated by one, axiom F, rule F → F−F++F−F.

Rendering…

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