It draws the Newton fractal of any given complex-variable function.
Python, 37 lines
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | # Newton fractals
# FB - 201003291
from PIL import Image
imgx = 512
imgy = 512
image = Image.new("RGB", (imgx, imgy))
# drawing area
xa = -1.0
xb = 1.0
ya = -1.0
yb = 1.0
maxIt = 20 # max iterations allowed
h = 1e-6 # step size for numerical derivative
eps = 1e-3 # max error allowed
# put any complex function here to generate a fractal for it!
def f(z):
return z * z * z - 1.0
# draw the fractal
for y in range(imgy):
zy = y * (yb - ya) / (imgy - 1) + ya
for x in range(imgx):
zx = x * (xb - xa) / (imgx - 1) + xa
z = complex(zx, zy)
for i in range(maxIt):
# complex numerical derivative
dz = (f(z + complex(h, h)) - f(z)) / complex(h, h)
z0 = z - f(z) / dz # Newton iteration
if abs(z0 - z) < eps: # stop when close enough to any root
break
z = z0
image.putpixel((x, y), (i % 4 * 64, i % 8 * 32, i % 16 * 16))
image.save("newtonFr.png", "PNG")
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