Tutorial Chapter 9
Generator IterationWHAT IS IT?
One way of creating fractals is by generator iteration. To do that, we start with a figure called the base. Then, every part of it is substituted with another figure, called the motif or generator. In the new figure, we again substitute every part with the motif. If we iterate these substitutions an infinite number of times, we end up with a fractal. For example, letís try making a fractal with the following base and motif:
base: /_\ motif: _/\_
We start with a triangle and substitute every side with the motif
We again substitute each of the 12 segments with the motif and continue the process to form a fractal called the Koch Snowflake
Another fractal, called the Cantor Set can be made by using a line segment as a base and a line segment with the middle cut out as a motif:
base: ------ motif: -- --
WHAT YOU CAN USE IT FOR
With different bases, motifs, and ways of placing the motifs we can get a great variety of base-motif fractals. They include a number of specific subcategories, such as dusts, Peano Curves, and sweeps. Generator iteration can also be used to make paper-folding fractals.