Sketchpad (1963) let a user draw on a screen with a light pen and attach constraints: this line parallel to that, these two equal in length (Sutherland, 1963). The system solved for a drawing that satisfied all of them at once. A drawing became a set of relationships rather than a set of marks. GenerativeComponents (2003) carried the same solver into architecture, and the Smithsonian courtyard roof (2007) was modeled with it (Aish; Foster + Partners). The constraint solver is still the engine under every parametric tool.

A shape grammar is a set of rewriting rules applied to shapes: find this configuration, replace it with that one, repeat (Stiny and Gips, 1972). The first grammars generated paintings; later ones produced Palladian villa plans (Stiny and Mitchell, 1978) and new prairie houses indistinguishable in style from the originals (Koning and Eizenberg, 1981). The pattern language of the same decade (Alexander, 1977) rests on the same conviction: a way of building can be written down as rules. Conceptual art had made the parallel claim a few years earlier: "the idea becomes a machine that makes the art" (LeWitt, 1967). Wall drawings that exist only as written instructions for others to execute apply the same principle.

Evolutionary architecture encodes a building as a genome, grows it in a simulated environment, and selects over generations, with the architect setting the fitness test rather than the form (Frazer, 1995). The lineage runs through cybernetics: a system that senses its environment and adjusts, applied to the design process itself. Evolved Virtual Creatures (1994) bred both the bodies and the nervous systems of simulated animals the year before, and showed that selection alone could produce swimmers and walkers nobody drew (Sims). In this approach the architect designs the generative system rather than the final form.

A parametric model defines geometry as dependencies: change one input and everything downstream updates. Grasshopper (2007) made this a visual graph of nodes and wires on top of Rhino and became the default tool in architecture schools and large practices (Rutten). The cost is that the graph fixes which relationships exist at the moment they are least understood, and a late change to the logic can mean rebuilding the model. A parametric model by itself does not search for solutions. It updates a single design in response to changed inputs.

Topology optimization removes material from a volume wherever it carries little load and leaves bone-like structure behind (Bendsøe and Kikuchi, 1988). Genetic solvers such as Galapagos, shipped with Grasshopper since 2010, breed populations of parameter sets and keep the ones that perform on daylight, weight, or embodied carbon. Growth simulations that build form from local rules, the subject of computational morphogenesis, trade a single objective for the accumulation of many small interactions. Each method needs a measurable objective. Choosing that objective is a large part of the design work.