revised 10 December 2014
Except its obvious that there is some regular arrangement of them within the white square. For example, they don't touch the sides. Or each other. What's going on?
In fact, the dots are more regularly placed than is immediately apparent. Each dot is placed in an invisible cell on an eight by eight grid. It's their location within that cell that is random.
This is an example of Regular Randomness. Its the kind of pattern that we find in nature. And in Art.
Let me explain. In nature many things (maybe all things) are organised according to some pattern. Think of the branches of a tree. Or the petals of a flower. Or the feathers on a thrush. Neatly organised into regular patterns. Except no two trees are identical. No two flowers. No two thrushes.
Nor in fact are any two parts of the same tree identical. But they are very similar. Their parts are organised randomly within a regular pattern. The source of this randomness is the interaction of many parameters of the environment in which each part of the tree grows.
As it is with nature, so it is with Art.
Pollock, for example, (who I have written about just recently, calling his method Splash till Done), can be looked at as achieving Regular Randomness. He may not have had a regular grid exactly, but his marks are arranged so as to occupy the entire canvas and to interact with each other in particular ways, such as being separate from each other and repeated in such numbers as to create a regular random effect.
Not unlike our trivial dot picture above.
If we were to replace the dots in our our trivial dot picture by splashes, oriented randomly as well as placed randomly, we would begin to approach a Pollock, as I have illustrated in an earlier article, Systematic Pollock, where the following image, among others, is described.
Actually, the grid used here is not, as you might imagine, larger than the one used for dots. It's actually smaller. It's just that there are many layers of splashes, each a different colour and each a slightly different size, to create a phasing of the patterns. It sort of reproduces how Pollock worked, adding layer after layer and working round the canvas systematically.
Pollock is an easy target for this analysis however. To be convincing, I need to be able to show that it applies to many other artists and not just abstract artists.
This is a major undertaking. But let me give you a feel of how it proceeds.
Take another artists that I am interested in, Malevich, currently on show at the Tate Modern. Working in the 20's and producing abstract art. In what sense is he regularly random?
Apart from the obvious, that each of his works is a random variation on a theme that derives from his previous work, is there any sense in which an individual painting is regularly random?
I would argue that there is. And that this analysis can be applied to almost any artist.
Take, for example some of Malevich's Supremacist Compositions (try this google images search).
He covers the canvas with various approximately rectangular shapes. They lie adjacent to each other and some lie on top of others. His components form a collage. The components are regularly random in that they are variations on the theme of a thin-rectangle. Their locations are regularly random in that they are arranged in groups with regularly random spacing.
So, why is this Malevich painting so esteemed, if it could be carried out systematically by a robot, with a regularly random algorithm and a little guidance?
In an essay on Mondrian (in this book), Bridget Riley praises that artist's achievement of "balance" in his paintings. For Riley, this mystical property is a mixture of geometry and colouration. For example, Riley praises the location of the coloured squares in the Mondrian compositions.
As with Mondrian, so it is with Malevich, in my opinion. His collection of similar Supremacist Compositions have a mystical composition, not readily explained with mathematics.
What we do with geometry, we can also do with photographs. Take a look at the following image.
Where is the regular randomness here? Well, the image is based on a photograph, obviously, bu one that has been processed in some way. The process it has undergone is to swap pairs of pixels throughout the image. The swapped pixels are constrained somewhat. They are not too far apart. This constraint, and the fact that swapping ensures that all the original pixels are retained, ensures that the original image is still apparent.
This is regular randomness because the randomness is constrained, just as it was earlier by a grid.
I have since added another image of this sort in the post Ghost Ranch (all the right pixels, not necessarily in the right order).