Taxonomy of plane-filling curves

The Family Tree of Fractal Curves
(a taxonomy of plane-filling curves using complex integer lattices)





E(3,1) norm 7 family

This is a prime family (Eisenstein prime). The integers (line segments) in each generator have norm 1 (length 1). Only a few of the curves in this family are included here.


name: Gosper Curve ("flowsnake")
reference: Wikipedia
comment: This is a self-avoiding curve
name: Gosper Dragon
reference: The Family Tree of Fractal Curves
comment: This is a self-avoiding curve, with Gosper skin



name: 7-Dragon
reference: The Family Tree of Fractal Curves
comment: palindrome (point symmetry); Gosper skin
name: Gosper Hook
reference: The Family Tree of Fractal Curves
comment: Gosper skin



name:
reference: The Family Tree of Fractal Curves
comment:
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reference: Brainfilling Curves
comment:



name:
reference: Brainfilling Curves
comment: Gosper skin
name:
reference: Brainfilling Curves
comment: Gosper skin



name:
reference: Brainfilling Curves
comment: Gosper skin
name: Headless Gosper Dragon
reference: Brainfilling Curves
comment: This is a self-avoiding curve, with Gosper skin



name: Ventrella's Curve
reference: Planefilling Curves on all Uniform Grids
comment: described by Jorg Arndt
name: V-Curve flipped
reference: Brainfilling Curves
comment:



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