Use python to generate nice and famous fractals

fractals.py

import sys
import turtle


# -- Settings

sys.setrecursionlimit(100000)

wn = turtle.Screen()
wn.bgcolor('black')

cursor = turtle.Turtle()
cursor.color('white')
cursor.pensize(2)
cursor.speed(90000000)
cursor.pila = []


def fixPosition():
  cursor.pila.append(list(cursor.position()) + [cursor.heading()])


def backToPosition():
  if not len(cursor.pila) is 0:
    toPosition(cursor.pila[-1][0], cursor.pila[-1][1])
    cursor.setheading(cursor.pila[-1][2])
    cursor.pila.pop()
  return


def toPosition(x, y):
  cursor.up()
  cursor.goto(x, y)
  cursor.down()
  return 

fractal = {
  'koch': {
    'constants': {
      'F': 'cursor.forward(5)',
      '+': 'cursor.left(90)',
      '-': 'cursor.right(90)'
    },
    'initialState': 'F',
    'rules': {
      'F':  'F+F-F-F+F'
    },
    'steps': 4
  },
  'koch2': {
    'constants': {
      'F': 'cursor.forward(5)',
      '+': 'cursor.left(90)',
      '-': 'cursor.right(90)'
    },
    'initialState': 'F+F+F+F',
    'rules': {
      'F':  'F+F-F-FF+F+F-F'
    },
    'steps': 3
  },
  'cesaro': {
    'constants': {
      'F': 'cursor.forward(7)',
      '+': 'cursor.right(85)',
      '-': 'cursor.left(85)'
    },
    'initialState': 'F',
    'rules': {
      'F':  'F-F++F-F'
    },
    'steps': 6
  },
  'sierpinski': {
    'constants': {
      'A': 'cursor.forward(4)',
      'B': 'cursor.forward(4)',
      '+': 'cursor.left(60)',
      '-': 'cursor.right(60)'
    },
    'initialState': 'A',
    'rules': {
      'A':  'B-A-B',
      'B':  'A+B+A'
    },
    'steps': 6
  },
  'sierpinski2': {
    'constants': {
      'F': 'cursor.forward(7)',
      'G': 'cursor.forward(7)',
      '+': 'cursor.right(120)',
      '-': 'cursor.left(120)'
    },
    'initialState': 'F-G-G',
    'rules': {
      'F':  'F-G+F+G-F',
      'G':  'GG'
    },
    'steps': 5
  },
  'dragon': {
    'constants': {
      'X': 'cursor.color("white")',
      'Y': 'cursor.color("white")',
      'F': 'cursor.forward(5)',
      '+': 'cursor.right(90)',
      '-': 'cursor.left(90)'
    },
    'initialState': 'FX',
    'rules': {
      'X':  'X+YF',
      'Y':  'FX-Y'
    },
    'steps': 15
  },
  'plant': {
    'constants': {
      'F': 'cursor.forward(5)',
      'X': 'cursor.color("white")',
      '+': 'cursor.right(25)',
      '-': 'cursor.left(25)',
      '[': 'fixPosition()',
      ']': 'backToPosition()'
    },
    'initialState': 'X',
    'rules': {
      'X': 'F-[[X]+X]+F[+FX]-X',
      'F': 'FF'
    },
    'steps': 6
  },
  'plant2': {
    'constants': {
      'F': 'cursor.forward(2)',
      'X': 'cursor.color("white")',
      '+': 'cursor.right(25.7)',
      '-': 'cursor.left(25.7)',
      '[': 'fixPosition()',
      ']': 'backToPosition()'
    },
    'initialState': 'X',
    'rules': {
      'X': 'F[+X][-X]FX',
      'F': 'FF'
    },
    'steps': 5
  },
}


def chainGeneration(fractalName='koch', s='', step=0):
  if s is '':
    return chainGeneration(fractalName,
               fractal[fractalName]['initialState'],
               step - 1)
  if step >= 0:
    rules = fractal[fractalName]['rules']
    L = [rules[c] if c in rules else c for c in s]
    L = ''.join(L) 
    return chainGeneration(fractalName, L, step - 1)
  return s


def paintChain(fractalName='koch', s=''):
  print "steps: ", len(s)
  for c in s:
    eval(fractal[fractalName]["constants"][c])
  return 


drawFractal = 'koch'
toPosition(0, 0)
cursor.left(90)
for i in range(1):
  c = chainGeneration(
      fractalName = drawFractal,
      step = fractal[drawFractal]['steps']
      )
  paintChain(fractalName=drawFractal, s=c)
  toPosition(-50 * i, -50 * i)
  print "Done", i
turtle.exitonclick()