The venation lattice
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Nature offers an inexhaustible source of inspiration for design. Among the various lenses deployed to look at nature, symmetry continues to play one of the most profound ones that have continuously used in the description and interpretation of the study of natural form. This study takes on the five fundamental translational structures of the Euclidean plane, the five Dirichlet domains, and correlates them with motifs extracted front the vein architecture of leaf growth patterns, to propose: a) a particular class of designs characterized by planar translational structure; b) a formal specification of these designs in terms of a shape grammar, the venation lattice grammar; c) an automated implementation of the venation lattice grammar in the Shape Machine – the first general purpose shape grammar interpreter that can carry visually shape computations; and d) a series of digital fabrications of designs in the language. Implications pertain to the visual study of shape, the immediacy of working directly with shapes as opposed to a symbolic or discursive representation of shape in a programming language, and its automated computation in a visual interpreter are discussed throughout the work.