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







This family corresponds to a Gaussian integer with norm 8. Since 8 is a power of 2 (2^3), this family allows generator segments with norm 1 (2^0), norm 2 (2^1) and norm 4 (2^2).

(This list is not yet complete).
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 curve resolves to the same shape as the classic dragon curve.
name: Brainfiller

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This curve, and it's partner in the sub-family (above) has large variation in flesh density, due to the difference in generator segment lengths.
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This curve resolves to the same shape as the Dragon of Eve.
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

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:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:

comment: It is questionable as to whether this can called a plane-filling curve, since it may not be possible distinguish boundary from interior.
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 curve resolves to the same shape as the classic dragon curve.
name:

attribution: Jeffrey Ventrella

reference:

comment: This curve resolves to the same shape as the classic dragon curve.
name:

attribution: Jeffrey Ventrella

reference:

comment: This curve resolves to the same shape as the classic dragon curve.
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: This is a self-touching curve, which resolves to the shape of the dragon curve.
name: Broken Twins

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: Resembles a pair of twin dragons
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
name:

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment:
The First Nine Families



















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