The links below are to Julia sets of Weierstrass elliptic functions.
The graphics were produced by Jane Hawkins,

Lorelei Koss, and Michael Taylor.

1. A
Weierstrass elliptic function on a square lattice with a superattracting
fixed point. More pictures

of this example can be seen here
on Jane Hawkins' site at UNC-Chapel Hill.

2. Julia
sets of Weierstrass elliptic functions with toral band components.
More pictures

of this example can be seen here
on Jane Hawkins' site at UNC-Chapel Hill.