How are fractals made?

Fractals can be generated with computer programs like Sterling or Apophysis. Both of these are freeware you can easily download. There are other programs, like Ultra Fractal and Tierazon, as well. With Sterling, you are given a default fractal that you can transform using various modes, and then zoom in and search for a good design.

With Apophysis, you are given a set of randomly-generated "flames" that you can transform using various "plug-ins", some of which are included in the download, others can be downloaded free. Apophysis flames are can be edited by manipulating the triangles that define it. Each triangle can be manipulated using plug-ins such as "spiral." Several tutorials are on the Internet, at places like deviantart.com, which has groups liked I linked below.

An example of fractals generated with Sterling and Apophysis can be found in a gallery I also linked below.