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
"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
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.