# Peano Curve Explorer

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Many plane-filling curves can be created by beginning with a seed shape—in this case, an S-shaped curve—and rotating or reflecting copies of the seed shape in a 3×3 grid in such a way that the end point of one copy is adjacent to the start point of the next copy. Connecting the figures and repeating the process indefinitely results in a plane-filling curve.

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Contributed by: Robert Dickau (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: every curve begins (iteration 0) with the S-shaped starting shape

Snapshot 2: any curve indexed by a power of 2 flips only a single copy of the shape; in this case, curve 16 flips only the center copy in the 3×3 grid

Snapshot 3: a greater iteration level for an index that is a power of 2 shows the effect of the flip on the smaller copies as well as the overall figure

## Permanent Citation

"Peano Curve Explorer"

http://demonstrations.wolfram.com/PeanoCurveExplorer/

Wolfram Demonstrations Project

Published: March 7 2011