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Revision d08cec6d62394c2b5cc0986a59354fc09868ec1e authored by Georg Brandl on 26 June 2012, 07:43:40 UTC, committed by Georg Brandl on 26 June 2012, 07:43:40 UTC
1 parent dba3b5c
Tip revision: d08cec6d62394c2b5cc0986a59354fc09868ec1e authored by Georg Brandl on 26 June 2012, 07:43:40 UTC
Bump version to 3.3.0b1.
Bump version to 3.3.0b1.
Tip revision: d08cec6
penrose.py
#!/usr/bin/env python3
""" xturtle-example-suite:
xtx_kites_and_darts.py
Constructs two aperiodic penrose-tilings,
consisting of kites and darts, by the method
of inflation in six steps.
Starting points are the patterns "sun"
consisting of five kites and "star"
consisting of five darts.
For more information see:
http://en.wikipedia.org/wiki/Penrose_tiling
-------------------------------------------
"""
from turtle import *
from math import cos, pi
from time import clock, sleep
f = (5**0.5-1)/2.0 # (sqrt(5)-1)/2 -- golden ratio
d = 2 * cos(3*pi/10)
def kite(l):
fl = f * l
lt(36)
fd(l)
rt(108)
fd(fl)
rt(36)
fd(fl)
rt(108)
fd(l)
rt(144)
def dart(l):
fl = f * l
lt(36)
fd(l)
rt(144)
fd(fl)
lt(36)
fd(fl)
rt(144)
fd(l)
rt(144)
def inflatekite(l, n):
if n == 0:
px, py = pos()
h, x, y = int(heading()), round(px,3), round(py,3)
tiledict[(h,x,y)] = True
return
fl = f * l
lt(36)
inflatedart(fl, n-1)
fd(l)
rt(144)
inflatekite(fl, n-1)
lt(18)
fd(l*d)
rt(162)
inflatekite(fl, n-1)
lt(36)
fd(l)
rt(180)
inflatedart(fl, n-1)
lt(36)
def inflatedart(l, n):
if n == 0:
px, py = pos()
h, x, y = int(heading()), round(px,3), round(py,3)
tiledict[(h,x,y)] = False
return
fl = f * l
inflatekite(fl, n-1)
lt(36)
fd(l)
rt(180)
inflatedart(fl, n-1)
lt(54)
fd(l*d)
rt(126)
inflatedart(fl, n-1)
fd(l)
rt(144)
def draw(l, n, th=2):
clear()
l = l * f**n
shapesize(l/100.0, l/100.0, th)
for k in tiledict:
h, x, y = k
setpos(x, y)
setheading(h)
if tiledict[k]:
shape("kite")
color("black", (0, 0.75, 0))
else:
shape("dart")
color("black", (0.75, 0, 0))
stamp()
def sun(l, n):
for i in range(5):
inflatekite(l, n)
lt(72)
def star(l,n):
for i in range(5):
inflatedart(l, n)
lt(72)
def makeshapes():
tracer(0)
begin_poly()
kite(100)
end_poly()
register_shape("kite", get_poly())
begin_poly()
dart(100)
end_poly()
register_shape("dart", get_poly())
tracer(1)
def start():
reset()
ht()
pu()
makeshapes()
resizemode("user")
def test(l=200, n=4, fun=sun, startpos=(0,0), th=2):
global tiledict
goto(startpos)
setheading(0)
tiledict = {}
a = clock()
tracer(0)
fun(l, n)
b = clock()
draw(l, n, th)
tracer(1)
c = clock()
print("Calculation: %7.4f s" % (b - a))
print("Drawing: %7.4f s" % (c - b))
print("Together: %7.4f s" % (c - a))
nk = len([x for x in tiledict if tiledict[x]])
nd = len([x for x in tiledict if not tiledict[x]])
print("%d kites and %d darts = %d pieces." % (nk, nd, nk+nd))
def demo(fun=sun):
start()
for i in range(8):
a = clock()
test(300, i, fun)
b = clock()
t = b - a
if t < 2:
sleep(2 - t)
def main():
#title("Penrose-tiling with kites and darts.")
mode("logo")
bgcolor(0.3, 0.3, 0)
demo(sun)
sleep(2)
demo(star)
pencolor("black")
goto(0,-200)
pencolor(0.7,0.7,1)
write("Please wait...",
align="center", font=('Arial Black', 36, 'bold'))
test(600, 8, startpos=(70, 117))
return "Done"
if __name__ == "__main__":
msg = main()
mainloop()
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