Tool

Dragon playground

Three dragon-curve variants. The Heighway dragon is the original paper-folding curve. The twin dragon places four copies that tile a square. The terdragon uses 60° turns instead of 90°.

Iterations: 12

L-system rules

axiom: FX
rules:
  X → X + Y F +
  Y → − F X − Y
angle: 90°

turtle:
  F           step forward
  +           turn right 90°
  −           turn left 90°

Hausdorff dim: 2  (boundary ≈ 1.5236)

Heighway is space-filling (dim 2), boundary fractal dim ≈ 1.5236. Twin dragon tiles the plane (four rotations form a square). Terdragon uses 60° turns instead of 90°.

Background at /fractals/dragon-curve.

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