🚀 go-pugleaf

L-systems (Lindenmeyer systems) start with an axiom string and use production
rules to create new strings. For example,

Axiom: aabc
Production rules: a -> ab
                  b -> c
                  c -> c

All production rules are applied in parallel, so the string might develop as
follows:

aabc
ababcc
abcabccc
abccabcccc
etc.

So, how is this string graphically interperted? An interpertation based
on LOGO called turtle interpertation is used. A turtle in LOGO, follows simple
rules to draw pictures on the screen. A turtle can be told to move forward and
turn angles. In a string:

  F - can be used to tell the turtle to move forward a set distance,
      drawing a line behind it. 
  f - can be use to tell the turtle to move forward a set distance,
      without drawing a line behind it.
  + - turn to the left a set angle.
  - - turn to the right a set angle.

Even with just these simple rules, fractal shapes can be generated.
Here is one taken from _The Algorithmic Beauty of Plants_, Prusinkiewicz
et al. pp. 9.

Axiom: F-F-F-F
Production Rules: F -> F+FF-FF-F-F+F+FF-F-F+F+FF+FF-F
	          - -> -
                  + -> +

This L-system generates a koch curve. Many further refinements of this basic
scheme have been used to model the branching and flowering patterns of trees
and plants, as well as the development of cells in simple animals. _The
Algorithmic Beauty of Plants_ is a fairly easy to read introduction to the
subject that contains many pictures (and is thus a little bit pricey).

justin