Mandelbrot set: Difference between revisions

Line 10,916:

direction, height = 45, 1.5 # direction and height of the incoming light

stripes, damping = ~~5.0~~, 2.0 # stripe density and damping parameter

stripes, damping = 10, 2.0 # stripe density and damping parameter

x = np.linspace(0, 2, num=d+1)

Line 10,932:

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~~

N = abs(Z) >= r # normal map effect 1 (potential function)

D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])

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)

P, Q = S[N] / T[N], (S[N] + np.sin(stripes * np.angle(Z[N]))) / (T[N] + 1)

F = ~~1 -~~ np.log2(np.log(np.abs(Z[N])) / np.log(r))

F = np.log2(np.log(np.abs(Z[N])) / np.log(r)) # fraction between 0 and 1 (for interpolation)

H = P + (Q - P) * F * F * (3 - ~~2 * F~~) ~~# hermite interpolation~~

H = F * P + (1 - F) * Q # height perturbation (by linear interpolation)

U = Z[N] / dZ[N] # normal vectors to the equipotential lines

U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and unit 2D vector

Line 10,949:

Line 10,943:

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, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and unit 2D vector