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Koch Curves as Attractors and Repellers
November/December 1988 (vol. 8 no. 6)
pp. 26-40

Two methods are presented for generating Koch curves, analogous to the commonly used iterative methods for producing images of Julia sets. The attractive method is based on a characterization of Koch curves as the smallest nonempty sets closed with respect to a union of similarities on the plane. The repelling method is in principle dual to the attractive one but involves a nontrivial problem of selecting the appropriate transformation to be applied at each iteration step. Both methods are illustrated with a number of computer-generated images. The mathematical presentation emphasizes the relationship between Koch construction and formal languages theory.

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Przemyslaw Prusinkiewcz, Glen Sandness, "Koch Curves as Attractors and Repellers," IEEE Computer Graphics and Applications, vol. 8, no. 6, pp. 26-40, Nov.-Dec. 1988, doi:10.1109/38.20316
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