# 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.
Download PDF here (2.2 Mb)