Generator iteration is easy - all you have to do is take a shape and substitute it with a different one several times. For the computer, however having a picture of the base and motif is not enough. We need a way of storing data about fractals that doesn’t take up a lot of memory with pictures and makes it easy to create algorithms for drawing fractals. The best way of doing it is by using l-systems. L-systems were developed by A... L... (the "L" in l-systems is his initial). They are composed of an angle definition, an axiom, and at least one rule. The axiom is the initial shape (base) used in the process of generating a fractal. The rules tell what symbols in the axiom should be replaced with other symbols. The symbols used are the following:

Common symbols:

F draw forward
G move forward (without drawing)
+ turn counterclockwise
- turn clockwise
| turn back (180 degrees rotation)

Advanced symbols:

@n multiply the length of the segment by n
I before the number means take inverse (divide instead of multiplying)
Q before the number means take the square root
! reverse the meaning of + and --
[ push (store current position on a stack)
] pop (go back to the last stored position)

Coloring symbols:

Cn set the color to n
<n increment the color by n
>n decrement the color by n

Other symbols, such as X do not have any special meaning, but are often very important in intermediate steps.

A SIMPLE EXAMPLE

For example, the Koch snowflake uses the following base and motif:

As an l-system, we can write it as:

USES