Observing a pattern allows us to appreciate its visual characteristics and how it was created. A likely construction process is enacted in the perceiver's mind, suggesting how to explain and implement the pattern. We see the pattern and understand its construction, but we explain it in one way and produce it in another. Analyzing the form of the pattern and how it was created corresponds to two different ways of seeing. This research contributes to formally representing the production of two-dimensional patterns in both a visual and physical sense. Central to this study is shape grammar theory, which uses shape rules and algebras to formalize the manipulation of shapes. The production of a pattern can be explained figuratively, where we identify its parts and transformations to produce the pattern conceptually. It can also be  performed physically, using a set of parts and rules to generate the pattern based on a given apparatus. The differences between figurative and physical construction  inform how we perceive and implement designs. Three examples of ornaments, including straight lines, arcs, and combinations of lines and arcs, demonstrate how designs are explained and drawn using ink. Decompositions with structures such as Boolean algebras, topologies, and hierarchies capture the parts and the order of execution. Shape rules provide instructions on how and where to draw. A notable feature of drafting hierarchies is that the sets of their components are diagonal shape decompositions. Lastly, it is shown how a design machine models the figurative and physical construction of designs.