Random is a misnomer. When I think of random I think of clouds, leaves on trees and white caps on waves. These are not random, at least they aren’t what most people consider random. Many people think of random as perfectly and evenly distributed.
Fractals use a lot of Random numbers but Fractals themselves are not Random. Clouds for example are quite Random, however if we are using them in a picture they are less random, they are restricted to the area of the picture that we have designated as sky. Fractals do a great job of mimicking the world around us and they use lots of random numbers. Close up they are really random but zoom out to see the entire picture and like the clouds restricted to sky, they become less random.
One of the basic traits of randomness is clumping. If you generate a truly random set of numbers and use them to simulate clouds, for example, you will notice that the numbers/clouds tend to clump together.
A good explanation of randomness;
One of the most used examples of randomness is background radiation. A sample of background radiation is used in many things that require a set of random numbers. A good example of background radiation is noise on your TV set or on your radio; set the frequency between stations. This method of generating random numbers is used because it’s really difficult to generate a set of truly random numbers.
So after all of this highly technical discussion, how can an artist use it?
When I am painting leaves I purposely clump them a little. When I look at a tree I see that the leaves are occasionally clumped together. They are not sticky or attached, they just clump. Take two steps to the right or left and the clumps will change location, but they will still be clumped. Many other things that I paint have similar behavior. So if I want to make an area of a painting look real I try to clump components. I use this idea to good effect in many paintings. A portrait for example you wouldn’t think of having any random components but with hair I use the same technique I use in leaves and it seems to work.