fern leaf fractal

frond.py

# Iterated_function_system to draw fern leaf
# http://en.wikipedia.org/wiki/Iterated_function_system

funcs = (
lambda x, y: (0, .16*y),
lambda x, y: (.2*x-.26*y, .23*x+.22*y+1.6),
lambda x, y: (-.15*x+.28*y, .26*x+.24*y+.44),
lambda x, y: (.85*x+.04*y, -.04*x+.85*y+1.6),
)

# probability to choose re-write functions
t = (.01,.07,.07,.85)
# cumulative probability
func_probs = [sum(t[:i+1]) for i in range(len(t))]

import matplotlib.pyplot as plt
from random import random
from bisect import bisect

ITERATIONS = 100000

x, y = 0., 0.
dots = []

for i in range(ITERATIONS):
    dots.append((x, y))
    r = bisect(func_probs, random())
    f = funcs[r]
    x, y = f(x, y) # rewrite rules

xs, ys = zip(*dots)

plt.figure(1, (4,5))
ax = plt.gca()
ax.set_axis_off()    
ax.plot(xs, ys, "g.", ms=1)
ax.text(.05,.05, "My dear frond", transform=ax.transAxes) 
plt.savefig("ifs.png")