# L-System (Lindenmayer system), IFS (Iterated function system)

By Xah Lee. Date: .

## Lindenmayer system

Lindenmayer system (aka L-system) is a string-rewriting system that can model recursive processes such as recursive geometric transformation.

## Koch Toy

http://www.efn.org/~jcburg/software.shtml Mac OS 9 (2003-10)

Koch Toy by Jim Burgess is another excellent simple program. It draws simple fractal curves like that of Koch snowflake. User drag points on a line and immediately see its effects after n iterations. The number of kinks can be adjusted by dragging the nodes. Clicking on a arrow button increase or decrease recursion depth.

## Vectal

http://www.hot.ee/bntren/Program.html (2003-10)

Vectal draws simple fractal curves like that of Koch snowflake. User drag points on a line and immediately see its effects after n iterations. One feature of Vectal not in the mac Koch Toy is that user can change the sided-ness of the fractal on each line.

#### IFS (Iterated Function System)

IFS Another program by mathematician J D Meiss. This program does the Iterated Function Systems. It comes with a tutorial on IFS. Nice. After reading the one-page tutorial, I understand that IFS is as follows: we have n mappings of the plane. For each iteration, one of them is chosen by a given probability function. So, we start with some points or line in a plane, then apply the functions in each iteration, and plot the transformed points or line accumulatively.

http://amath.colorado.edu/faculty/jdm/ifs.html Mac OS 9 (2003-10, 2012)