All Plane-filling Curves (using edge-replacement)
by Jeffrey Ventrella







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

(This list is not yet complete).
name: Snowflake Sweep

attribution: Benoit Mandelbrot

reference:The Fractal Geometry of Nature

comment: This is a self-avoiding curve that fills the interior of the Koch Snowflake.
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: Fills the same shape as the ter-dragon
name: Scroll Curve

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name: Maple Leaf

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-avoiding curve.
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment: This is a self-avoiding curve.


Curves in this family with dimension < 2
name: Koch Curve

attribution: Helge von Koch

reference:Wikipedia

comment:


The First Nine Families



















fractalcurves.com