<p>I'm looking for a good way to represent organic growth - especially trees and flowers - using code.</p>

<p>I've found Lindenmayer Systems as a reasonable way to portray this, but need a good place to start programming this.</p>

<p>Any good suggestions?</p>

I am not sure how much you already know on the topic, but I believe Wikipedia's article on
L-system
should be a good start.
"using code" is a bit fuzzy, so I can hardly answer. You might find some freeware to experiment with L-systems, you can play with some graphical language like Processing, do that in GDI or Java2D (or 3D), etc.
There are other methods too, my own
Ferns - Static view
was made with Processing, drawing short lines, using a hierarchical class system to represent trunk, branches and leaves.