Reticular systems are in many aspects a distinct taxonomy of volumetric geometries. In contrast with the conventional embodiment of a ‘volume’ that encapsulates a certain quantity of space with a shell reticular geometries emerge from the accumulation of micro elements to define a gradient of space. Such structures directly result from their material properties and formation processes as well as often ‘simple’ axioms that produce complex results.Built upon a ‘weaving’ organization and the high performance material properties of carbon fiber composite, this research focuses on a formal grammar that initiates the complex system of a reticular volume. A finite ‘lexical’ axiom is consisted of the basic characters of H, M and L responding to the anchor points on the high, middle and low levels of the extruding loom. The genome thus produces a string of data that in the second phase of programming are assigned to 624 points on the loom. The code is to distribute the nodes across the flat line cloud and organize the sequence for the purpose of overlapping the tensioned strings. The virtually infinite results are assessed through an evolutionary solver for confining an array of favorable results that can be then selected from by the designer.