Interactive Lab / The Peano Curve

L-System Discovered 1890 Dimension log 9 / log 3 = 2

The Peano Curve

L→LFRFL−F−RFLFR+F+LFRFL,angle 90∘L \to LFRFL{-}F{-}RFLFR{+}F{+}LFRFL, \qquad \text{angle } 90^\circ
★Cool Fact
The first published space-filling curve. A 1-D line, in the limit, whose image is an entire filled 2-D square — proof that “continuous” and “one-dimensional” aren’t the same thing.

Rendering…

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