Conceptual Model

The Pattern Analysis, Typology, and Holarchy (PATH) framework, developed through my doctoral research, includes a conceptual model for understanding relationships among the underlying structure, topological type, and variable expression of non-maze labyrinths.

An underlying structure captures structural organization from which a labyrinth path may be developed or which may be derived through analysis. Underlying structures include circuit permutations, axis configurations, and component compositions. A topological type is the invariant path topology of a viable labyrinth, independent of variable form and realization. A labyrinth expression is a particular form or realization of a topological type. These concepts are related through complementary analytical and generative processes, described below.

Underlying structure describes structural organization that can serve as a starting point for generating a labyrinth type or can be derived through analysis of an existing type.

PATH currently considers three complementary forms of underlying structure:

• Circuit permutation: the ordered arrangement of circuit levels without path connections.

• Axis configuration: the structural organization of path connections at an axis.

• Component composition: the organization of smaller structural components within a larger labyrinth structure.

These forms of underlying structure provide different ways of describing and working with the same labyrinth topology. They are not separate categories of labyrinths, and more than one may be useful in analyzing or generating a particular type.

A topological type represents the invariant path topology of a viable labyrinth. It describes how the path is connected and organized independently of variable features of its visible form or physical realization.

Different labyrinth expressions therefore belong to the same topological type when differences in shape, proportion, orientation, style, materials, or other variable features do not change the underlying path topology.

Within PATH, a potential path structure is evaluated against applicable viability conditions before it is recognized as a topological type. Additional structural characteristics can then be used to classify and compare viable types.

A labyrinth expression is a variable form or realization of a topological type. A single topological type can therefore have many different expressions.

Variation may include features such as overall shape and proportion, visual style, orientation, dimensions, materials, path and boundary treatment, or other design choices. An expression may remain a design or specification, or it may be instantiated as a particular constructed, drawn, or otherwise realized labyrinth.

The distinction between topological type and labyrinth expression makes it possible to recognize structurally equivalent labyrinths even when they look substantially different, while also describing meaningful variation among their forms and realizations.