By A.H. Pavel
ISBN-10: 0273086510
ISBN-13: 9780273086512
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I would like to thank the co-editor of both volumes, Reza Sarhangi, for permission to reproduce several of the figures. 2 first appeared in [2]. , The Flowering of String Rewriting Systems, The College Mathematics Journal, 23(3), (May 1992), 225–236. [2] ——, Imaginary Gardens: A Model for Imitating Plant Growth, Proceedings of Bridges Donostia 2007, Edited by Reza Sarhangi and Javier Barrallo. [3] ——, Recursion: Real and Imaginary Inflorescences, The UMAP Journal, 21(4), (Winter 2000). [4] ——, Modeling Trees with a Stochastic Matrix, The College Mathematics Journal, 29(3), (May 1998), 230–236.
1= 2 / D l = 2 , because they are on the tops of level 2 subtrees SRL and SLR . 1= 3 / D l = 3. This is because the gap side is the third side of an equilateral triangle with the other two sides being the top of level 3 subtrees S RLL and SLRR . 5. Thus we have a visual representation on the self-contacting fractal tree of one of the many equations involving . 2 log /. 11). RL/1 is replaced with four line segments. Two of these segments have length l = 2 (because they are the tops of level 2 subtrees) and the other two have length l = 3 (because they are the tops of level 3 subtrees).
1= ; 108 ı/ along with the self-contacting trees with branching angles 106ı and 110ı. 21. 22. 1= ; 120ı/ The third golden self-contacting tree has branching angle 120 ı. This angle is not as commonly associated with the golden ratio as 108 ı is. However, we shall see that the appearance of equilateral triangles implies that the golden ratio also appears. RL/1 /. RL/1 . RL/k /, for k 0, are vertical if  D 120ı, the calculations for this tree are simplified. 0; 1/, which of course is 1= . r 2 / 46 Chapter 3.
The space of closed subsets by A.H. Pavel
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