The strings generated by L-systems are lists of symbols. To produce visible
L-system plants, an interpretation based on the concept of Turtle Graphics
[&make_named_href('',
"node22.html#Pape80","[Pape80]")] is given below.

A turtle is sitting on a sheet of paper facing in a certain direction,
denoted by the triple , where *x* and *y* are the
coordinates and is the direction angle. The tail of the turtle
is a bit dirty. Thus, it leaves a trail along the paper. The L-system has
only four symbols - *F*, *f*, +, and -. *F* means the turtle moves one unit
distance along the current direction , while means of *f* is the same
as *F*, except that the turtle lifts its tail this time without leaving a trail
on the paper. Symbols + and - denote the turtle rotating its heading to left
or right by a specific angle. By this simple interpretation, a two dimensional
L-systems plant is drawn on the paper.

To generate plants in three-dimensional space, more symbols are needed. For
three-dimensional graphics,
the turtle state changes to (*x*, *y*, *z*, *h*, *l*, *u*). The triple of (*x*, *y*, *z*) denotes
the current position of the turtle, and the triple of (*h*, *l*, *u*) denotes the
current heading vector of the turtle in three dimensional space. Rotation of the turtle is
expressed by the equation:

The interpretations of the different symbols are the following:

Note that there are two additional symbols - [ and ]. The symbol
[ denotes that the Turtle starts to sprout a substring and
the symbol [ denotes the Turtle returns to the original heading
direction and position.

Tong Lin (tlin2@cs.umbc.edu)