Taxonomy of plane-filling curves

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





G(3,0) norm 9 family

This family corresponds to a Gaussian integer with norm 9. Since it is a prime, all generators have nine integers of norm 1.


name: Original Peano Curve
reference: The Fractal Geometry of Nature
comment: One of the oldest - by Guiseppi Peano
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reference: Brainfilling Curves
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reference: Brainfilling Curves
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reference: Brainfilling Curves
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reference: Brainfilling Curves
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reference: Brainfilling Curves
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Some curves in this family with fractal dimension < 2

name: Quadradic Koch Curve
reference: The Fractal Geometry of Nature
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