#/usr/bin/env python
import Tkinter, sys
from math import sqrt, pi, atan2
from cmath import exp
from optparse import OptionParser
def get_parent_indices(i, j, nbran):
return (i-1, j//nbran)
class fractal_tree:
def __init__(self, ratio=0.8, angle=pi/2., ngen=3, nbran=2):
"""
ratio: ratio of branch length with respect to previous generation
angle: fan angle, how wide spread the branches will be (0<angle<2*pi)
ngen: number of generations.
nbran: number of new branches.
"""
# coords in complex notation
self.ratio = ratio
self.angle = angle
self.ngen = ngen
self.nbran = nbran
# the root is at (0,0)
# the top of the trunk is at position (0,1), this will be the
# starting node
self.pts2xy = {(-1,0): 0j, (0,0): 1j}
self.xmax, self.ymax = 0, 1
alpha_0 = angle/2.
delta_alpha = angle / float(nbran-1)
for i in range(1, ngen):
for j in range(nbran**i):
# child
ij = (i,j)
# parent
kl = get_parent_indices(i, j, nbran)
k, l = kl
xy_kl = self.pts2xy[kl]
xy_mn = self.pts2xy[(k-1, l//nbran)]
ph_ij = atan2(xy_kl.imag - xy_mn.imag, xy_kl.real - xy_mn.real)
self.pts2xy[ij] = self.pts2xy[kl] + \
ratio**i * \
exp(1j*(ph_ij+ alpha_0 - (j%nbran)*delta_alpha))
x, y = self.pts2xy[ij].real, self.pts2xy[ij].imag
self.xmax = max(x, self.xmax)
self.ymax = max(y, self.ymax)
def get_pixel_coordinates(self, x, y, width, height):
xpix = 0.5 * width * (1 + x/self.xmax)
ypix = height * (1. - y/self.ymax)
return (xpix, ypix)
def draw(self, root, height=600):
"""
Draw the tree using Tkinter
"""
aspect_ratio = 2*self.xmax/self.ymax
width = aspect_ratio*height
canvas = Tkinter.Canvas(root, height=height, width=width,
background='white')
canvas.pack()
for i in range(0, self.ngen):
for j in range(max(1, self.nbran**i)):
ij = (i,j)
x, y = self.pts2xy[ij].real, self.pts2xy[ij].imag
xpix, ypix = self.get_pixel_coordinates(x,y,
width=width,
height=height)
# parent
kl = get_parent_indices(i,j, self.nbran)
u, v = self.pts2xy[kl].real, self.pts2xy[kl].imag
upix, vpix = self.get_pixel_coordinates(u, v,
width=width,
height=height)
canvas.create_line(upix,vpix, xpix,ypix, fill='black')
##############################################################################
def main():
parser = OptionParser()
parser.add_option('-r', '--ratio', action='store', type="float",
dest="ratio",
help='Ratio of branch length with respect to previous generation (<1.).',
default=0.5,
)
parser.add_option('-n', '--ngen', action='store', type="int",
dest="ngen",
help='Number of generations (>1).',
default=4,
)
parser.add_option('-y', '--ysize', action='store', type="int",
dest="ysize",
help='Number of vertical pixels.',
default=400,
)
parser.add_option('-a', '--angle', action='store', type="float",
dest="angle",
help='Fan angle between group of branches in deg.',
default=90,
)
parser.add_option('-N', '--Nbran', action='store', type="int",
dest="nbran",
help='Number of new branches.',
default=2,
)
options, args = parser.parse_args(sys.argv)
t = fractal_tree(ngen=options.ngen, ratio=options.ratio,
angle=options.angle*pi/180.0, nbran=options.nbran)
root = Tkinter.Tk()
t.draw(root, height=options.ysize)
root.mainloop()
if __name__=='__main__': main()
