Edmund Harriss developed a branching spiral based on a decomposition of a rectangle whose sides are in the plastic ratio into a square and two smaller rectangles. This concept was inspired by the golden spiral, a classical self-similar figure induced by decomposing a rectangle into a square and a similar rectangle. Neither of these decompositions can be realized in a medium where the side lengths of individual components must be integers, but the golden spiral’s discrete variant, the Fibonacci spiral, can be so realized. This work proposes and analyzes an integer-side-length variant of the Harriss spiral.