Visualization in two and three dimensions of the Jacobi elliptic sine along straight lines in the complex plane:
The two-dimensional parametrization combines the real and imaginary parts of the elliptic sine:
\[ [ ~ \operatorname{Re} \operatorname{sn}[ (a+ib)x, m ] ~ , ~ \operatorname{Im} \operatorname{sn}[ (a+ib)x, m ] ~ ] \]The three-dimensional version adds an extra vertical parameter to make the periodic nature of the curves explicit.
This example requires the higher-level mathematics of Math. What appear at first to be errors in calculation are in fact not. Large absolute values are reported in the JavaScript console as Mathematica strings that can be copied and evaluated in that program. Being able to step through a variety of input parameters indicates that these curves are not nearly as pretty as expected.
Complete code for this example: