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The Computer Journal 1994 37(1):58-66; doi:10.1093/comjnl/37.1.58
© 1994 by British Computer Society
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A Complete L-system Specification for Generating an Exact Self-affine Growth-Decay Function with a Random Walk Scaling Property

J. Bradley *

Department of Computer Science, University of Calgary, Calgary, Alberta, Canada

The existence of at least four exact-affine time functions, called E5:3 functions, that allow for an infinite number of exact replications of Growth-Decay 12345abc structures, is demonstrated. These E5:3 functions are defined by algorithms and have no derivative anywhere. One of these E5:3 functions, called the standard E5:3 function, has the property of scaling like a random walk. This function also depends on the Golden Mean and rotates congruently with the Golden Spiral. A complete L-system specification for generating the standard E5:3 function is presented.

Received December 3, 1992. revised August 20, 1993.

* Department of Computer Science, University of Calgary, Calgary, Alberta, Canada


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