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Data Update

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Ingy döt Net 2023-07-18 13:51:12 -07:00
parent e50b5c3114
commit 633b36288a
206 changed files with 4762 additions and 965 deletions
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34
Task/Mandelbrot-set/Python/mandelbrot-set-5.py
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@ -5,7 +5,7 @@ d, h = 800, 500 # pixel density (= image width) and image height
n, r = 200, 500 # number of iterations and escape radius (r > 2)
direction, height = 45, 1.5 # direction and height of the incoming light
v = np.exp(direction / 180 * np.pi * 1j) # unit 2D vector in this direction
stripes, damping = 4, 2.0 # stripe density and damping parameter
x = np.linspace(0, 2, num=d+1)
y = np.linspace(0, 2 * h / d, num=h+1)
@ -14,30 +14,28 @@ A, B = np.meshgrid(x - 1, y - h / d)
C = (2.0 + 1.0j) * (A + B * 1j) - 0.5
Z, dZ, ddZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
D, T = np.zeros(C.shape), np.zeros(C.shape)
D, S, T = np.zeros(C.shape), np.zeros(C.shape), np.zeros(C.shape)
for k in range(n):
M = Z.real ** 2 + Z.imag ** 2 < r ** 2
M = abs(Z) < r
S[M], T[M] = S[M] + np.cos(stripes * np.angle(Z[M])), T[M] + 1
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])
N = abs(Z) > 2 # exterior distance estimation
D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])
N = abs(Z) >= r # normal map effect 1 (potential function)
P, Q = S[N] / T[N], (S[N] + np.cos(stripes * np.angle(Z[N]))) / (T[N] + 1)
F = np.log2(np.log(np.abs(Z[N])) / np.log(r)) # fraction between 0 and 1 (for interpolation)
R = Q + (P - Q) * F * F * (3 - 2 * F) # hermite interpolation (r is between q and p)
U, H = Z[N] / dZ[N], 1 + R / damping # normal vectors to the equipotential lines and height perturbation
U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and vector in light direction
D[N] = np.maximum((U.real * v.real + U.imag * v.imag + H * height) / (1 + height), 0)
plt.imshow(D ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")
plt.savefig("Mandelbrot_distance_est.png", dpi=200)
N = abs(Z) > 2 # normal map effect 1 (potential function)
U = Z[N] / dZ[N] # normal vectors to the equipotential lines
U, S = U / abs(U), 1 + np.sin(100 * np.angle(U)) / 10 # unit normal vectors and stripes
T[N] = np.maximum((U.real * v.real + U.imag * v.imag + S * height) / (1 + height), 0)
plt.imshow(T ** 1.0, cmap=plt.cm.bone, origin="lower")
plt.imshow(D ** 1.0, cmap=plt.cm.bone, origin="lower")
plt.savefig("Mandelbrot_normal_map_1.png", dpi=200)
N = abs(Z) > 2 # normal map effect 2 (distance estimation)
N = abs(Z) >= r # normal map effect 2 (distance estimation)
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]))
U = U / abs(U) # unit normal vectors to the equidistant lines
T[N] = np.maximum((U.real * v.real + U.imag * v.imag + height) / (1 + height), 0)
U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and vector in light direction
D[N] = np.maximum((U.real * v.real + U.imag * v.imag + height) / (1 + height), 0)
plt.imshow(T ** 1.0, cmap=plt.cm.afmhot, origin="lower")
plt.imshow(D ** 1.0, cmap=plt.cm.afmhot, origin="lower")
plt.savefig("Mandelbrot_normal_map_2.png", dpi=200)