""" =================================== Shaded & power normalized rendering =================================== The Mandelbrot set rendering can be improved by using a normalized recount associated with a power normalized colormap (gamma=0.3). Rendering can be further enhanced thanks to shading. The ``maxiter`` gives the precision of the computation. ``maxiter=200`` should take a few seconds on most modern laptops. """ import numpy as np def mandelbrot_set(xmin, xmax, ymin, ymax, xn, yn, maxiter, horizon=2.0): X = np.linspace(xmin, xmax, xn).astype(np.float32) Y = np.linspace(ymin, ymax, yn).astype(np.float32) C = X + Y[:, None] * 1j N = np.zeros_like(C, dtype=int) Z = np.zeros_like(C) for n in range(maxiter): I = abs(Z) < horizon N[I] = n Z[I] = Z[I]**2 + C[I] N[N == maxiter-1] = 0 return Z, N if __name__ == '__main__': import time import matplotlib from matplotlib import colors import matplotlib.pyplot as plt xmin, xmax, xn = -2.25, +0.75, 3000 // 2 ymin, ymax, yn = -1.25, +1.25, 2500 // 2 maxiter = 200 horizon = 2.0 ** 40 log_horizon = np.log2(np.log(horizon)) Z, N = mandelbrot_set(xmin, xmax, ymin, ymax, xn, yn, maxiter, horizon) # Normalized recount as explained in: # https://linas.org/art-gallery/escape/smooth.html # https://web.archive.org/web/20160331171238/https://www.ibm.com/developerworks/community/blogs/jfp/entry/My_Christmas_Gift?lang=en # This line will generate warnings for null values but it is faster to # process them afterwards using the nan_to_num with np.errstate(invalid='ignore'): M = np.nan_to_num(N + 1 - np.log2(np.log(abs(Z))) + log_horizon) dpi = 72 width = 10 height = 10*yn/xn fig = plt.figure(figsize=(width, height), dpi=dpi) ax = fig.add_axes([0, 0, 1, 1], frameon=False, aspect=1) # Shaded rendering light = colors.LightSource(azdeg=315, altdeg=10) M = light.shade(M, cmap=plt.cm.hot, vert_exag=1.5, norm=colors.PowerNorm(0.3), blend_mode='hsv') ax.imshow(M, extent=[xmin, xmax, ymin, ymax], interpolation="bicubic") ax.set_xticks([]) ax.set_yticks([]) # Some advertisement for matplotlib year = time.strftime("%Y") text = ("The Mandelbrot fractal set\n" "Rendered with matplotlib %s, %s - https://matplotlib.org" % (matplotlib.__version__, year)) ax.text(xmin+.025, ymin+.025, text, color="white", fontsize=12, alpha=0.5) plt.show()