Mandelbrot集的最新变化形态一览——MandelBox，Mandelbulb，Burning Ship，NebulaBrot

import numpy as np
from scipy.spatial import SphericalVoronoi
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

def mandelbulb(x, y, z, max_iter=8):
    c = complex(np.sqrt(x*x + y*y), z)
    z = 0.0j
    for i in range(max_iter):
        z = z*z + c
    return abs(z)

x, y, z = np.ogrid[-2:1:100j, -2:1:100j, -2:1:100j]
vals = np.vectorize(mandelbulb)(x, y, z)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.voxels(vals < 2.0, facecolors='red')

plt.show()

def mandelbox(x, y, z, max_iter=8):
    z = complex(x, y) + z
    for n in range(max_iter):
        if abs(z) > 2:
            break
        # Box folding
        z = 2 - abs(z) if abs(z) > 1 else 2*z*z + z
    return n

x, y, z = np.ogrid[-2:1:100j, -2:1:100j, -2:1:100j]
vals = np.vectorize(mandelbox)(x, y, z)

# Plotting the Mandelbox using matplotlib or any other plotting library

def burning_ship(x, y, max_iter=8):
    z = complex(x, y)
    for i in range(max_iter):
        z = (z.real ** 2 - z.imag ** 2, 2 * z.real * z.imag)  # Complex conjugate
        z = complex(abs(z[0]), abs(z[1])) + z
    return abs(z)

x, y = np.ogrid[-2:1:100j, -1.5:1.5:100j]
vals = np.vectorize(burning_ship)(x, y)

plt.imshow(vals.T, extent=[-2, 1, -1.5, 1.5], cmap='hot')
plt.show()

def nebulabrot(x, y, max_iter=8):
    z = complex(x, y)
    for i in range(max_iter):
        z = z*z + z.conjugate()  # Example formula
    return abs(z)

x, y = np.ogrid[-2:1:100j, -1.5:1.5:100j]
vals = np.vectorize(nebulabrot)(x, y)

plt.imshow(vals.T, extent=[-2, 1, -1.5, 1.5], cmap='plasma')
plt.show()