Patterns and Index Cells

According to Christopher Alexander, a pattern is a morphological law that establishes a set of relationships in space. In the most general form:

X -> r (A, B, ...), which means:

Within a context of type X, the parts A, B, ... are related by the relationship r.

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Later he expanded his definition as follows:

Each pattern is a three-part rule r(P, X, S), which expresses a relation r between a certain context X, a problem P, and a solution S.

(The 'problem' part can be understood as the semantics of the pattern)