Experiments in Processing: curious eels in hyperbolic sea.
I love hyperbolic geometry, heptagons, and Escher.
The eels move on the sides of a triheptagonal tiling of the hyperbolic plane in the Poincaré disk model. You better appreciate this because getting the coordinates is a real pain in the *** (done with a python script, <a href=“https://github.com/rantonels/poincare“>source</a>).
These pictures are pieces of art that have been made based off of the Klein and Poincare disk models for hyperbolic geometry (where through any given point there are an infinite number of parallel lines)
This is a tiling of regular right angled dodecahedron in three dimensional hyperbolic space shown through 4 iterations. 12 generators of the tiling are reflections in each of the 12 dodecahedron’s faces.
Ok. MIND : BLOWN. Margaret Wertheim is officially my newest crush. In this TED talk she explains how hyperbolic geometrical shapes that look very much like coral can be expressed through crochet.
The idea of translating hyperbolic planes into crochet was first thought by Daina Taimina (you can watch her TED talk about it here) and for the first time, an actual hyperbolic shape could be translated into a real, physical shape.
Here is a fresh, astute social and cultural history of physics, from ancient Greece to our own time. From its inception, Margaret Wertheim shows, physics has been an overwhelmingly male-dominated activity; she argues that gender inequity in physics is a result of the religious origins of the enterprise.
Now I’m pumped for reading AND doing some hyperbolic crochet! (iomikron, are you up for some crafts?)
Escher’s Circle Limit I - IV and Hyperbolic Geometry
All four of M.C. Escher’s Circle Limit woodcuts are great works of art and superb examples of hyperbolic geometry. Hyperbolic geometry is a form of geometry where the parallel postulate of Euclidean geometry does not hold. This is reflected in the world represented in each of the woodcuts. In each one, the figures are not getting smaller as the reach the edge of the circle as they would in Euclidean geometry. From the figures’ perspective, they are all the same size, regardless of where they are in the circle. Their entire world lies completely within the flat plain of the circle, the edge of which to them remains infinitely far away.