Grids create a structural rhythm for spatial compositions. Paul Klee in his notebooks, The Thinking Eye, characterised these structural compositions as divisible, with (repeated) parts having measure and weight. He set the organic and individual, which could also have rhythm and structure, in contrast to the divisible. Shape computation reconciles these views. Shapes may be a rhythmic composition of parts but new parts, new shapes, emerge through the formalisms and mechanisms of shape computation. This paper illustrates two directions to exploit the structural rhythm of a grid. First, compositions develop a grid through new rules (the grid as generator). Second, new structural rhythms are generated from spatial relations among emergent parts of the grid.