Unfolding Symmetric Fractal Trees
Inhaltsverzeichnis
Reference
Bernat Espigulé Pons: Unfolding Symmetric Fractal Trees. In: Bridges 2013. Pages 295–302
DOI
Abstract
This work shows how the angles and ratios of side to diagonal in the regular polygons generate interesting nested motifs by branching a canonical trunk recursively. The resulting fractal trees add new material to the theory of proportions, and may prove useful to other fields such as tessellations, knots and graphs. I call these families of symmetric fractal trees harmonic fractal trees because their limiting elements, i.e., when the polygon is a circle, have the overtones or harmonics of a vibrating string 1/2, 1/3, 1/4, ... as their scaling branch ratios. The term harmonic is also used here to distinguish them from other types of self-contacting symmetric fractal trees that don’t have a constantly connected tip set under a three-dimensional unfolding process. Binary harmonic trees represent well-known L ́evy and Koch curves, while higher-order harmonic trees provide new families of generalized fractal curves. The maps of the harmonic fractal trees are provided as well as the underlying parametric equations.
Extended Abstract
Bibtex
Used References
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Links
Full Text
http://archive.bridgesmathart.org/2013/bridges2013-295.pdf
