File:Mandelbrot numpy set 5.png
Summary
| Description |
Deutsch: Die Mandelbrot-Menge wird mit NumPy unter Verwendung komplexer Matrizen berechnet. Es wird eine von Adam Saka popularisierte und von Adam Majewski beschriebene Hillshading-Methode verwendet. Diese Technik erzeugt die Illusion dreidimensionaler Stufen. English: The Mandelbrot set is calculated with NumPy using complex matrices. A hillshading method popularized by Adam Saka and described by Adam Majewski is used. This technique creates the illusion of three-dimensional steps. |
| Date | |
| Source | Own work |
| Author | Majow |
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| PNG development | |
| Source code | Python codeimport numpy as np
import matplotlib.pyplot as plt
d, h = 500, 600 # pixel density (= image width) and image height
n, r = 200, 500 # number of iterations and escape radius (r > 2)
direction, height = 45.0, 1.5 # direction and height of the light
x = np.linspace(0, 2, num=d+1)
y = np.linspace(0, 2 * h / d, num=h+1)
A, B = np.meshgrid(x - 1, y - h / d)
C = (2.0 + 1.0j) * (A + B * 1j) - 0.5
def iteration(C):
Z, dZ = np.zeros_like(C), np.zeros_like(C)
def iterate(C, Z, dZ):
Z, dZ = Z * Z + C, 2 * Z * dZ + 1
return Z, dZ
for i in range(n):
M = abs(Z) < r
Z[M], dZ[M] = iterate(C[M], Z[M], dZ[M])
return Z, dZ
Z, dZ = iteration(C)
D, S = np.zeros(C.shape), np.zeros(C.shape)
fig = plt.figure(figsize=(12.8, 9.6))
fig.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
N = abs(Z) >= r # blended normal map effect and linear steps (potential function)
U, V = Z[N] / dZ[N], np.log2(np.log(np.abs(Z[N])) / np.log(r))
U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and light vector
D[N], S[N] = np.maximum((U.real * v.real + U.imag * v.imag + height) / (1 + height), 0), V
ax1 = fig.add_subplot(2, 3, 1)
ax1.imshow(D ** 1.0, cmap=plt.cm.gray, origin="lower")
ax2 = fig.add_subplot(2, 3, 2)
ax2.imshow(S ** 1.0, cmap=plt.cm.gray, origin="lower")
ax3 = fig.add_subplot(2, 3, 3)
ax3.imshow((D + S) ** 1.0, cmap=plt.cm.gray, origin="lower")
N = abs(Z) >= r # blended normal map effect and linear steps (potential function)
U, V = Z[N] / dZ[N], np.maximum(1 - np.log2(np.log(np.abs(Z[N])) / np.log(r)), 0)
U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and light vector
D[N], S[N] = np.maximum((U.real * v.real + U.imag * v.imag + height) / (1 + height), 0), V
ax4 = fig.add_subplot(2, 3, 4)
ax4.imshow(D ** 1.0, cmap=plt.cm.gray, origin="lower")
ax5 = fig.add_subplot(2, 3, 5)
ax5.imshow(S ** 1.0, cmap=plt.cm.gray, origin="lower")
ax6 = fig.add_subplot(2, 3, 6)
ax6.imshow((D + S) ** 1.0, cmap=plt.cm.gray, origin="lower")
fig.savefig("Mandelbrot_numpy_set_5.png", dpi=200)
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