Fractals and randomness

I’m working on a painting that has a pebble beach. The pebbles seem random but are not. The size varies but there is an upper and lower limit. Actually there appear to be two limit sets; larger and smaller.  I’ve talked to quite a few artists who have problems with randomness. There aren’t many things in nature that are truly random but there are a lot of things with random components. Fractals, as made famous by Mandelbrot, do represent what we see in nature very well and include some random components.

This does not mean that reality has anything to do with Fractals; it just means that with a small number of calculations we can simulate reality with Fractals. It is certainly suggestive that Fractals appear so similar to what we see. There have been and still are several computer applications that use Fractals to represent reality. The pebbles on my beach have upper and lower size limits so they are not random. Bigger ones usually migrate to the top. Clouds are probably the most random things we see in nature although Fractals can represent them very well. There is a level of randomness in all Fractals.

I find this highly interesting although it doesn’t really help an artist. Fractals are not a quantum phenomenon although water reflections are. Now before one of you physics whizzes out there jump down my throat; the specular reflections are likely not a quantum phenomenon but the secondary reflections probably are. And yet again this doesn’t help. It’s useful to know that pebble sizes are not random; they have an upper and lower size limit like a Fractal. Although that doesn’t mean you can’t have the odd bolder. I try to make everything appear random but with some structure; I think that is the closest to what I see. Ultimately it’s what I see that defines the painting. My observations are not particularly helpful but it’s just the way I see things.

I don’t paint or draw in a random way, so as long as I let that non-random structure through, the resulting image usually appears realistic. I often let the image get too random. Then I have to go back and repaint the structure and add a little less randomness. The trick is to add just enough randomness. I often get it wrong the first time. Thank god for acrylics. I think the pebbles will look good. Although I’m going to have to include some larger rocks.