Catalan Surface

catalan 1 periodic grow 001
The Catalan surface is a 1-periodic minimal surface with branch points. The parameter lines which grow in the animation are parabolas.
Catalan wire anaglyph
Catalan wire anaglyph
catalan patch anaglyph
catalan patch anaglyph
            Catalan Minimal Surface Parametric  Equations

  x = cos(aa*pi)*(u-sin(u)*cosh(v))+sin(aa*pi)*(v-cos(u) * sinh(v))-4
  y = cos(aa*pi) * (1 - cos(u) * cosh(v)) + sin(aa*pi) * sin(u) *sinh(v)
  z = 4 *sin(aa*pi)*(cos(u /2)*cosh(v/2)-1)+4*cos(aa*pi)*sin(u/2)*sinh(v/2)

Related Surface

  1. Catalan Surface
  2. Henneberg Surface
  3. Scherk Surface