3 problems

Let $\mathcal Q$ be the class of two-step rules, and let $\mathcal N_\ell$ denote the set of rules in $\mathcal Q$ whose symmetry group has order $\ell$, with $\ell=\infty$ allowed…

Let $\mathcal Q$ be the class of two-step rules, and let $G_e,G_n,G_w,G_s$ denote the corresponding groups for the four directions. Directional group-order conjecture. For every tw…

Let $P_m^{{\mathrel{\tikz{\draw (0ex,1ex) -- (0ex,0ex) -- (1ex,0ex) (-0.2ex,0ex)}}}}$ be the number of quarter-plane spiral walks of length $m$. Let…