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January 12, 2012
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Hyperbolic Rep Tile 05 by rosshilbert Hyperbolic Rep Tile 05 by rosshilbert
A hyperbolic transformation applied to a Rep-Tile IFS fractal formed from a set of Affine transformations.

The method used to produce this image is based on Rep-N Tile attractors. The term Rep-Tile (replicating figures on the plane) was coined by mathematician Solomon W. Golomb in 1962. See the Rep-Tile page at [link] for a brief description.

Created with the Fractal Science Kit fractal generator. See [link] for details.
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:iconsnupi988:
snupi988 Featured By Owner Jan 13, 2012
nice exploration:)
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:iconrosshilbert:
rosshilbert Featured By Owner Jan 13, 2012
Thank you :-)
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:icongolem1:
golem1 Featured By Owner Jan 13, 2012  Professional Digital Artist
Fantastic...
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:iconrosshilbert:
rosshilbert Featured By Owner Jan 13, 2012
Thanks!
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:iconlyc:
lyc Featured By Owner Jan 12, 2012
beautiful geometric work, well done :)
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:iconrosshilbert:
rosshilbert Featured By Owner Jan 13, 2012
Thank you :-)
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:iconhop41:
Hop41 Featured By Owner Jan 12, 2012
This reminds me Escher's Circle Limit prints.

Rep Tiles are a form of L substitution? I am wondering if Escher explored this way of suggesting infinity. The closest thing that occurs to me at the moment is Fish and Scales [link] where each scale of the fish can be substituted with a fish.
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:iconrosshilbert:
rosshilbert Featured By Owner Jan 12, 2012
Yes, like Escher's Circle Limit IV, this image is based on a hyperbolic tessellation visualized in the Poincare disk model of hyperbolic geometry.

A Rep-N Tile is a polygon that can be dissected into N smaller copies of itself. See [link] for examples. I have seen Rep-Tiles visualized using L-System programs as you suggest but this was generated using an IFS (Iterated function system [link]). See [link] for additional info.
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