Taxonomy of plane-filling curves

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





G(2,0) norm 4 family

This family corresponds to a Gaussian integer with norm 4. Since it is a power of 2, some of its curves have similarities with the 2 family (the classic dragon curve and the Polya Sweep). Generators in this family can have integers with norm 2 as well as with norm 1.



name: Peano Sweep
reference: The Fractal Geometry of Nature
comment: (This curve has overlapping segments)
name: Dragon of Eve
reference: Brainfilling Curves
comment: This is a self-avoiding curve



name: Carbajo curve
reference: Victor Carbajo
comment: self-avoiding curve
name: Tile Curve
reference: Brainfilling Curves
comment:



name: V1 Dragon
reference: Brainfilling Curves
comment: This curve has interesting similarities to the classic dragon curve
name: Textured Dragon
reference:
comment: same overall body shape as the classic dragon curve



name: Triangle 4
reference: Brainfilling Curves
comment:
name: City 4
reference:
comment:



name: Box 4
reference: Brainfilling Curves
comment: This curve has similarities to the Peano Sweep
name: Tossed City
reference:
comment:



name: Cesaro Sweep
reference: The Fractal Geometry of Nature
comment:



























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