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See publications [1],[6], or [14] for the mathematics.

Rhombic square elliptic functions – J(P) is the whole sphere for all such lattices

Rhombic square lattice with g2=-4
How P mixes quadrants
Connected Julia set for G=P+b
How G=P+b mixes quadrants
How P^2 mixes quadrants
How G^2 mixes quadrants
P^3 starts to lose all regions of normality
Rhombic square lattice with g2=-1
How H=P+c mixes quadrants
How H^2 mixes quadrants
J(H) is Cantor
How P mixes quadrants