Overlapping trees in L-system forest

Question

I created an a program using python's turtle graphics that simulates tree growth in a forest. There's 3 tree patterns that are randomly chosen, and their starting coordinates and angles are randomly chosen as well. I chose some cool looking tree patterns, but the problem I'm having is that many of the trees are overlapping, so instead of looking like a forest of trees, it looks like a bad 5 year old's painting.

Is there a way to make this overlapping less common? When you look at a forest, some trees and their leaves do overlap, but it definitely doesn't look like this:

Since there's a lot of randomization involved, I wasn't sure how to deal with this.

Here's my code:

import turtle
import random

stack = []

#max_it = maximum iterations, word = starting axiom such as 'F', proc_rules are the rules that 
#change the elements of word if it's key is found in dictionary notation, x and y are the 
#coordinates, and turn is the starting angle 

def createWord(max_it, word, proc_rules, x, y, turn):

    turtle.up()
    turtle.home()
    turtle.goto(x, y)
    turtle.right(turn)
    turtle.down()

    t = 0
    while t < max_it:
        word = rewrite(word, proc_rules)
        drawit(word, 5, 20)
        t = t+1


def rewrite(word, proc_rules):

   #rewrite changes the word at each iteration depending on proc_rules

    wordList = list(word)

    for i in range(len(wordList)):
        curChar = wordList[i]
        if curChar in proc_rules:
            wordList[i] = proc_rules[curChar]

    return "".join(wordList)


def drawit(newWord, d, angle):

    #drawit 'draws' the words

    newWordLs = list(newWord)
    for i in range(len(newWordLs)):
        cur_Char = newWordLs[i]
        if cur_Char == 'F':
            turtle.forward(d)
        elif cur_Char == '+':
            turtle.right(angle)
        elif cur_Char == '-':
            turtle.left(angle)
        elif cur_Char == '[':
            state_push()
        elif cur_Char == ']':
            state_pop()


def state_push():

    global stack

    stack.append((turtle.position(), turtle.heading()))


def state_pop():

    global stack

    position, heading = stack.pop()

    turtle.up()
    turtle.goto(position)
    turtle.setheading(heading)
    turtle.down()


def randomStart():

    #x can be anywhere from -300 to 300, all across the canvas
    x = random.randint(-300, 300)

    #these are trees, so we need to constrain the 'root' of each
    # to a fairly narrow range from -320 to -280
    y = random.randint(-320, -280)

    #heading (the angle of the 'stalk') will be constrained 
    #from -80 to -100 (10 degrees either side of straight up)
    heading = random.randint(-100, -80)

    return ((x, y), heading)


def main():

    #define the list for rule sets.
    #each set is iteration range [i_range], the axiom and the rule for making a tree.  
    #the randomizer will select one of these for building.

    rule_sets = []
    rule_sets.append(((3, 5), 'F', {'F':'F[+F][-F]F'}))
    rule_sets.append(((4, 6), 'B', {'B':'F[-B][+ B]', 'F':'FF'}))
    rule_sets.append(((2, 4), 'F', {'F':'FF+[+F-F-F]-[-F+F+F]'}))

    #define the number of trees to build
    tree_count = 50

    #speed up the turtle
    turtle.tracer(10, 0)

    #for each tree...
    for x in range(tree_count):

        #pick a random number between 0 and the length
        #of the rule set -1 - this results in selecting
        #a result randomly from the list of possible rules.

        rand_i = random.randint(0, len(rule_sets) - 1)
        selected_ruleset = rule_sets[rand_i]

        #unpack the tuple stored for this ruleset
        i_range, word, rule = selected_ruleset

        #pick a random number inside the given iteration_range to be the 
        #iteration length for this command list.
        low, high = i_range
        i = random.randint(low, high)

        #get a random starting location and heading for the tree
        start_position, start_heading = randomStart()

        #unpack the x & y coordinates from the position
        start_x, start_y = start_position

        #build the current tree
        createWord(i, word, rule, start_x, start_y, start_heading)

if __name__ == '__main__': main()

Answer 1

I think the problem lies more in the regularity of features among the trees themselves, rather than their placement per se.

A possible solution would be to add mutations. For a global control of "stunted growth", you could suppress say 5% of the production applications. This should give sparser trees that follow the model more loosely.

For finer control, you can suppress each production with a different weight.

Check out The Algorithmic Beauty of Plants section 1.7 Stochastic L-systems for more. They use probability to select among several variants of single rule.