Created
August 28, 2019 05:34
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Lindenmayer system
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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 = [ | |
{ | |
"S":"F", "F":"F+F--F+F", | |
"direct":180, | |
"angle":60, | |
"iter":5, | |
"title":"Koch curve" | |
}, | |
{ | |
"S":"F--F--F", "F":"F+F--F+F", | |
"direct":180, | |
"angle":60, | |
"iter":5, | |
"title":"Koch snowflake" | |
}, | |
{ | |
"X":"X+YF+", "Y":"-FX-Y", "S":"FX", | |
"direct":0, | |
"angle":90, | |
"iter":11, | |
"title":"Dragon" | |
}, | |
{ | |
"f":"F-f-F", "F":"f+F+f", "S":"f", | |
"direct":0, | |
"angle":60, | |
"iter":7, | |
"title":"Sierpinski 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":5, | |
"title":"Hilbert" | |
} | |
] | |
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("papayawhip") | |
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() |
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