毕达哥拉斯树与python代码

毕达哥拉斯树与python代码

这棵树叫“毕达哥拉斯树”(Pythagorean Tree)。因为它是相对勾股定理而言的，我们也可以称之为“勾股树”。作者使用了Python 的“PYX package”来产生图片，然后用GIMP产生动太的GIF。下面是作者公布的一个简化了的程序：

from math import acos, sin, cos, pi, sqrt

from pyx import *

import os

def draw_layer(color):

global c

for square in layer:

if square[1] > .0001:

c.stroke(rect, [ deco.filled([color]), color,

trafo.translate(square[0][0],square[0][1]) *

trafo.rotate(square[2]*180/pi) *

trafo.scale(square[1]) ])

def next_left():

return set( [ ((t[0]-s*sin(r), t[1]+s*cos(r)), s*ls, r+theta ) for (t,s,r) in layer ] )

def next_right():

return set( [ ((t[0]+s*(ls*cos(r+theta)-sin(r)),

t[1]+s*(cos(r)+ls*sin(r+theta))),

s*rs, r-phi )

for (t,s,r) in layer ] )

if __name__ == "__main__":

## INITIALIZE

N = 15 # NUMBER OF LAYERS

imgname = 'Ptree_7-7' # IMAGE NAME

ls = .7 # LEFT BRANCH SIZE

rs = .7 # RIGHT BRANCH SIZE ; ls+rs >= 1 theta = acos( (ls**2-rs**2+1) / (2*ls) )

phi = acos( (rs**2-ls**2+1) / (2*rs) )

layer = set([ ((0.0,0.0), 1.0, 0.0) ])

c = canvas.canvas()

rect = path.rect(0,0,1,1)

for i in xrange(N-1):

draw_layer(color.cmyk.RawSienna)

layer = next_left() | next_right()

print 'Layer', i+1

draw_layer(color.rgb.green)

c.writePDFfile(imgname)