ArcTan Riemann Surface

This object is a Riemann surface.

This surface is represents the complex function: f(z) = arctan(z). Since the function is 4-dimensional, the complex and imaginary parts of f(z) are merged. The x and y components are Re(z) and Im(z) respectively and the z component is (Re(f(z) + Im(f(z))/2. This is nice because it allows you to see the behavior of the real and imaginary components of the function's image. Both have asymptotic behavior as |z| increases.

The surface was generated using Mathematica, and the supports were created in openSCAD. Code is included for both. The stl files were merged in MeshLab.

This was created for a course at George Mason University: Math through 3D Printing under the instruction of Dr. Evelyn Sander.