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

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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