About the Author

Bernat Espigulé Pons received a BSc in physics from Universitat Autònoma de Barcelona in 2012, completing the last two years of his studies abroad, first as an EAP student at the University of California, Santa Barbara 2010-2011, and then as an ERASMUS student at Heidelberg Universität, Germany 2011-2012. Equipped with Mathematica, Bernat has discovered and mapped the generalized families of self-contacting symmetric fractal trees. His main results have been presented in two peer-reviewed papers at the Bridges Conference and the Symmetry Festival 2013.

His strong interest in the study of complex systems started at High School where he developed a research project about Geometry and Nature. From past to present, his interests are: fractal geometry, chaos theory, fractal space-time, complex networks, non-linear phenomena, morphogenesis, dynamical systems, topology, complex oscillations, fractal trees and NKS. Bernat’s other interests are photography, hiking, surfing, couchsurfing, capoeira, architecture, generative art, education and, more recently, the art of 3D printing Trees. He also enjoys receiving feedback from his left-handed twin brother who is doing research in physics, and her younger sister majoring in math.


The author thanks Susanne Krömker for her enthusiastic support of the author’s research during an Erasmus exchange at Heidelberg Universität. Susanne’s past research on fractals at her Numerical Geometry Group inspired the author in many different ways. The initial research for this project was partially done under the inestimable help of Jofre Espigulé, author’s twin brother, and it was enriched with many constructive comments of several professors and friends including Warren Dicks, Gaspar Orriols, Carlos Castro and Pere Pascual.

Bernat also wants to acknowledge Michael Frame, Stephen Wolfram, Todd Rowland, Vitaliy Kaurov, George Hart, Robert Fathauer, Tom Verhoeff and Tara Taylor for all the great conversations about fractal trees that they had with him.

Past Research

Author's self-portrait, 2006.

✭ High School "IES Ramon Muntaner", Figueres 2004/07

TdR "Observant el laberint geomètric de la natura" 2006. Supervisor: Fede Luque.

✭ Universitat Autònoma de Barcelona 2007/10

15-minutes talk "Caos determinista" PPT (language: Catalan).

Project "Complex Networks". Supervisor: David Jou.

BSc Thesis TdG "L'entrellat del món, un camí cap a la complexitat". Supervisor: Gaspar Orriols.

✭ University of California, Santa Barbara 2010/11

"California's Plants Patterns". Supervisor: Omer Blaes.

✭ Heidelberg Universität 2011/13

50-minutes lecture "Classification of fractal trees by symmetry" Supervisor: Susanne Krömker. 2012

45-minutes lecture "Critical Points for Topological Changes in Generalized Self-Contacting Fractal Trees" in Susanne Krömker's seminar "Parametrisierte und topologische Methoden in der Computergraphik". 2013

✭ Wolfarm Science Summer School, July 2013

"Generalized Self-Contacting Symmetric Fractal Trees in 3D". Project Paper, CDF Demonstration, 10-minutes talk and poster.

✭ Bridges Conference, NL Enschede, 26-31 July 2013

"Unfolding Symmetric Fractal Trees". Regular paper, 30 minutes talk.

✭ Symmetry Festival, NL Delft, 2-7 August 2013

"Generalized Self-Contacting Symmetric Fractal Trees". PDF 20-pages article, 30 minutes talk.

Future Research

Analysis on Self-Contacting Symmetric Fractal Trees. Dynamic book about fractal trees, "mathematics for dummies". Rendered 3D trees animations. Technological applications and scientific aspects of the present mathematical theory.

Support Bernat's Project

This project is a continued working-process. The fractal forest is infinite but its hierarchical structure indicates that it is possible to understand its universal aspects. I would like to think that the general knowledge gained in this project could one day be wisely used to fully exploit the huge amounts of new resources that this forest contains. There are so many applications hidden out there. Support the author ordering your favorite fractal tree ($5) or support him directly using PayPal:


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