Black-and-white (inscribed square)   Index


This example shows a derivation (Stiny, 1985) applying a rule to inscribe a square with a rotated square, alternating the color between black and white. Originally, this constituted a three-rule grammar: one rule creates a square from an initial marker, another creates a rotated square inscribed within the original square, and a final rule removes the marker. The role of the marker, a point, is to guide the generation, by moving from one square to the next. Stiny does consider an alternating infill of the squares in black and white, however without explicating the relevant rules. This infill requires the specification of a fourth rule, as the infill alternates between black and white. The example uses points, line segments, plane segments and gray-tone weights as primitive sortal structures.

An exemplar result:

The four rules (left) and the derivation (right):


Stiny (1985) also shows a variant derivation based on a parametric rule set applied to quadrilaterals. The figure below illustrates the use of parametric-associative rules to achieve the same, or similar, including the alternating infill. The only difference is the fact that the inscribed quadrilateral always links the midpoints of the sides of the previous quadri- lateral. This is a current limitation of parametric-associative matching.

The four rules (left) and the derivation (right):

The relevant Rhino/GH files form part of the SortalGI plug-in.


  1. G. Stiny, 1985, Computing with Form and Meaning in Architecture, Journal of Architectural Education 39(1), 7-19.

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