Taxonomy of plane-filling curves

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





  E(2,0) norm 4 family

This family corresponds to an Eisenstein integer with norm 4. Since it is a prime, all generator segments have a length of 1.



name:
reference: The Family Tree of Fractal Curves
comment: Ambiguously plane-filling (locally)
name:
reference: The Family Tree of Fractal Curves
comment: Ambiguously plane-filling (locally)



name: Splotch
reference: Brainfilling Curves
comment: self-contacting boundary
name: 4-Dragon
reference: Brainfilling Curves
comment: self-contacting boundary



name:
reference: Brainfilling Curves
comment:
name:
reference: Brainfilling Curves
comment:




Some curves in this family with fractal dimension < 2

name: Sierpinski Arrowhead Curve
reference: Wikipedia
comment:
name: Sierpinski Family
reference: Brainfilling Curves
comment:



























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