This is a modification of code posted at http://code.activestate.com/recipes/577715/ (r3)
The original code produces a png image using the PIL module. It generates a Random 2D Slice of a 4D Mandelbrot Fractal.
This extends the program into 3D with Visual Python 5.4, running under Python 2.7.1
Changing vp_flag from 0 to 1 will restore program to original functionality. The program is interactive with keys q,w,e,r and x used to control visual points object.
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# Random 2D Slice Of 4D Mandelbrot Fractal
# FB - 201105231
"""Random 2D Slice Of 4D Mandelbrot Fractal.
Modified by Symion 2011
Now works with Visual Python v5.40.
Produce 2D slice of 4D Mandelbrot Fractal and Map it in 3D!
Visual Python Controls:
Click Left Mouse Key = Navigate
Press Right Mouse Key = Spin
Press Both Keys = Zoom
q = Point size - 1
w = Point size + 1
e = Point shape + 1
r = Scene Alignment
"""
vp_flag = 0
if vp_flag == 0:
from visual import *
else:
import random
from math import *
from PIL import Image
imgx = 512
imgy = 512
forge = 0
pcc = 0
pii = 0
psize = 3
pshape = 0
if vp_flag == 0:
scene.width=imgx
scene.height=imgy
image = [points(size=psize, shape="square")]
forward = vector(scene.forward)
print "Number of Points objects: {0}".format(len(image))
else:
image = Image.new("RGB", (imgx, imgy))
#
print __doc__
# drawing area (xa < xb & ya < yb)
xa = -2.0
xb = 2.0
ya = -2.0
yb = 2.0
maxIt = 32 # max number of iterations allowed
maxit = maxIt / 2.0
if True:
# random rotation angles to convert 2d plane to 4d plane
xy = random.random() * 2.0 * pi
xz = random.random() * 2.0 * pi
xw = random.random() * 2.0 * pi
yz = random.random() * 2.0 * pi
yw = random.random() * 2.0 * pi
zw = random.random() * 2.0 * pi
else:
# default rotation angles
xy=1.3536589728
xz=2.30808965705
xw=3.50029464114
yz=3.37449518258
yw=4.23401560176
zw=2.44695022478
sxy = sin(xy)
cxy = cos(xy)
sxz = sin(xz)
cxz = cos(xz)
sxw = sin(xw)
cxw = cos(xw)
syz = sin(yz)
cyz = cos(yz)
syw = sin(yw)
cyw = cos(yw)
szw = sin(zw)
czw = cos(zw)
origx = (xa + xb) / 2.0
origy = (ya + yb) / 2.0
for ky in range(imgy):
b = ky * (yb - ya) / (imgy - 1) + ya
for kx in range(imgx):
a = kx * (xb - xa) / (imgx - 1) + xa
x = a
y = b
z = 0 # c = 0
w = 0 # d = 0
# 4d rotation around center of the plane
x = x - origx
y = y - origy
x0 = x * cxy - y * sxy
y = x * sxy + y * cxy
x = x0 # xy-plane rotation
x0 = x * cxz - z * sxz
z = x * sxz + z * cxz
x = x0 # xz-plane rotation
x0 = x * cxw - z * sxw
w = x * sxw + z * cxw
x = x0 # xw-plane rotation
y0 = y * cyz - z * syz
z = y * syz + z * cyz
y = y0 # yz-plane rotation
y0 = y * cyw - w * syw
w = y * syw + w * cyw
y = y0 # yw-plane rotation
z0 = z * czw - w * szw
w = z * szw + w * czw
z = z0 # zw-plane rotation
x = x + origx
y = y + origy
if forge:
for i in range(maxIt):
# iteration using quaternion numbers
x0 = x * x - y * y - z * z - w * w + a
y = 2.0 * x * y + b
z = 2.0 * x * z
w = 2.0 * x * w
x = x0
s = x * x + y * y + z * z + w * w # 4d absolute value squared
if s > 4.0:
break
else:
for i in range(maxIt):
# iteration using hyper-complex numbers
x0 = x * x - y * y - z * z - w * w + a
y0 = 2.0 * x * y - 2.0 * z * w + b
z0 = 2.0 * x * z - 2.0 * y * w
w = 2.0 * x * w + 2.0 * z * y
x = x0
y = y0
z = z0
s = x * x + y * y + z * z + w * w # 4d absolute value squared
if s > 4.0:
break
pcc += i
pii += 1
if (i%maxIt) != 0:
if vp_flag == 0:
if len(image[-1].pos) > 9999:
image.append(points(size=psize, shape="square"))
print "Number of Points objects: {0}".format(len(image))
c = (i/maxit, i/maxit, i/maxit)
image[-1].append((kx-256, ky-256, i/maxit))
image[-1].color[-1] = c
else:
image.putpixel((kx, ky), (i % 4 * 64, i % 8 * 32, i % 16 * 16))
if vp_flag == 0:
scene.autoscale=False
scene.range=mag(scene.mouse.camera)/sqrt(3)
scene.visible = True
else:
image.save("4D_Mandelbrot_Fractal.png", "PNG")
print "Finished!"
print "{0} / {1} = {2}".format(pcc, pii, pcc / pii)
mess = "Base Set:\nxy={0}, xz={1}, xw={2}, yz={3}, yw={4}, zw={5}"
print mess.format(xy, xz, xw, yz, yw, zw)
if vp_flag == 0:
while 1:
if scene.mouse.events>0:
mk = scene.mouse.getevent()
if mk.release == "left":
scene.center = mk.pos
elif scene.kb.keys:
km = scene.kb.getkey()
if km in ["x", "X"]:
break
elif km in ["w"]:
psize = psize%50
psize += 1
for a in image:
a.size = psize
elif km in ["q"]:
psize -= 1
if psize<1:
psize = 50
for a in image:
a.size = psize
elif km in ["e"]:
pshape = (pshape+1)%2
for a in image:
a.shape = ["square","round"][pshape]
elif km in ["r"]:
scene.forward = forward
|
Mapping fractals into 3D with visual python points object produces interesting topologies.
