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%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import hsv_to_rgb
plt.style.use('dark_background')
# Parameter
l = 8      # Arme
k = 3.0     # Torsion
r0 = 3.0    # Grundradius
a = 0.7    # Arm-Modulation
wz = 3.0    # Gauß-Hüllkurve entlang z
zmax = 15.0  # Länge
Nu, Nv = 100, 100  # Auflösung

# Parameterflächen
u = np.linspace(0, 2*np.pi, Nu)
v = np.linspace(-zmax, zmax, Nv)
U, V = np.meshgrid(u, v)

phase = l * U + k * V
R = r0 * (10.0 + a * np.cos(phase)) * np.exp(-(V / wz)**2)

X = R * np.cos(U)
Y = R * np.sin(U)
Z = V

# Farben (HSV → RGB)
hue = (np.mod(phase, 2*np.pi)) / (2*np.pi)
sat = np.ones_like(hue)
val = np.exp(-(V / wz)**2) * (0.5*(1 + np.cos(phase)))**0.8
rgb = hsv_to_rgb(np.dstack([hue, sat, val]))

# Plot
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, facecolors=rgb, rstride=1, cstride=1, antialiased=False)

ax.set_axis_off()

# >>> Sicht von oben (Blick entlang der z-Achse) <<<
ax.view_init(elev=45, azim=20)

plt.show()