如何最好地在python中创建Lorenz Attractor的填充体积以进行体积渲染

I am trying to create a 3D array to then perform volume rendering on (in other software or volume rendering packages) of strange attractor like Lorenz Attractor. It is easy enough to plot the attractor from data points and provide a value to assign a color and visualize in matplotlib for example.

However I would like a filled volume array. I have tried interpolation methods like griddata but it doesn't give the desired result. What I am envisioning is something like:

这是从维基百科页面。

这是我尝试过的方法，但是如果您在简单的查看器中打开结果，则效果并不理想。我在想，也许只在组成x，y，z数组的点之间进行插值...在玩了几个小时后，我有点迷失了。我认为我需要做的就是对这些点进行一些插值或将其填充到数组中，在这里我称为interp_im。然后可以在体积渲染中查看它。任何帮助都将不胜感激！

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.interpolate import griddata
from scipy.interpolate import LinearNDInterpolator
from skimage.external import tifffile

rho = 28.0
sigma = 10.0
beta = 8.0 / 3.0

def f(state, t):
    x, y, z = state  # Unpack the state vector
    return sigma * (y - x), x * (rho - z) - y, x * y - beta * z  # Derivatives

state0 = [1.0, 1.0, 1.0]
t = np.arange(0.0, 40.0, 0.01) #t = np.arange(0.0, 40.0, 0.01)

states = odeint(f, state0, t)

# shift x,y,z positions to int for regular image volume

x = states[:, 0]
y = states[:, 1]
z = states[:, 2]
x_min = x.min()
y_min = y.min()
z_min = z.min()
states_int = states + [abs(x_min),abs(y_min),abs(z_min)] + 1
states_int = states_int * 10
states_int = states_int.astype(int)

# values will be in order of tracing for color
values = []
for i,j in enumerate(states_int):
    values.append(i*10)

values = np.asarray(values)

fig = plt.figure()
ax = fig.gca(projection='3d')
sc = ax.scatter(states_int[:, 0], states_int[:, 1], states_int[:, 2],c=values)
plt.colorbar(sc)
plt.draw()
plt.show()

#print(x.shape, y.shape, z.shape, values.shape)

#Interpolate for volume rendering
x_ = np.linspace(0,999,500)
y_ = np.linspace(0,999,500)
z_ = np.linspace(0,999,500)
xx,yy,zz = np.meshgrid(x_,y_,z_, sparse = True)
#
# X = states_int.tolist()
#
interp_im = griddata(states_int, values, (xx,yy,zz), method='linear')
interp_im = interp_im.astype(np.uint16)

np.save('interp_im.npy', interp_im)

tifffile.imsave('LorenzAttractor.tif', interp_im)