mandelbrot-bifurcation.py

#!/usr/bin/env python3

import numpy as np
from PIL import Image, ImageColor # pillow fork of PIL

height, width = 599, 750
grid = np.ogrid[-1.0:1.0:1j*height, -2.0:.5:1j*width]
c = grid[1] + 1j * grid[0]
z = c.copy()

logisticmap = np.zeros((height, width), dtype=np.uint8)
x = np.arange(width, dtype=np.int64)

for iterate in range(500):
    mandelbrot = abs(z) < 50.0
    np.putmask(z, mandelbrot, z*z + c)

    realaxis = z[height // 2 ].real
    y = np.int16( 0.15 * (4.5 - realaxis) * (height - 1))
    np.clip(y, 0, height - 1, y)
    if iterate > 100:
        logisticmap[y,x]  = 1

colors = ("white","black","red", "black")
rgbcolors = np.uint8(list(map(ImageColor.getrgb, colors)))
rgb = rgbcolors[logisticmap + 2 * mandelbrot]
image = Image.fromarray(rgb, mode="RGB")
image.save('mandelbrot-bifurcation.png')
image.show()