Graphical applications of L-systems
Proceedings on Graphics Interface '86/Vision Interface '86
Tilings and patterns
Construction of fractal objects with iterated function systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Mathematical Theory of L Systems
Mathematical Theory of L Systems
Plants, fractals, and formal languages
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Ray tracing deterministic 3-D fractals
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
Towards Realistic Modeling and Rendering of 3-D Escape-Time Deterministic Fractal Shapes
VSMM '01 Proceedings of the Seventh International Conference on Virtual Systems and Multimedia (VSMM'01)
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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.