L-system

The documentation for a new Graph library is coming along nicely, and you can also expect some good improvements to the Core Image library in the coming days. Meanwhile, I've put an L-system library online.

You can use it to model plants, trees, fractals, etc.

We'd like to thank Mark Meyer for his L-system code in the gallery.

Enjoy!

Tom, this looks fantastic. Nice work.

Thanks Mark!

I'm currently adding some improvements. Right now the library is good for growing trees but a bit unwieldy for modeling geometric shapes (like Penrose etc.)

So expect an update soon.

Tom,

In my original attempts with the L-system I had trouble with a lot of the geometric shapes--especially the Penrose tiles. I realized that the way I worked out the algorithm made rules that drew but didn't recurse difficult if not impossible. Attached is a slightly different script that creates the Penrose P3 pattern. This just uses the rules from wikipedia (which didn't work before).

size(500, 400)
translate(250, 200) #center starting point
transform(mode=CORNER)
 
colormode(HSB)
strokewidth(.35)
strokeColor = color(.6, .3, .7, .3)
stroke(strokeColor)
 
def draw():
    line(0, 0, segmentLength, 0)
 
def iterate(n, rule):
    global strokeColor
    if rule == '-':
        rotate(rightTurnAngle)
    elif rule == '+':
        rotate(leftTurnAngle)
    elif rule == "[": 
        push()
    elif rule == "]":
         pop()
    else:
        if n >= 0:
            for step in rules[rule]:
                iterate(n-1, step)
        elif rule=='1':
            draw()
            translate(segmentLength, 0)
 
segmentLength = 20.0
rightTurnAngle = -36.0
leftTurnAngle =  36.0
        
rules= {}
 
rules['6'] ='81++91----71[-81----61]++'
rules['7'] = '+81--91[---61--71]+'
rules['8'] = '-61++71[+++81++91]-'
rules['9'] = '--81++++61[+91++++71]--71'
rules['1'] = ''
rules['start'] = '[7]++[7]++[7]++[7]++[7]'
iterate(5, 'start')

Ah yes, this one has a subtly different nesting scheme. The L-system in the library has this scheme:

for step in rules[rule]:
    if step == "F":
        # draw segment
    elif step in rules:
        # recursion
    elif step == "-": rotate(-angle)
    # etc. all the transformations