Endogenous Flip Clocks from Anisotropic Local Memory in a Heading-Carrying Lattice Walker

We study a heading-carrying self-interacting walker on a two-dimensional lattice. At each step, the walker deposits an anisotropic wake and then chooses its next cardinal move from the resulting local decision field, optionally perturbed by a weak ambient background. This minimal rule set is sufficient to generate nontrivial behavior. With ambient forcing disabled, the walker settles into a compact endogenous flip clock with sharply regular reversals. Across the tested lag sweep, the inter-flip coefficient of variation is zero at every sampled lag value. With ambient forcing enabled, the same local mechanism broadens into more exploratory behavior with summary statistics that depend on wake geometry and lag. The model belongs to the broader family of self-interacting and local-memory walkers, but differs from standard examples by combining a heading-carrying anisotropic wake rule, restricted cardinal response channels, and an explicit turning cost. We use this model to study what structure can arise from anisotropic self-interaction alone and how that structure is modulated by ambient forcing, lag, and controlled null ablations. The results show that flips concentrate at low decision margins, that the ambient-off system supports a robust endogenous clock, and that under ambient forcing lag no longer acts as a simple period dial but instead modulates flip activity, spatial extent, and chirality-related statistics.