Sphere Spirals

import numpy as np
from matplotlib import pyplot as plt
import s3dlib.surface as s3d
import s3dlib.cmap_utilities as cmu

#.. influenced by M.C.Escher - Sphere Spirals
#.. https://mcescher.com/gallery/mathematical/

# 1. Define function to examine .....................................
ttlcolor =  [0.502, 0.200, 0.278, 0.1] 
fgbgcolor = [0.957, 0.925, 0.882]
outercolor = [0.875, 0.682, 0.388]
innercolor = [0.847, 0.525, 0.471]

elev, azim = 45,30
light_direction = [1,-1,2 ]

def twist(rtp, twists=1) :
    r,t,p = rtp
    f = np.cos(t) + 1
    b =  2*p/np.pi -1
    g = ( 1 + np.sign(b)*np.power(  np.abs(b), 6 ) )/2
    T = t - 2*twists*(p+g*2*np.pi)
    return r,T,p

def clipFunc(rtp) :
    T = (8*rtp[1]/(2*np.pi)).astype(int)
    return T%2 == 1

def getGrid(axis) :
    viewDir = -1*s3d.elev_azim_2vector(axis.elev,axis.azim)
    grid = s3d.SphericalSurface(4,color='.45',lw=0.2)
    grid.clip_plane(0, direction=viewDir )
    grid.transform(scale=1.01)
    grid.set_facecolor([0,0,0,0])
    return grid

# 2. Setup and map surfaces .........................................
bcmap= cmu.binary_cmap(innercolor,outercolor)

surface = s3d.SphericalSurface.grid(9*20,8*10,'x',color='w',edgecolor='k')
surface.clip(clipFunc)
surface.map_geom_from_op(twist)

# 3. Construct figure, add surface, plot ............................

fig = plt.figure(figsize=plt.figaspect(1), facecolor=fgbgcolor)
text = fig.text(0.97, 0.52, 'S3Dlib.org', color=ttlcolor, ha='right',
    va='center', rotation=90, fontsize=55, fontweight='bold'  )
ax = plt.axes(projection='3d', aspect='equal')
minmax = ( -0.75,0.75 )
ax.set(xlim=minmax, ylim=minmax, zlim=minmax )
ax.set_axis_off()
ax.view_init(elev, azim)
ax.set_facecolor(fgbgcolor)

surface.map_cmap_from_normals(bcmap,direction=ax)
surface.shade(ax=ax,direction=light_direction)
surface.hilite(0.5,ax=ax,direction=light_direction)
ax.add_collection3d(getGrid(ax))
ax.add_collection3d(surface)

fig.tight_layout(pad=0)
plt.show()