# 繪制L-System的分形圖 相關文檔： [_L-System分形_](fractal_chaos.html#sec-lsystem)  ``` # -*- coding: utf-8 -*- #L-System(Lindenmayer system)是一種用字符串替代產生分形圖形的算法 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 xrange(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() ```