# Random Spiral Fractals
# FB36 - 20130929
import math
import random
from collections import deque
from PIL import Image
imgx = 512; imgy = 512
image = Image.new("RGB", (imgx, imgy))
pixels = image.load()
xa = -1.5; xb = 1.5; ya = -1.5; yb = 1.5 # view
n = random.randint(2, 9) # of spiral arms
a = 2.0 * math.pi / n # angle between arms
t = 2.0 * math.pi * random.random() # rotation angle of central copy
r1 = 0.1 * random.random() + 0.1 # scale factor of outmost copies of the spiral arms
r0 = 1.0 - r1 # scale factor of central copy
ts = math.sin(t) * r0; tc = math.cos(t) * r0
maxIt = 64 # max number of iterations allowed
for ky in range(imgy):
print str(100 * ky / (imgy - 1)).zfill(3) + "%"
for kx in range(imgx):
x = float(kx) / (imgx - 1) * (xb - xa) + xa
y = float(ky) / (imgy - 1) * (yb - ya) + ya
queue = deque([])
queue.append((x, y, 0))
while len(queue) > 0: # iterate points until none left
(x, y, i) = queue.popleft()
# apply all (inverse) IFS transformations
for k in range(n + 1): # n outmost copies + central copy
if k == n: # central copy
# inverse rotation and scaling
xnew = (y + x * tc / ts) / (ts + tc * tc / ts)
ynew = (y - x / tc * ts) / (tc + ts / tc * ts)
else: # outmost copies on the spiral arms
c = k * a # angle
# inverse scaling and translation
xnew = (x - math.cos(c)) / r1
ynew = (y - math.sin(c)) / r1
if xnew >= xa and xnew <= xb and ynew >= ya and ynew <= yb:
if i + 1 == maxIt: break
queue.append((xnew, ynew, i + 1))
pixels[kx, ky] = (i % 16 * 16 , i % 8 * 32, i % 4 * 64)
image.save("RandomSpiralFractal_" + str(n) + ".png", "PNG")
Diff to Previous Revision
--- revision 1 2013-09-14 23:51:33
+++ revision 2 2013-09-29 05:35:20
@@ -1,27 +1,20 @@
# Random Spiral Fractals
-# FB36 - 20130914
+# FB36 - 20130929
import math
import random
from collections import deque
from PIL import Image
-imgx = 1024; imgy = 1024
+imgx = 512; imgy = 512
image = Image.new("RGB", (imgx, imgy))
pixels = image.load()
-xa = -1.5; xb = 1.5
-ya = -1.5; yb = 1.5
-n = random.randint(2, 9) # of spiral arms
-m = random.randint(6, 12) # of spirals in each arm
-a = 2.0 * math.pi / n # angle between arms
-b = 2.0 * math.pi * random.random() # max rotation (bending) angle for each arm
-rmax = 0.1 * random.random() + 0.1 # max spiral radius on each arm
-maxIt = 8 # max number of iterations allowed
-# create random color palette
-rd = []; gr = []; bl = []
-for c in range(maxIt):
- rd.append(random.randint(0, 255))
- gr.append(random.randint(0, 255))
- bl.append(random.randint(0, 255))
-
+xa = -1.5; xb = 1.5; ya = -1.5; yb = 1.5 # view
+n = random.randint(2, 9) # of spiral arms
+a = 2.0 * math.pi / n # angle between arms
+t = 2.0 * math.pi * random.random() # rotation angle of central copy
+r1 = 0.1 * random.random() + 0.1 # scale factor of outmost copies of the spiral arms
+r0 = 1.0 - r1 # scale factor of central copy
+ts = math.sin(t) * r0; tc = math.cos(t) * r0
+maxIt = 64 # max number of iterations allowed
for ky in range(imgy):
print str(100 * ky / (imgy - 1)).zfill(3) + "%"
for kx in range(imgx):
@@ -32,16 +25,18 @@
while len(queue) > 0: # iterate points until none left
(x, y, i) = queue.popleft()
# apply all (inverse) IFS transformations
- for k in range(n): # of arm
- for j in range(m): # of a spiral on the arm
- c = k * a + b * (j + 1.0) / m # angle of the spiral in the arm
- d = (j + 1.0) / m # distance of the spiral to the center
- r = d * rmax # radius of the spiral in the arm
- if r != 0.0:
- xnew = (x - math.sin(c) * d) / r
- ynew = (y - math.cos(c) * d) / r
- if xnew >= xa and xnew <= xb and ynew >= ya and ynew <= yb:
- if i + 1 == maxIt: break
- queue.append((xnew, ynew, i + 1))
- pixels[kx, ky] = (rd[i], gr[i], bl[i])
-image.save("RandomSpiralFractal_" + str(n) + "_" + str(m) + ".png", "PNG")
+ for k in range(n + 1): # n outmost copies + central copy
+ if k == n: # central copy
+ # inverse rotation and scaling
+ xnew = (y + x * tc / ts) / (ts + tc * tc / ts)
+ ynew = (y - x / tc * ts) / (tc + ts / tc * ts)
+ else: # outmost copies on the spiral arms
+ c = k * a # angle
+ # inverse scaling and translation
+ xnew = (x - math.cos(c)) / r1
+ ynew = (y - math.sin(c)) / r1
+ if xnew >= xa and xnew <= xb and ynew >= ya and ynew <= yb:
+ if i + 1 == maxIt: break
+ queue.append((xnew, ynew, i + 1))
+ pixels[kx, ky] = (i % 16 * 16 , i % 8 * 32, i % 4 * 64)
+image.save("RandomSpiralFractal_" + str(n) + ".png", "PNG")
