Fractal Space Filling Curves 2009

These are two new curves I created since 2002.

I hope there will be more.


A Four Tile Triangle



This curve is closely related to the last one on the previous page. This is also a closed loop and each tile is drawn in an out and back fashion, starting and ending on the same sub-tile, and the curve can pass through some sub-tiles as many as six times.



Above shows the first, second, third, and fourth order curve. Below is the highest order curve, reveling this Sierpinski like, half fill, half gasket.




A Five Tile Right Triangle



I came up with three different curves through this tiling, they are very similar looking so I just show one here. This curve is made of two different tiles shown above.

The A curve is made of three A's, and two B's.
The B curve is made of three B's, and two A's.

The four below are the A shape, and are the same except for how they are colored. The first shows how the A shape divides into sub tiles. The rest show how sub tiles further divide into smaller tiles.

The A sub tiles are shown in shades of red.
The B sub tiles are shown in shades of green.




Space Filling Curves
Space Filling Curves 2002
Space Filling Curves 2009
Space Filling Curves 2010
Dragons
IFS Dragons
Interactive Turtle Tree
Interactive Sierpinski Curve
Interactive Turtle Dragon
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Gary Teachout