Zamet Center

The Zamet Center in Rijeka, Croatia by 3LHD architects. A beautiful application of the cairo tiling. Thanks to Calgar for advising me of this project.

Homotopy of Boy and Roman Surface

In topology, a smooth deformation from one surface in an other is called homotopy. The parameterization of this homotopy can be found on wolfram's page.

The grasshopper definition, download here.

This figures from Werner Boy's paper (1903) show the topological construction of the boy surface.

A proposal for a pavillion by Christophe Delsart and Yvan Ngnodjom based on the boy surface for the ARPAM project.

Boy Surface

The Boy Surface has been found 1901 by Werner Boy. One obtains a topologicaly equivalent surface by attaching a Möbius strip to a disk along its boundary. Like the Möbius strip this surface is nonorientable.




This beautiful parameterization, based on complex numbers, was discovered in the late 1980s by Rob Kusner and Robert Bryant. In this post the boy surface has already been mentioned on eat-a-bug.



Download the definition here

Crocheting the Lorenz Manifold

In 2003, Hinke Osinga and Bernd Krauskopf from the Bristol Centre for Applied Nonlinear Mathematics produced the first real model of the Lorenz Attractor surface by knitting.






















Download the paper by Osinga & Krauskopf here.

For more information on this topic please visit The Home of Mathematical Knitting

Lorenz Attractor

The Lorenz attractor has chaotic behaviour, named for Edward N. Lorenz. The movie shows the changing of the attractor with increasing Prandtl number.



Downlad definition here

Istanbul Street Parametrics

Spirograph toys for sale at the Sultan Ahmet station in Istanbul,Turkey.

Spirograph patterns generated with grasshopper.

Download the definition here

Cairo Attractor

A diamond grid locally distorted by a cairo attractor


The moving attractor

Download the definition here