Generally workings or mechanics are represented by very simple networked relations between parts, such as the relations between atoms in large molecules or between rooms in a system of circulation. From the carpets of William Morris, however, we will learn relations can be much more complex than simple black lines connecting up black dots. Though at first it seems strange to look at Morris’ patterns not as representations of nature, after some careful study we will find what a precise logic drives his intricate intertwinings of twigs, leaves and flowers. Things do not merely connect, but can slide along each other, or lock into each other, or overlap to form complex knots. We will look at properties such as “entanglement,” “bifurcation,” “sprouting” and “flourishing” etc. to understand what the rules behind Morris’s compositions are. We will find that the designs form a closed family where the variations between the rugs are wholly computable.