Thursday, 13 June 2013

Systematic Cracking

This is a much simpler image than it may appear.

Each composite four-sided polygon in the arrangement has been divided into two parts by a line that runs from 1/3 along one side to 1/3 along the opposite side. This division simulates cracking in a hard material such as glass. Obviously, since this pattern is totally regular it is nothing like cracking in nature, where materials and the environment are far from regular.

The construction is simple. Start with a four-sided polygon. I started here with an approx A4 rectangle. Choose two opposite sides and mark a point 1/3 along either side. Draw a line joining these two points. Now you have two adjacent four-sided polygons. Repeat the construction within each of these and repeat on down into the even smaller four-sided polygons thus formed until you get tired or reach a degree of satisfaction.

This exercise can be a very meditative experience. Very zen, if you take it slowly and carefully with a pen and straight-edge. The pleasure comes slowly as you see the image build and satisfying as you see the symmetries appear in a geometry that is not quite like it was in school.

The exercise can also be more orgasmic. All your pleasure in one big moment. If, like I have done here, you write a computer program to generate the image, all the pleasure of seeing the generated image is there in an instant, when the program runs and the image appears.

This geometrically simple image is part of the ongoing search for the systematic in visual art. It's apparent "beauty" comes from the fact that each composite four-sided polygon is a simple geometric transformation of  each of the other composite four-sided polygons. The only simple symmetry (an isometry) is a rotation of the whole image about its centre. However, composite four-sided polygons with the same number of nested components are related to each other by an exact transformation (a stretching, in effect) that guarantees that the eye will see them as similar.