True-color Mandelbrot Fractal. It uses |x|, |y|, |z|, |angle(z)| values of the final iteration point for coloring.
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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 38 39 40 41 42 43 44 45 | # True-color Mandelbrot Fractal
# FB36 - 20130113
import math
from PIL import Image
imgx = 800; imgy = 800
image = Image.new("RGB", (imgx, imgy))
pixels = image.load()
xa = -2.0; xb = 1.0
ya = -1.5; yb = 1.5
maxIt = 256 # of iterations
# find max values for |x|, |y|, |z|
maxAbsX = 0.0; maxAbsY = 0.0; maxAbsZ = 0.0
for ky in range(imgy):
b = ky * (yb - ya) / (imgy - 1) + ya
for kx in range(imgx):
a = kx * (xb - xa) / (imgx - 1) + xa
c = complex(a, b); z = c
for i in range(maxIt):
z = z * z + c
if abs(z) > 2.0: break
if abs(z.real) > maxAbsX: maxAbsX = abs(z.real)
if abs(z.imag) > maxAbsY: maxAbsY = abs(z.imag)
if abs(z) > maxAbsZ: maxAbsZ = abs(z)
# paint
for ky in range(imgy):
b = ky * (yb - ya) / (imgy - 1) + ya
for kx in range(imgx):
a = kx * (xb - xa) / (imgx - 1) + xa
c = complex(a, b); z = c
for i in range(maxIt):
z = z * z + c
if abs(z) > 2.0: break
v0 = int(255 * abs(z.real) / maxAbsX)
v1 = int(255 * abs(z.imag) / maxAbsY)
v2 = int(255 * abs(z) / maxAbsZ)
v3 = int(255 * abs(math.atan2(z.imag, z.real)) / math.pi)
v = v3 * 256 ** 3 + v2 * 256 ** 2 + v1 * 256 + v0
colorRGB = int(16777215 * v / 256 ** 4)
red = int(colorRGB / 65536)
grn = int(colorRGB / 256) % 256
blu = colorRGB % 256
pixels[kx, ky] = (red, grn, blu)
image.save("MandelbrotFractal.png", "PNG")
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