Dear Qfwfq, where do fractals come from?

Well, let’s start with something simple, like life … the game of life invented by John Conway that is. Imagine a grid in which each cell of the grid is colored according to a set of rules based on the cell’s starting value. These rules repeat over and over to color the whole grid in successive generations. The rules say that any dot with 2 or 3 orthogonal neighbors will be colored in, it will live. Dots with zero, one or four neighbors will not be colored, they will die of loneliness or overcrowding. As successive generations are displayed, the grid becomes animated. Some kinds of starting figures (populations) thrive and some die off. There are patterns that move through repeating cycles and some that settle into static figures. More at Cellular Automaton.

Games like that are called cellular automata. They are not necessarily fractal generators but they are similar in that they color each pixel by testing its previous state with a series of repeating calculations. When the whole array of pixels is plotted, many interesting patterns emerge. This is so for fractals as well as for cellular automata.

Fractal programs are like Jack Frost simulators. The window pane of the simulator follows rules that are reminiscent of natural processes to generate patterned light fields that evoke recognition of things seen or imagined. There are lots of examples in nature of processes that generate patterns that tickle our cognitive faculties.

The surrealists often used natural patterns of complexity to make art that is partially discovered in physical perception and partially created in the eye of the beholder. see Surrealist Techniques.

The math behind the formulas used to make fractal images follows complex rules that we don’t necessarily need to understand to appreciate. The complexity of the rules ensures that the mathematicians can keep finding more and more interesting Jack Frost patterns.

You don’t have to be a mathematician to make fractals. On the other hand, fractals do not just emerge from the computer as ready made images of beauty and or wonder. A lot of chaos has to be sorted through just to find something promising.

The tools of fractal generation need lots of ways to manipulate the image and they need lots of controls for managing light and shadow and color. Creating an interesting fractal image with these tools is like wandering through chaotic regions where images appear and disappear mysteriously; where much mayhem is found before the discovery of an interesting patch of pixel frost that might be sculpted, framed, illuminated, colored and coaxed into something that attracts attention.