70 lines
2.3 KiB
Python
70 lines
2.3 KiB
Python
import numba
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import numpy as np
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import matplotlib.pyplot as plt
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import decimal as dc # decimal floating point arithmetic with arbitrary precision
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dc.getcontext().prec = 80 # set precision to 80 digits (about 256 bits)
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d, h = 100, 2000 # pixel density (= image width) and image height
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n, r = 80000, 100000.0 # number of iterations and escape radius (r > 2)
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a = dc.Decimal("-1.256827152259138864846434197797294538253477389787308085590211144291")
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b = dc.Decimal(".37933802890364143684096784819544060002129071484943239316486643285025")
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S = np.zeros(n+1, dtype=np.complex128)
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u, v = dc.Decimal(0), dc.Decimal(0)
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for i in range(n+1):
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S[i] = float(u) + float(v) * 1j
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if u * u + v * v < r * r:
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u, v = u * u - v * v + a, 2 * u * v + b
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else:
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print("The reference sequence diverges within %s iterations." % i)
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break
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x = np.linspace(0, 2, num=d+1, dtype=np.float64)
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y = np.linspace(0, 2 * h / d, num=h+1, dtype=np.float64)
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A, B = np.meshgrid(x * np.pi, y * np.pi)
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C = (- 8.0) * np.exp((A + B * 1j) * 1j)
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@numba.njit(parallel=True)
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def iteration_numba(S, C):
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I = np.zeros(C.shape, dtype=np.intp)
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E, Z, dZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
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def iteration(S, C):
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I = np.zeros(C.shape, dtype=np.intp)
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E, Z, dZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
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def abs2(z):
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return z.real * z.real + z.imag * z.imag
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def iterate(C, I, E, Z, dZ):
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I, E = I + 1, (2 * S[I] + E) * E + C
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Z, dZ = S[I] + E, 2 * Z * dZ + 1
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return I, E, Z, dZ
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for i in range(n):
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M = abs2(Z) < abs2(E) # rebase when z is closer to zero
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I[M], E[M] = 0, Z[M] # reset the reference orbit
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M = abs2(Z) < abs2(r)
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I[M], E[M], Z[M], dZ[M] = iterate(C[M], I[M], E[M], Z[M], dZ[M])
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return I, E, Z, dZ
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for j in numba.prange(d+1):
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I[:, j], E[:, j], Z[:, j], dZ[:, j] = iteration(S, C[:, j])
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return I, E, Z, dZ
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I, E, Z, dZ = iteration_numba(S, C)
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D = np.zeros(C.shape, dtype=np.float64)
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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.T ** 0.015, cmap=plt.cm.gist_ncar, origin="lower")
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plt.savefig("Mercator_Mandelbrot_deep_map.png", dpi=200)
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