Data update
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Ingy döt Net
parent
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07c7092a52
140 changed files with 2712 additions and 241 deletions
5
Task/Mandelbrot-set/Python/mandelbrot-set-10.py
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5
Task/Mandelbrot-set/Python/mandelbrot-set-10.py
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@ -0,0 +1,5 @@
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from functools import reduce
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def mandelbrot(x, y, c): return ' *'[abs(reduce(lambda z, _: z*z + c, range(99), 0)) < 2]
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print('\n'.join(''.join(mandelbrot(x, y, x/50 + y/50j) for x in range(-100, 25)) for y in range(-50, 50)))
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@ -4,38 +4,31 @@ 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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direction, height = 45, 1.5 # direction and height of the incoming light
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stripes, damping = 4, 2.0 # stripe density and damping parameter
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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 + 1.0j) * (A + B * 1j) - 0.5
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C = 2.0 * (A + B * 1j) - 0.5
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Z, dZ, ddZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
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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.cos(stripes * np.angle(Z[M])), T[M] + 1
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Z[M], dZ[M], ddZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1, 2 * (dZ[M] ** 2 + Z[M] * ddZ[M])
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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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N = abs(Z) >= r # normal map effect 1 (potential function)
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P, Q = S[N] / T[N], (S[N] + np.cos(stripes * np.angle(Z[N]))) / (T[N] + 1)
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F = np.log2(np.log(np.abs(Z[N])) / np.log(r)) # fraction between 0 and 1 (for interpolation)
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R = Q + (P - Q) * F * F * (3 - 2 * F) # hermite interpolation (r is between q and p)
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U, H = Z[N] / dZ[N], 1 + R / damping # normal vectors to the equipotential lines and height perturbation
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U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and vector in light direction
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D[N] = np.maximum((U.real * v.real + U.imag * v.imag + H * height) / (1 + height), 0)
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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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plt.imshow(D ** 1.0, cmap=plt.cm.bone, origin="lower")
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plt.savefig("Mandelbrot_normal_map_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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N = abs(Z) >= r # normal map effect 2 (distance estimation)
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U = Z[N] * dZ[N] * ((1 + np.log(abs(Z[N]))) * np.conj(dZ[N] ** 2) - np.log(abs(Z[N])) * np.conj(Z[N] * ddZ[N]))
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U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and vector in light direction
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D[N] = np.maximum((U.real * v.real + U.imag * v.imag + height) / (1 + height), 0)
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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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plt.imshow(D ** 1.0, cmap=plt.cm.afmhot, origin="lower")
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plt.savefig("Mandelbrot_normal_map_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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@ -1,37 +1,40 @@
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import numpy as np
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import matplotlib.pyplot as plt
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d, h = 200, 1200 # pixel density (= image width) and image height
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n, r = 8000, 10000 # number of iterations and escape radius (r > 2)
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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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a = -.743643887037158704752191506114774 # real coordinate of the zoom center
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b = 0.131825904205311970493132056385139 # imaginary coordinate of the center
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direction, height = 45, 1.5 # direction and height of the incoming light
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stripes, damping = 4.0, 2.0 # stripe density and damping parameter
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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 * np.pi, y * np.pi)
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C = 8.0 * np.exp((A + B * 1j) * 1j) + (a + b * 1j)
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A, B = np.meshgrid(x - 1, y - h / d)
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C = (2.0 + 1.0j) * (A + B * 1j) - 0.5
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Z, dZ = np.zeros_like(C), np.zeros_like(C)
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D = np.zeros(C.shape)
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Z, dZ, ddZ = np.zeros_like(C), 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 = Z.real ** 2 + Z.imag ** 2 < r ** 2
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Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1
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M = abs(Z) < r
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S[M], T[M] = S[M] + np.cos(stripes * np.angle(Z[M])), T[M] + 1
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Z[M], dZ[M], ddZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1, 2 * (dZ[M] ** 2 + Z[M] * ddZ[M])
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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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N = abs(Z) >= r # normal map effect 1 (equipotential lines)
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P, Q = S[N] / T[N], (S[N] + np.cos(stripes * np.angle(Z[N]))) / (T[N] + 1)
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R = Q + (P - Q) * np.log2(np.log(np.abs(Z[N])) / np.log(r)) # linear interpolation
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U, V = Z[N] / dZ[N], 1 + R / damping # normal vectors and variations in inclination
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U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit vectors
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D[N] = np.maximum((U.real * v.real + U.imag * v.imag + V * height) / (1 + height), 0)
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plt.imshow(D.T ** 0.05, cmap=plt.cm.nipy_spectral, origin="lower")
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plt.savefig("Mercator_Mandelbrot_map.png", dpi=200)
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plt.imshow(D ** 1.0, cmap=plt.cm.bone, origin="lower")
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plt.savefig("Mandelbrot_normal_map_1.png", dpi=200)
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X, Y = C.real, C.imag # zoom images (adjust circle size 100 and zoom level 20 as needed)
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R, c, z = 100 * (2 / d) * np.pi * np.exp(- B), min(d, h) + 1, max(0, h - d) // 20
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N = abs(Z) > 2 # normal map effect 2 (equidistant lines)
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U = Z[N] * dZ[N] * ((1 + np.log(abs(Z[N]))) * np.conj(dZ[N] ** 2) - np.log(abs(Z[N])) * np.conj(Z[N] * ddZ[N]))
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U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit vectors
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D[N] = np.maximum((U.real * v.real + U.imag * v.imag + height) / (1 + height), 0)
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fig, ax = plt.subplots(2, 2, figsize=(12, 12))
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ax[0, 0].scatter(X[1*z:1*z+c,0:d], Y[1*z:1*z+c,0:d], s=R[0:c,0:d]**2.0, c=D[1*z:1*z+c,0:d]**0.5, cmap=plt.cm.nipy_spectral)
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ax[0, 1].scatter(X[2*z:2*z+c,0:d], Y[2*z:2*z+c,0:d], s=R[0:c,0:d]**2.0, c=D[2*z:2*z+c,0:d]**0.4, cmap=plt.cm.nipy_spectral)
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ax[1, 0].scatter(X[3*z:3*z+c,0:d], Y[3*z:3*z+c,0:d], s=R[0:c,0:d]**2.0, c=D[3*z:3*z+c,0:d]**0.3, cmap=plt.cm.nipy_spectral)
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ax[1, 1].scatter(X[4*z:4*z+c,0:d], Y[4*z:4*z+c,0:d], s=R[0:c,0:d]**2.0, c=D[4*z:4*z+c,0:d]**0.2, cmap=plt.cm.nipy_spectral)
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plt.savefig("Mercator_Mandelbrot_zoom.png", dpi=100)
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plt.imshow(D ** 1.0, cmap=plt.cm.afmhot, origin="lower")
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plt.savefig("Mandelbrot_normal_map_2.png", dpi=200)
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@ -1,44 +1,37 @@
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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 = 200, 1200 # pixel density (= image width) and image height
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n, r = 8000, 10000 # number of iterations and escape radius (r > 2)
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d, h = 50, 1000 # pixel density (= image width) and image height
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n, r = 80000, 100000 # 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 k in range(n+1):
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S[k] = float(u) + float(v) * 1j
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if u ** 2 + v ** 2 < r ** 2:
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u, v = u ** 2 - v ** 2 + a, 2 * u * v + b
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else:
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print("The reference sequence diverges within %s iterations." % k)
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break
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a = -.743643887037158704752191506114774 # real coordinate of the zoom center
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b = 0.131825904205311970493132056385139 # imaginary coordinate of the center
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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 * np.pi, y * np.pi)
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C = 8.0 * np.exp((A + B * 1j) * 1j)
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C = 8.0 * np.exp((A + B * 1j) * 1j) + (a + b * 1j)
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E, Z, dZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
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D, I, J = np.zeros(C.shape), np.zeros(C.shape, dtype=np.int64), np.zeros(C.shape, dtype=np.int64)
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Z, dZ = np.zeros_like(C), np.zeros_like(C)
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D = np.zeros(C.shape)
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for k in range(n):
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Z2 = Z.real ** 2 + Z.imag ** 2
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M, R = Z2 < r ** 2, Z2 < E.real ** 2 + E.imag ** 2
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E[R], I[R] = Z[R], J[R] # rebase when z is closer to zero
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E[M], I[M] = (2 * S[I[M]] + E[M]) * E[M] + C[M], I[M] + 1
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Z[M], dZ[M] = S[I[M]] + E[M], 2 * Z[M] * dZ[M] + 1
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M = Z.real ** 2 + Z.imag ** 2 < r ** 2
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Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1
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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.nipy_spectral, origin="lower")
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plt.savefig("Mercator_Mandelbrot_deep_map.png", dpi=200)
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plt.imshow(D.T ** 0.05, cmap=plt.cm.nipy_spectral, origin="lower")
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plt.savefig("Mercator_Mandelbrot_map.png", dpi=200)
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X, Y = C.real, C.imag # zoom images (adjust circle size 100 and zoom level 20 as needed)
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R, c, z = 100 * (2 / d) * np.pi * np.exp(- B), min(d, h) + 1, max(0, h - d) // 20
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fig, ax = plt.subplots(2, 2, figsize=(12, 12))
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ax[0, 0].scatter(X[1*z:1*z+c,0:d], Y[1*z:1*z+c,0:d], s=R[0:c,0:d]**2.0, c=D[1*z:1*z+c,0:d]**0.5, cmap=plt.cm.nipy_spectral)
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ax[0, 1].scatter(X[2*z:2*z+c,0:d], Y[2*z:2*z+c,0:d], s=R[0:c,0:d]**2.0, c=D[2*z:2*z+c,0:d]**0.4, cmap=plt.cm.nipy_spectral)
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ax[1, 0].scatter(X[3*z:3*z+c,0:d], Y[3*z:3*z+c,0:d], s=R[0:c,0:d]**2.0, c=D[3*z:3*z+c,0:d]**0.3, cmap=plt.cm.nipy_spectral)
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ax[1, 1].scatter(X[4*z:4*z+c,0:d], Y[4*z:4*z+c,0:d], s=R[0:c,0:d]**2.0, c=D[4*z:4*z+c,0:d]**0.2, cmap=plt.cm.nipy_spectral)
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plt.savefig("Mercator_Mandelbrot_zoom.png", dpi=100)
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@ -1,8 +1,44 @@
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print(
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'\n'.join(
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''.join(
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' *'[(z:=0, c:=x/50+y/50j, [z:=z*z+c for _ in range(99)], abs(z))[-1]<2]
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for x in range(-100,25)
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)
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for y in range(-50,50)
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))
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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 = 50, 1000 # pixel density (= image width) and image height
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n, r = 80000, 100000 # 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 k in range(n+1):
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S[k] = float(u) + float(v) * 1j
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if u ** 2 + v ** 2 < r ** 2:
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u, v = u ** 2 - v ** 2 + a, 2 * u * v + b
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else:
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print("The reference sequence diverges within %s iterations." % k)
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break
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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 * np.pi, y * np.pi)
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C = 8.0 * np.exp((A + B * 1j) * 1j)
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E, Z, dZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
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D, I, J = np.zeros(C.shape), np.zeros(C.shape, dtype=np.int64), np.zeros(C.shape, dtype=np.int64)
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for k in range(n):
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Z2 = Z.real ** 2 + Z.imag ** 2
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M, R = Z2 < r ** 2, Z2 < E.real ** 2 + E.imag ** 2
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E[R], I[R] = Z[R], J[R] # rebase when z is closer to zero
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E[M], I[M] = (2 * S[I[M]] + E[M]) * E[M] + C[M], I[M] + 1
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Z[M], dZ[M] = S[I[M]] + E[M], 2 * Z[M] * dZ[M] + 1
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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.nipy_spectral, origin="lower")
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plt.savefig("Mercator_Mandelbrot_deep_map.png", dpi=200)
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from functools import reduce
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def mandelbrot(x, y, c): return ' *'[abs(reduce(lambda z, _: z*z + c, range(99), 0)) < 2]
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print('\n'.join(''.join(mandelbrot(x, y, x/50 + y/50j) for x in range(-100, 25)) for y in range(-50, 50)))
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print(
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'\n'.join(
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''.join(
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' *'[(z:=0, c:=x/50+y/50j, [z:=z*z+c for _ in range(99)], abs(z))[-1]<2]
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for x in range(-100,25)
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)
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for y in range(-50,50)
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))
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