The later paintings and prints of Josef Albers, known collectively as the Homage to the Square series, are the culmination of the artist’s investigations of the power of color to create illusions of depth in abstract painting. The compositional framework of the Homage series is comprised of only four nested squares of diminishing size, yet this simple arrangement yields a multitude of possible interpretations of space. The author makes a systematic examination of this compositional framework and introduces a system for classifying (1) composition types, (2) plane and frame combinations, (3) near-to-far layering orders, and (4) opaque and translucent orders. The range of combinatorial possibilities is reduced by perceptual “limiting rules,” yielding a total of 171 distinct illusory spaces and showing the considerable compositional potential in this simple arrangement of four nested squares.