Bernat Espigule

Mathematical Researcher & Visual Artist
Departament d'Informàtica, Matemàtica Aplicada i Estadística, Universitat de Girona
Sant Climent Sescebes, Catalonia, Spain
Bernat lives in Catalonia and works both as a tech consultant and a mathematical researcher. This involves spreading his love of maths via research articles, animations, 3D-printed sculptures, workshops, and school visits. Currently, Bernat is interested in exploiting the notion of complex tree to tackle unsolved problems in the field of algebraic geometry, complex dynamics, and the analysis on fractals.
The Starry Pentagasket
5 x 5 cm
Organic mathematical ornament with five-fold rotational symmetry. The laser cut regular star pentagons illustrate the inner structure of one of the earliest complex binary trees discovered and studied by the author back in 2011. The tree's branching process consists of a branch shrunk by the golden ratio rotated 36 degrees, and a second branch identical to its ancestor but rotated 72 degrees in the opposite direction. The intersection of this fractal with the boundary of its decagonal convex hull generates ten copies of a special type of Cantor set studied by Roger L. Kraft, see “A Golden Cantor Set.” The American Mathematical Monthly, vol. 105, no. 8, Mathematical Association of America, 1998, pp. 718–25,