阴影和增强标准化渲染

通过使用与幂归一化色图（gamma = 0.3）相关联的归一化重新计数，可以改善Mandelbrot集渲染。 由于阴影，渲染可以进一步增强。

maxiter给出了计算的精度。 在大多数现代笔记本电脑上，maxiter = 200应该需要几秒钟。

阴影和增强标准化渲染示例

  1. import numpy as np
  4. def mandelbrot_set(xmin, xmax, ymin, ymax, xn, yn, maxiter, horizon=2.0):
  5.     X = np.linspace(xmin, xmax, xn).astype(np.float32)
  6.     Y = np.linspace(ymin, ymax, yn).astype(np.float32)
  7.     C = X + Y[:, None] * 1j
  8.     N = np.zeros_like(C, dtype=int)
  9.     Z = np.zeros_like(C)
  10.     for n in range(maxiter):
  11.         I = np.less(abs(Z), horizon)
  12.         N[I] = n
  13.         Z[I] = Z[I]**2 + C[I]
  14.     N[N == maxiter-1] = 0
  15.     return Z, N
  18. if __name__ == '__main__':
  19.     import time
  20.     import matplotlib
  21.     from matplotlib import colors
  22.     import matplotlib.pyplot as plt
  24.     xmin, xmax, xn = -2.25, +0.75, 3000/2
  25.     ymin, ymax, yn = -1.25, +1.25, 2500/2
  26.     maxiter = 200
  27.     horizon = 2.0 ** 40
  28.     log_horizon = np.log(np.log(horizon))/np.log(2)
  29.     Z, N = mandelbrot_set(xmin, xmax, ymin, ymax, xn, yn, maxiter, horizon)
  31.     # Normalized recount as explained in:
  32.     # https://linas.org/art-gallery/escape/smooth.html
  33.     # https://www.ibm.com/developerworks/community/blogs/jfp/entry/My_Christmas_Gift
  35.     # This line will generate warnings for null values but it is faster to
  36.     # process them afterwards using the nan_to_num
  37.     with np.errstate(invalid='ignore'):
  38.         M = np.nan_to_num(N + 1 -
  39.                           np.log(np.log(abs(Z)))/np.log(2) +
  40.                           log_horizon)
  42.     dpi = 72
  43.     width = 10
  44.     height = 10*yn/xn
  45.     fig = plt.figure(figsize=(width, height), dpi=dpi)
  46.     ax = fig.add_axes([0.0, 0.0, 1.0, 1.0], frameon=False, aspect=1)
  48.     # Shaded rendering
  49.     light = colors.LightSource(azdeg=315, altdeg=10)
  50.     M = light.shade(M, cmap=plt.cm.hot, vert_exag=1.5,
  51.                     norm=colors.PowerNorm(0.3), blend_mode='hsv')
  52.     plt.imshow(M, extent=[xmin, xmax, ymin, ymax], interpolation="bicubic")
  53.     ax.set_xticks([])
  54.     ax.set_yticks([])
  56.     # Some advertisement for matplotlib
  57.     year = time.strftime("%Y")
  58.     text = ("The Mandelbrot fractal set\n"
  59.             "Rendered with matplotlib %s, %s - http://matplotlib.org"
  60.             % (matplotlib.__version__, year))
  61.     ax.text(xmin+.025, ymin+.025, text, color="white", fontsize=12, alpha=0.5)
  63.     plt.show()

Total running time of the script: ( 0 minutes 4.800 seconds)

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