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







This family corresponds to an Eisenstein integer with norm 7. Since it is a prime, all generator segments have a length of 1.

Many of the curves in this family have a "Gosper skin". The Gosper curve fills an area whose boundary has a particular fractal profile, which remains the same at all scales. Although these curves are clearly different in terms of gross anatomy, a particular set of them have identical skin, when viewed up-close.


(This list is not yet complete).
name: Gosper Curve

attribution: William Gosper

reference:Wikipedia

comment: This is a self-avoiding curve.
name: Inner-flip Gosper Curve

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: Same as Gosper Curve except that each segment is flipped in x.
name: 7-Dragon

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name: Alternate-Sweep 7-Dragon

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This curve has an alternate path for sweeping the interior of the 7-Dragon
name: Hook Dragon

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: Swan

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:

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

also:Dmitry Mekhontsev and Christoph Bandt

reference:IFStile

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
The First Nine Families



















fractalcurves.com