Golden Fractal Trees

T. D. Taylor
Bridges Donostia: Mathematics, Music, Art, Architecture, Culture (2007)
Pages 181–188


The famed golden ratio appears in many different forms of art. Historically there have been people who believe that the golden ratio can be used to create the most aesthetically pleasing figures. More recently, fractals have been used to create beautifully intricate art. In this paper, we present an interesting connection between the golden ratio and fractal trees. Four special self-contacting fractal trees that scale with the golden ratio possess remarkable symmetries and provide new visual representations of well-known results involving the golden ratio. Golden variations of familiar fractals including the Cantor set and the Koch curve appear as subsets of golden trees.