Cl := x->max(-1,min(1, x)):
M := 25:
f := (x,y)->Re(sqrt(x+_i*y)):
P1 := plot3d([seq([x, y, k*f(x,y)], k=[-1,1])
], x=-1..1, y=-1..1, labels=[x,y,Rew],style=surface, grid=[200,200], thickness=2, colorscheme=["xyzcoloring", [(x,y,z)->y^2,(x,y,z)->x*y,(x,y,z)->x^2]]):
P2 := seq(spacecurve([seq([Cl(t*cos(2*Pi/M*j)), Cl(t*sin(2*Pi/M*j)), sign(k)*(abs(k) - 1.5)/140 + sign(k)*f(Cl(t*cos(2*Pi/M*j)),Cl(t*sin(2*Pi/M*j))),color=[RGB(1,t^2*sin(2*Pi/M*j)^2,1)]], k=[-2,-1,1,2])], t=0..13, thickness=4, transparency=0.7, numpoints=1500),j=1..M):
The above draws a Riemann surface for sqrt(z).
The problem is that maple doesn't seem to make grid lines nicely project from the function. I added the lines myself but I cannot color them in a way that uses t. the parameter t is completely ignored in the graphing of the lines.
Also, the first graph cannot have transparency set and give meaningful results.
adding transparency=0.001 it looks like it is 10% transparent.... and going below that it just turns off all transparency. I want to barely see through the surface.
It's really hard to get a nice graph for maple. The lighting, lines, and coloring are always off to reduce the visual impact.