FINDING GOLD IN THE FOREST: SELF-CONTACTING SYMMETRIC BINARY FRACTAL TREES AND THE GOLDEN RATIO

Abstract. This paper presents the four self-contacting symmetric binary fractal trees that scale with the golden ratio. These trees possess remarkable symmetries in addition to the usual symmetries associated with symmetric bi-nary fractal trees. The trees provide new visual representations of well-known equations and geometrical objects involving the golden ratio. Golden vari-ations of familiar fractals including the Cantor set and the Koch curve are discussed, along with their connections to the golden fractal trees. The ob-servations about the golden trees presented here provide many interesting and entertaining exercises involving trigonometry, geometric series, fractal trees and the golden ratio. Various tilings of regular polygons with golden trees are also presented