Self-Replicating Tiles and Their Boundary |
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Authors: | A. Vince |
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Affiliation: | (1) Department of Mathematics, University of Florida, Gainesville, FL 32611, USA vince@math.ufl.edu, US |
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Abstract: | All self-replicating lattice tilings of the plane can be constructed using special iterated function systems (IFS). Certain self-replicating curves can be constructed using the recurrent set method (RS). A bijection between the IFS parameters and the RS parameters is such that the curve K produced by the RS parameters is the boundary of the tile T produced by the IFS parameters. The correspondence is algorithmic in that K can be drawn from the IFS data using turtle graphics and T can be drawn from the RS data using an IFS iteration. Received April 15, 1997, and in revised form November 13, 1997, and April 6, 1998. |
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