Catalan Surface Saddle

Jean-Marc Daviau-Williams MATH 401For this print, we were tasked with looking back at previous assignments and finding one to do again. I decided to redo saddle as described during the multivariable calculus assignment, but with one twist; I would make the saddle using parametric equations. Luckily, there was already a template to go off of - in particular, the Catalan surface.

As described by Eric Weisstein from Wolfram, a Catalan surface is "a minimal surface given by the parametric equations:
x(u,v) = u-sin[u]cosh[v] (1)
y(u,v) = 1-cos[u]cosh[v] (2)
z(u,v) = 4sin[u/2]sinh[v/2] (3)"

The result of this is a saddle-like shape when u is taken from 0 to 2*Pi*. However, when taken to 2*kPi*, where *k* is some integer greater than 0, the shape will generate *k* copies of that original shape, intersecting the tips of the saddles. Granted, this saddle shape if used as an actual horse saddle would be very uncomfortable, but is still a saddle nonetheless.

As for the actual code