Attractors and repellers of Koch curves
Przemyslaw Prusinkiewicz and Glen Sandness
Abstract
This paper presents two methods 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. This characterization was first studied by
Hutchinson. 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.
Reference
P. Prusinkiewicz and G. Sandness: Attractors and repellers of Koch curves.
Proceedings of Graphics Interface '88, pp. 217-228.
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