41 lines
1.3 KiB
Python
41 lines
1.3 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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d, h = 800, 500 # pixel density (= image width) and image height
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n, r = 200, 500 # number of iterations and escape radius (r > 2)
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x = np.linspace(0, 2, num=d+1)
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y = np.linspace(0, 2 * h / d, num=h+1)
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A, B = np.meshgrid(x - 1, y - h / d)
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C = 2.0 * (A + B * 1j) - 0.5
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Z, dZ = np.zeros_like(C), np.zeros_like(C)
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D, S, T = np.zeros(C.shape), np.zeros(C.shape), np.zeros(C.shape)
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for k in range(n):
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M = abs(Z) < r
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S[M], T[M] = S[M] + np.exp(- abs(Z[M])), T[M] + 1
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Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1
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plt.imshow(S ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")
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plt.savefig("Mandelbrot_set_1.png", dpi=200)
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N = abs(Z) >= r # normalized iteration count
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T[N] = T[N] - np.log2(np.log(np.abs(Z[N])) / np.log(r))
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plt.imshow(T ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")
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plt.savefig("Mandelbrot_set_2.png", dpi=200)
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N = abs(Z) > 2 # exterior distance estimation
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D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])
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plt.imshow(D ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")
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plt.savefig("Mandelbrot_set_3.png", dpi=200)
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N, thickness = D > 0, 0.01 # boundary detection
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D[N] = np.maximum(1 - D[N] / thickness, 0)
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plt.imshow(D ** 2.0, cmap=plt.cm.binary, origin="lower")
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plt.savefig("Mandelbrot_set_4.png", dpi=200)
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