# -*- coding: utf-8 -*-

#L-System(Lindenmayer system)是一种用字符串替代产生分形图形的算法

from math import sin, cos, pi

import matplotlib.pyplot as pl

from matplotlib import collections

class L_System(object):

def __init__(self, rule):

info = rule['S']

for i in range(rule['iter']):

ninfo = []

for c in info:

if c in rule:

ninfo.append(rule[c])

else:

ninfo.append(c)

info = "".join(ninfo)

self.rule = rule

self.info = info

def get_lines(self):

d = self.rule['direct']

a = self.rule['angle']

p = (0.0, 0.0)

l = 1.0

lines = []

stack = []

for c in self.info:

if c in "Ff":

r = d * pi / 180

t = p[0] + l*cos(r), p[1] + l*sin(r)

lines.append(((p[0], p[1]), (t[0], t[1])))

p = t

elif c == "+":

d += a

elif c == "-":

d -= a

elif c == "[":

stack.append((p,d))

elif c == "]":

p, d = stack[-1]

del stack[-1]

return lines

rules = [

{

"F":"F+F--F+F", "S":"F",

"direct":180,

"angle":60,

"iter":5,

"title":"Koch"

},

{

"X":"X+YF+", "Y":"-FX-Y", "S":"FX",

"direct":0,

"angle":90,

"iter":13,

"title":"Dragon"

},

{

"f":"F-f-F", "F":"f+F+f", "S":"f",

"direct":0,

"angle":60,

"iter":7,

"title":"Triangle"

},

{

"X":"F-[[X]+X]+F[+FX]-X", "F":"FF", "S":"X",

"direct":-45,

"angle":25,

"iter":6,

"title":"Plant"

},

{

"S":"X", "X":"-YF+XFX+FY-", "Y":"+XF-YFY-FX+",

"direct":0,

"angle":90,

"iter":6,

"title":"Hilbert"

},

{

"S":"L--F--L--F", "L":"+R-F-R+", "R":"-L+F+L-",

"direct":0,

"angle":45,

"iter":10,

"title":"Sierpinski"

},

]

def draw(ax, rule, iter=None):

if iter!=None:

rule["iter"] = iter

lines = L_System(rule).get_lines()

linecollections = collections.LineCollection(lines)

ax.add_collection(linecollections, autolim=True)

ax.axis("equal")

ax.set_axis_off()

ax.set_xlim(ax.dataLim.xmin, ax.dataLim.xmax)

ax.invert_yaxis()

fig = pl.figure(figsize=(7,4.5))

fig.patch.set_facecolor("w")

for i in range(6):

ax = fig.add_subplot(231+i)

draw(ax, rules[i])

fig.subplots_adjust(left=0,right=1,bottom=0,top=1,wspace=0,hspace=0)

pl.show()