Issue No. 06 - November/December (1988 vol. 8)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/38.20316
<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>
G. Sandness and P. Prusinkiewcz, "Koch Curves as Attractors and Repellers," in IEEE Computer Graphics and Applications, vol. 8, no. , pp. 26-40, 1988.