Enduring Illusions

Today’s Math Art is titled Enduring Illusions. It was created by Professor Mike Field, a British-born mathematician now based in Houston, Texas. If anyone, Prof. Field is extremely involved in the creation of mathematics and art.

In his own words, Prof. Field says this about Enduring Illusions:

Enduring Illusions was created using a random dynamical system (also known as an iterated function system) defined on the two-dimensional torus. The resulting invariant measure was lifted to the plane so as to produce a repeating pattern of the plane and EnduringIllusions is a section of that pattern. In fact, matters are a little more complicated as Enduring Illusions is a 2-color repeating pattern. Half of the symmetries of the pattern preserve colors and half interchange colors. (In Coxeter’s notation, the pattern is of type pm/cm.) A lot of the mathematical work that goes into the creation of these 2-color patterns relates to the development of algorithms that allow one to do the 2-coloring in a way consistent with the dynamics and symmetry of the pattern.

I mentioned in Chaotic Symmetry that Prof. Field is something of an expert in symmetrical chaos. As a matter of fact, all the art work that Prof. Field creates are realizations of measures of symmetric chaotic dynamical systems.

Enduring Illusions, 2004 is a Durst Lambda print on glossy photographic paper, 48 x 48 inches. It is On permanent display in the Zeeman Institute, University of Warwick, UK. A smaller print is currently on tour in France with the Mathématiques et les Arts exhibition organized by Claude Bruter.