We study zero forcing and ℓ-leaky zero forcing on induced subgraphs of d-dimensional grid graphs. Using ℓ-leaky forts, we prove structural results showing that for ℓ≤2d−1, every nonempty ℓ
Nearby in the stack
-leaky fort in an induced subgraph of
Pn1□⋯□Pnd
intersects the boundary of the graph. These results give general bounds and, in certain settings, exact values for the
ℓ
-leaky forcing number of induced subgraphs. Motivated by this framework, we introduce an integer lattice based definition of the Hopi rectangle graphs
HD(a,b)
as induced subgraphs of
Pa+b□Pa+b
. For this particular family of graphs, we show that the zero forcing number equals the maximum nullity, and we completely characterize the