GeCla, short for Generator and Classifier, is a program for exploring the symmetries of of patterns/friezes or rosettes in the plane. GeCla allows you to generate a pattern, a frieze or a rosette with a previously chosen kind of symmetry starting from an asymmetric motif. It also allows the classification (with or without help from the program) of the patterns, friezes, rosettes obtained in this manner.

The following 3d model is a simulation of a uniform random quadrangulation with 30 000 faces. You can think of it as follows. If you are given 30 000 rubber squares, you can stitch them together along their sides and obtain a surface homeomorphic to the sphere. In plain English, this means that if you pump up the rubber surface, you obtain a sphere (think of a soccer ball for example). Put all the possible structures you can obtain by stitching together your squares in a bag and pick one at random.

You can visit my webpage for many more simulations and my picture page for many more higher quality downloadable pictures. In particular, you will find simulations of maps on more complicated surfaces (torus, double torus, disk, cylinder…).