Influenced by the mathematical art of Salvador Dalí, and the original insights into nature's geometry by Antoni Gaudí, I have found in the field of fractals the right tools to realize my artistic ambitions. As I share Robert Fathauer's passion for fractal trees, I decided to carry out a long-term project using Mathematica that shed new light on the topological aspects of infinite symmetric trees. I moved from a two-dimensional generalization of self-contacting symmetric fractal trees, to the exploration of trees in the realm of the third dimension. My artwork shows some of my findings during this transition.
The Sierpinski SuperFractal has a Sierpinski triangle in one side and a carpet fractal in the other. This object nicely shows that these two fractals are topologically connected under a continuos transformation. Among the superfractals discovered by the author this one is special because it has a smooth external boundary.
In 2007, Tara Taylor presented the four self-contacting symmetric binary fractal trees that scale with the golden ratio. As she showed, these trees possess remarkable symmetries in addition to the usual symmetries associated with symmetric binary fractal trees. In my project carried out during the 2013 Wolfram Science Summer School I spotted six self-contacting ternary fractal trees that scale with the golden ratio. The present collection of trees are the 3D-printed versions of them. They show an analogous critical behavior to their binary 2D counterparts, and they add new possibilities to explore the connections between fractals and the golden ratio.