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







This family corresponds to a Gaussian integer with norm 4. Since it is a power of 2, some of its species have similarities with the 2 family (the classic dragon curve and the Polya Sweep).
name: V1 Dragon

Skin: 2G1 (Dragon Skin)

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: Similar to the classic Dragon curve, but different
name:

Skin: straight

attribution: Victor Carbajo

reference:Carbajo examples

comment: This is a self-avoiding curve
name: Textured Dragon

Skin: 2G1 (Dragon Skin)

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: Fills the same shape as the classic dragon
name:

Skin: straight

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: fractal dimension of boundary = 1
name: Cityscape Curve

Skin: 4G2 (Cityscape Skin)

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: ambiguous fractal dimension of boundary
name:

Skin: straight

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: fractal dimension of boundary = 1
name:

Skin: 4G2 (Cityscape Skin)

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: same profile as Cityscape Curve.
name: Dragon of Eve

Skin: 4G1 (Dragon of Eve Skin)

attribution: Jeffrey Ventrella

reference:Dragon of Eve Video

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

Skin: straight

attribution: Jeffrey Ventrella

reference:fractalcurves.com

comment: fractal dimension of boundary = 1
The following curves break the rule which disallows segments to overlap, but they are well-known and worth noting. The Peano Sweep fills a square, and it achieves this by distributing overlaps and open spaces evenly. The Cesaro sweep is everywhere twice-self-overlapping.
name: Peano Sweep

Skin: straight

attribution: Giuseppi Peano

reference:(Similarity to Hilbert Curve)

comment: (This curve has overlapping segments, but it is plane-filling at the limit).
name: Cesaro's Sweep

Skin: straight

attribution: Ernesto Cesaro

reference:(Relation to Koch Curve)

comment: At the limit, this curve becomes everywhere self-overlapping.


The First Nine Families



















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