L-Systems

L-Systems are described in the following book:

Przemyslaw Prusinkiewicz and Aristid Lindenmayer
The Algorithmic Beauty of Plants
Springer-Verlag, New York, 1990

Available software:

lsystem.c -- source for Unix/X11 or MS-DOS/VGA
lsystem.exe -- executable for MS-DOS/VGA
demos.zip -- dozens of example L-System definitions

Given a correct L-System definition, the program can:

Display an L-System on X11 (Unix) or on a VGA screen (MS-DOS)
Produce a PostScript figure, by specifying -p as a command line argument

Examples

Koch snowflake

seed    F + + F + + F          # Initial sequence of symbols
rule    F -> F - F + + F - F   # Symbol rewrite rule
delta   60                     # Angle of rotation in degrees
theta   60                     # Initial angel in degrees
leng    400                    # Length of line element
iter    3                      # Number of iterations
ratio   3                      # Scaling of length/iteration
x       0                      # Initial horizontal position
y       -235                   # Initial vertical position

Shrub

ignore  X                      # X will be ignored
seed    X
rule    F -> F F
rule    X -> F [+ X] F [+ X] - X
delta   22.5
theta   90
leng    230
iter    6
ratio   2
x       0
y       -230
red     0.0                    # color component between 0 and 1
green   0.6                    #
blue    0.2                    #

Islands

move    f                      # f produces invisible line
seed    F + F + F + F
rule    F -> F+f-FF+F+FF+Ff+FF-f+FF-F-FF-Ff-FFF
rule    f -> f f f f f f
delta   90
theta   90
leng    236
iter    2
ratio   6
x       128
y       -128

Any letter may be used as a non-terminal. For any used letter, there has to be a a corresponding rule. The program is case sensitive for letters used in rules and seed.

Use of color is optional.

Use of ratio is optional (default = 1). The value of leng is divided by ratio^iter. For many (but not all) figures, ratio can be defined such that, when the value for iter is altered, no other values need to be adjusted.

Not (yet?) implemented

Parameters could be used to specify length, width, color, etc.:
```
F(x) -> F(x * 1.41)
```

Parametric conditionals, such as:

F(x <  .5) -> F(x * 1.41)
F(x >= .5) -> [ + F(x)] - F(x)

Probabilistic conditionals, such as:

F(.8, .2) -> F
          -> [ - F ] [ + F ] F