Koch curves as attractors and repellers
- 1 November 1988
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Computer Graphics and Applications
- Vol. 8 (6) , 26-40
- https://doi.org/10.1109/38.20316
Abstract
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.Keywords
This publication has 7 references indexed in Scilit:
- Mathematical models for cellular interactions in development I. Filaments with one-sided inputsPublished by Elsevier ,2004
- The Beauty of FractalsPublished by Springer Nature ,1986
- Construction of fractal objects with iterated function systemsACM SIGGRAPH Computer Graphics, 1985
- Iterated function systems and the global construction of fractalsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1985
- Plants, fractals, and formal languagesACM SIGGRAPH Computer Graphics, 1984
- Recurrent setsAdvances in Mathematics, 1982
- Une méthode géométrique élémentaire pour l’étude de certaines questions de la théorie des courbes planesActa Mathematica, 1906