This is a publicly available part of COEL focused on the exploration of shift-symmetry in two-dimensional CAs (toroids).
Here you can enumerate the shift-symmetric configurations in two-dimensional cellular automata and calculate the probability of selecting shift-symmetric configuration randomly generated from a uniform or density-uniform distribution.
Moreover, to demonstrate how CA dynamics preserves shift-symmetry we provide an embedded simulator which runs CA with a random transition function, Moore neighborhood, and a random two-dimensional shift-symmetric configuration generated using a single shift (vector). Note that in general shift-symmetric configurations might be generated using several (more than one) independent shifts.
The presented functionality is intended as a complementary material for the publication: