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Issue No. 06 - November/December (1988 vol. 8)
ISSN: 0272-1716
pp: 26-40
ABSTRACT
<p>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.</p>
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CITATION
Glen Sandness, Przemyslaw Prusinkiewcz, "Koch Curves as Attractors and Repellers", IEEE Computer Graphics and Applications, vol. 8, no. , pp. 26-40, November/December 1988, doi:10.1109/38.20316
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