Feynman Checkerboard (1948): Feynman's discrete lattice model for the 1D Dirac equation.
A relativistic spinless fermion travels on a checkerboard at speed ±c. At each time step it either continues straight
or changes direction (a "kink"). The amplitude for a path with R direction reversals is (iε/ℏ)^R where ε is the lattice spacing.
Summing over all paths gives the Dirac propagator in the continuum limit. This is the path integral: quantum
amplitudes arise from coherent superposition of classical trajectories weighted by e^{iS/ℏ}.