Rules · Geometry · Theory · Modules
Define a form by a few parameters and a rule, and let every element vary continuously with them, instead of repeating identical elements.
floor i: rotation = i × θ, scale = 1 − (1 − τ)·(i ⁄ n)^1.3
In a modern tower every floor is the same; in a parametric tower every floor is different, but all are generated by one rule. In the model the twist per floor sets how tightly the tower winds and the taper how much it slims toward the top, and the rule adjusts itself to the number of floors. Schumacher’s manifesto demands exactly this: no rigid platonic forms or simple repetitions, but gradual differentiation and correlation throughout.
The Turning Torso in Malmö (Santiago Calatrava, 2001–05) turns through 90° over its 54 storeys; the Shanghai Tower (Gensler, 2008–15) twists by about 120° as it tapers.
A saddle surface in which two opposite corners are raised and two lowered is a hyperbolic paraboloid; it contains two families of straight lines, so it can be formed with straight boards and yet has double curvature.
y = k·x·z (or any bilinear patch through four points not in one plane)
Place a point (or curve) in the design and let a property of every element (size, rotation, opening) be a function of its distance from that point.
r(panel) = r_min + (r_max − r_min) · d ⁄ d_max
Take the lines of the roads that arrive at the site from its surroundings and bundle them into a grid that bends and swells to meet them, instead of imposing a rigid orthogonal grid.
Make the building types a continuum governed by parameters: let the perimeter block morph by gradual steps into a block with a tower, and into towers alone, so that neighbouring blocks differ by degree, never by collage.
Cite this page Chris Paton, “Vary everything by rule”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/parametric-variation. Text, drawings and models licensed under CC BY-NC 4.0.