Nate ♥s L-systems

1 screencast_1.py

class LSystem(object):
    def __init__(self, axiom, rules):
        self.axiom = axiom
        self.rules = rules

        self.string = self.axiom
        self.generation = 0

    def reset(self):
        self.string = self.axiom
        self.generation = 0

    def print_system(self):
        print u"n = {} : '{}'".format(self.generation, self.string)

    def step(self):
        self.string = ''.join([self.rules[char] for char in self.string])
        self.generation += 1


ALGEA_AXIOM = 'A'
ALGAE_RULE = {
    'A': 'AB',
    'B': 'A',
}

system = LSystem(ALGEA_AXIOM, ALGAE_RULE)
for _ in xrange(10):
    system.print_system()
    system.step()

2 screencast_3.py

# -*- coding: utf-8 -*-
# 
# Turtle documentation resources:
#   * Reference: https://docs.python.org/2/library/turtle.html
#   * Examples: https://michael0x2a.com/blog/turtle-examples
# 
import turtle


class LSystem(object):
    def __init__(self, axiom, rules):
        self.axiom = axiom
        self.rules = rules

        self.string = self.axiom
        self.generation = 0

    def reset(self):
        self.string = self.axiom
        self.generation = 0

    def step(self):
        self.string = ''.join([self.rules.get(char, char) for char in self.string])
        self.generation += 1

    def print_system(self):
        print u"n = {} : '{}'".format(self.generation, self.string)


def interpret_koch_curve(string):
    """Turns an l-system string into a turtle drawing."""
    t = turtle.Turtle()
    t.speed(10)
    t.screen.setworldcoordinates(-10, -10, 1000, 1000)

    # F means "draw forward", + means "turn left 90°", and − means "turn right 90°"
    for char in string:
        if char == 'F':
            t.forward(20)
        elif char == '+':
            t.left(90)
        elif char == '-':
            t.right(90)

    turtle.done()


KOCH_AXIOM = 'F'
KOCH_RULES = {
    'F': 'F+F-F-F+F'
}

koch = LSystem(KOCH_AXIOM, KOCH_RULES)
koch.print_system()
for _ in xrange(3):
    koch.step()
    koch.print_system()

interpret_koch_curve(koch.string)

3 fancy_fractal_lsystem.py

# -*- coding: utf-8 -*-
import turtle


class LSystem(object):
    def __init__(self, axiom, rules):
        self.axiom = axiom
        self.rules = rules

        self.string = self.axiom
        self.generation = 0

    def reset(self):
        self.string = self.axiom
        self.generation = 0

    def step(self):
        self.string = ''.join([self.rules.get(char, char) for char in self.string])
        self.generation += 1

    def print_system(self):
        print u"n = {} : '{}'".format(self.generation, self.string)


FRACTAL_AXIOM = 'X'
FRACTAL_RULES = {
    'X': 'F-[[X]+X]+F[+FX]-X',
    'F': 'FF',
}


def interpret_fractal_system(string):
    """Turns an l-system string into a fractal drawing."""
    # * F means "draw forward"
    # * − means "turn left 25°"
    # * + means "turn right 25°".
    # * X does not correspond to any drawing action and is used to
    #   control the evolution of the curve.
    # * [ corresponds to saving the current values for position and angle,
    #   which are restored when the corresponding ] is executed.
    t = turtle.Turtle()
    t.speed(10)
    t.screen.setworldcoordinates(-10, -1000, 1000, 1000)

    # The list of saved positions and angles, saved by the '[' command.
    stack = []

    for char in string:
        if char == 'F':
            t.forward(20)
        elif char == '+':
            t.right(25)
        elif char == '-':
            t.left(25)
        elif char == '[':
            state = (t.xcor(), t.ycor(), t.heading())
            stack.append(state)
        elif char == ']':
            x_coord, y_coord, heading = stack.pop()

            # Stop drawing, move the pen, start drawing again.
            t.penup()
            t.setx(x_coord)
            t.sety(y_coord)
            t.setheading(heading)
            t.pendown()
        else:
            pass

    turtle.done()



fractal = LSystem(FRACTAL_AXIOM, FRACTAL_RULES)
fractal.print_system()
for _ in xrange(4):
    fractal.step()
    fractal.print_system()

interpret_fractal_system(fractal.string)