如何绘制 Buddhabrot 分形？

Question

我正在尝试在 Python 中实现 Buddhabrot 分形。我阅读了很多文章和帖子，但我认为我误解了一些东西（只看图片）。有人可以写个伪代码吗？

我的代码是这样的：

from multiprocessing import Pool
from random import randrange
import matplotlib.pyplot as plt
import numpy as np
from math import ceil


maxiter       = 1000
points        = 1000
xmin, xmax    = -2, 1
ymin, ymax    = -2, 1
cores         = 4
width, height = 200, 200


maxn         = width * height
incrx, incry = abs(xmax - xmin) / width, abs(ymax - ymin) / height

def randomComplexGenerator():
  for i in range(points):
    n = randrange(maxn)
    yield complex(n // height * incrx, n % width * incry)

def buddhabrot(c):
  m, z, i = np.zeros((width, height)), c, 0
  while i < maxiter and abs(z) < 2:
    x, y     = ceil(z.real / incrx), ceil(z.imag / incry)
    m[x, y] += 1
    z        = z ** 2 + c
    i       += 1
  return m if i == maxiter else 0

if __name__ == '__main__':
  a = np.linspace(xmin, xmax, width)
  b = np.linspace(ymin, ymax, height)
  with Pool(cores) as p:
    ms = p.map(buddhabrot, (c for c in randomComplexGenerator()))
  res = 0
  for m in ms:
    res += m
  plt.axis('off')
  plt.imshow(res)
  plt.show()

用我的代码生成的图像是这样的（lel）：

Answer 1

几天后，这是我创建的代码，它似乎适当地生成了分形。欢迎任何性能建议。

from multiprocessing import Pool
from random import randrange
import matplotlib.pyplot as plt
import numpy as np


cores         = 4
maxiter       = 10000
points        = 1000000
width, height = 200, 200
rdom, idom    = (-2, 2), (-2, 2)

xdom, ydom    = (0, width - 1), (0, height - 1)

def randomComplex():
  r = np.interp(randrange(xdom[0], xdom[1]), xdom, rdom)
  i = np.interp(randrange(ydom[0], ydom[1]), ydom, idom)
  return (r, i)

def complex2pixel(c):
  x = int(np.interp(c[0], rdom, xdom))
  y = int(np.interp(c[1], idom, ydom))
  return (x, y)

def escapedPixels(c):
  pixels, z = {}, c
  for i in range(maxiter):
    z2 = (z[0] * z[0], z[1] * z[1]) 
    if z2[0] + z2[1] > 4: break
    p = complex2pixel(z)
    try: pixels[p] += 1
    except: pixels[p] = 1
    z = (z2[0] - z2[1] + c[0], 2 * z[0] * z[1] + c[1])
  return pixels if i < maxiter - 1 else {}

if __name__ == '__main__':
  with Pool(cores) as p:
    ds = p.map(escapedPixels, (randomComplex() for i in range(points)))
  m = np.zeros((width, height))
  for d in ds:
    for p in d:
      m[p] += d[p]
  plt.axis('off')
  plt.imshow(m)
  plt.show()

如何绘制 Buddhabrot 分形？

How to draw Buddhabrot fractal?

python

fractals