Taxonomy of plane-filling curves

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





G(2,1) norm 5 family

This family corresponds to a Gaussian integer with norm 5. Since it is a prime, all generator segments have length 1.



name: Quartet
reference: The Fractal Geometry of Nature
comment: This is a self-avoiding curve. Mandelbrot claims to have designed it, but it was found previously by Doug McKenna, and possibly Alan Fry. A closed-loop variation was discoverd by Bill Gosper
name: 5-Dragon
reference: Brainfilling Curves
comment:



name:
reference: Brainfilling Curves
comment: This is a self-avoiding curve
name:
reference: Brainfilling Curves
comment:



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



name:
reference: Brainfilling Curves
comment: This is a self-avoiding curve



























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