A design is a vector
This little tower is nothing but four numbers: how tall, how tapered, how twisted, how bowed. Change a number and the building follows, because the building is the numbers plus a recipe for drawing them. That's a parametric model — and the vector underneath is the design's true identity.
Work the sliders and watch the vector.
The map of all designs
Take any two of those parameters and lay them out as axes, and you get a map: every point on it is a complete design, neighbours are near-identical siblings, and far corners are strangers. Designers usually walk this terrain blind, one slider at a time. Seeing it as territory is the first step to searching it.
Drag the dot across the map; the tower travels with it.
Rules spend freedom
Four sliders means four degrees of freedom. Now impose a rule — say, the silhouette must keep a fixed area. The rule welds height and taper together: push one and the other answers, and your four freedoms become three. On the map, the constraint collapses the plane you could roam into a curve you must follow. Every requirement a brief adds spends freedom exactly like this.
Toggle the rule, then move Height and watch Taper obey.
The space is bigger than you think
Here's the trap. To survey one slider you might try ten settings. Two sliders: a ten-by-ten grid, a hundred designs. Every knob you add multiplies — eight modest parameters at ten steps each is a hundred million designs, three years at one per second. This is the curse of dimensionality, and it's why brute force dies young and the rest of this part exists.
Add dimensions and watch the bill.
The design space explorer
The full instrument. The tower on the right, the map on the left, and you choose which two of the four parameters the map shows — the other two ride along on sliders. Wander by dragging, leave a breadcrumb trail of everywhere you've been, or hit random to be teleported and feel how vast even four dimensions are. Searching starts next chapter; today, learn the terrain.