Taxonomy of plane-filling curves

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





E(3,0) norm 9 family

This family corresponds to an Eisenstein integer with norm 9. Since this is a power integer (3^2), it allows generators with integers having norm 3.


name: Snowflake Sweep
reference: The Fractal Geometry of Nature
comment: This is a self-avoiding curve that fills the interior of the Koch Snowflake.
name: Scroll
reference: The Family Tree of Fractal Curves
comment: This is a self-avoiding curve



name:
reference: The Family Tree of Fractal Curves
comment: self-avoiding curve
name:
reference: The Family Tree of Fractal Curves
comment: self-avoiding curve



name: Frayed Carpet
reference: Brainfilling Curves
comment: self-avoiding curve
name:
reference: Brainfilling Curves
comment:



name: Holiday Tree
reference: Brainfilling Curves
comment:
name:
reference:
comment:



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



name:
reference: The Family Tree of Fractal Curves
comment: self-avoiding curve
name: Maple
reference: Brainfilling Curves
comment: described by Julia Handl



name:
reference: fractalcurves.com
comment: self-avoiding curve
name:
reference: fractalcurves.com
comment:



name:
reference: Douglas McKenna
comment:
name:
reference: Brainfilling Curves
comment:



name:
reference: Brainfilling Curves
comment: self-avoiding curve
name:
reference: Brainfilling Curves
comment: self-avoiding curve



name:
reference: Brainfilling Curves
comment: self-avoiding curve
name:
reference: Brainfilling Curves
comment: self-avoiding curve



name:
reference: Brainfilling Curves
comment: self-avoiding curve
name:
reference: Brainfilling Curves
comment: self-avoiding curve



name:
reference: Brainfilling Curves
comment: self-avoiding curve
name:
reference: Brainfilling Curves
comment: self-avoiding curve



name:
reference: Brainfilling Curves
comment: self-avoiding curve
name:
reference: Brainfilling Curves
comment: self-avoiding curve



name:
reference: Brainfilling Curves
comment: self-avoiding curve
name:
reference: Brainfilling Curves
comment: self-avoiding curve



name:
reference: Brainfilling Curves
comment: self-avoiding curve




Some curves in this family with fractal dimension < 2



name: Koch Curve
reference: Koch Snowflake
comment:



























fractalcurves.com