Reimann Surface e^(z^2)

This 3D object is made for Math 401: Mathematics Through 3D Printing at George Mason University under course instructor Dr. Evelyn Sander.

For this assignment, we are exploring Riemann Surfaces by looking at complex valued function of (z) where it can be divided into real and imaginary parts on the complex plane. I choose f(z) = e^(z^2) which is known as a holomorphic function. Holomorphic function essentially means it is complex differentiable in some neighborhood of a point that belongs to the domain in complex C space. The function f(z) = e^(z^2) is the composition of e^z and z^2.

The Cauchy-Riemann holds for this situation where we know that z = x+iy. Therefore, with having z^2, we can derive z^2 = x^2-y^2+2ixy. Thus, e^(z^2) = e^(x^2-y^2)*(cos(2xy)+i sin(2xy). For my object, I am plotting the real part e^(x^2-y^2)*cos(2xy) and imaginary e^(x^2-y^2)*sin(2xy) by parameterizing the equation. Using ParametricPlot3D on Mathematica, I used the intervals x from -1 to 1 and similar