Taxonomy of plane-filling curves

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





E(2,1) norm 3 family

This family corresponds to an Eisenstein integer with norm 3. Since it is a prime, all generator integers have norm 1. There are two generator shapes in this family. Two of the curves are self-avoiding.


name: Terdragon
reference: Larry Riddle
comment: Palindrome curve (point-symmetry)
name: Inverted Terdragon
reference: fractalcurves.com
comment: Different skin than the Terdragon



name: Half-Terdragon
reference: Tom Karzes' fractal page
comment:
name: Walking Terdragon
reference: The Family Tree of Fractal Curves
comment: This is a self-avoiding curve.



name: Fractal Chair
reference:
comment: Christoph Bandt
name:
reference:
comment:



name: Avoid-3
reference: fractalcurves.com
comment: This is a self-avoiding curve.
name: Hook 3
reference: fractalcurves.com
comment:



name: Box 3
reference: The Family Tree of Fractal Curves
comment: similar to the Original Peano Curve
name: Blob 3
reference: fractalcurves.com
comment:



























fractalcurves.com