I'm interested in physics. Years ago, I decided that one of the ways that I could get around my lack of math was to try and use my experience in art to visualize what was going on in the subatomic world. I wasn't interested in representations of things like electrons whizzing around protons. [insert image of planetary view of atom] This kind of representation wouldn't tell me anything that I didn't already know.

I have found several ways of representing the physical processes. The most obvious is to write computer programs that simulate the behaviour of the process I wish to consider. This is the basis of the Linofo images, [insert linofo image] as well as explorations of biological structures using L-systems [insert l-system image]. I've also written programs that simulate the action of gravity on objects floating in space. [insert gravity image]

The physicists were saying that they didn't know what subatomic particles were, but they knew what some of their properties were. They were content to not attempt visualization, and just work with what they knew about the properties. So I started to see subatomic particles in terms of their properties, instead of in visual terms like, say, billiard balls. This lead to the thought that subatomic particles were things with "intrinsic properties". This lead me to wonder if I could find forms, or shapes, that had intrinsic properties, and whether I could use those intrinsic properties to help me visualize the intrinsic properties of the objects of subatomic reality. So I started looking for forms that would behave like an electron, instead of look like an electron, because after all, an electron doesn't look like anything.

The first step was to find a shape that would behave like anything. At first I wasn't sure what it meant for a shape to behave. One night I made a little shape I call a "spinner". This shape had visual properties. Groups of spinners had visual properties that individual spinners didn't. [insert images of spinners here] Not only that, these simple shapes had several different kinds of visual properties.

A year or so after I started exploring this, I picked up Grunbaum and Shephard's wonderful "Tilings and Patterns" in the library [insert isbn of grunbaum sheppard here.] . This book was a revelation. I saw at once that "tiles" were "forms with intrinsic properties". The book was a book of mathematics, and it provided a systematic survey of all of the possible ways of tiling a plane. Fortunately for me, the language used was largely diagramatic, and I could understand a lot of it. This book also made me realize how my interests were linked to those of MC Escher, whose work I had admired for years.

Among the many interesting types of tiles listed were tiles that produced "aperiodic" tilings. These are wonderful things. They are patterned, and there are elements that repeat throughtout the pattern, but the repetition is more like flowers in a field {link here to image of penrose tiling] than like squares in a grid. There are many kinds of aperiodic tilings, but my favourite are those invented by Roger Penrose. Penrose tiles are bihedral (two differnent tile shapes are used to make the tiling) and generate a pattern that has a 5 sided symettry. One can make tilings with stars and rhombs or with pentagons and rhombs that are very closely related to the Penrose Tilings. Also, anything with a 5 sided symmetry has the proportion of the Golden Mean [link here to description of Golden Mean] occuring and reoccuring throughout the piece. This proportion was considered by the Greeks to be the most perfect possible, and is also a proportion that is found again and again in nature.

Gradually, the metaphor that I was attaching to tiled patterns shifted from an image of the subatomic world to an image of cultures and socieies. There are many kinds of patterns that can be generated by any one set of tiles. Often, there is no smooth transition between one kind of pattern and another. At the boundaries of the domains of the two patterns is a crack. This has become a metaphor for me for the circumstance found when cultures intermingle. Individual tiles (a metaphor for individual people) seem much the same when seen outside the pattern (a metaphor for culture), but the various patterns generated (cultures) are not consistent with each other. Most individuals, even at the boundaries, can only be a part of one culture or another. Only very rarely can one individual span the crack between domains and have a functional role in two patterns. [insert image of crack here] This is just a function of geometry in the case of tiles. Could it be that there is a "geometry" that will help us understand the interactions of cultures?