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)