Conceptual Model

Quantum Potential > Dynamic Thread > Static Expression

The three states conceptual model, part of my doctoral research, provides a theoretical framework for understanding the generative processes underlying labyrinth patterns.

Labyrinth types can be thought of as having three states: a quantum potential state, a dynamic thread state, and a static expression state.

Each circuit permutation in the quantum potential state maps to multiple possible subsets in the dynamic thread state.
Each thread that satisfies the conditions of a subset is a viable labyrinth type.
Each viable labyrinth type maps to unlimited static expressions with a variety of recognizable general styles and highly individualized specific styles.

Conversely, we can analyze a static expression (i.e., a labyrinth) and derive the dynamic thread diagram and level sequence, and the underlying quantum potential circuit permutation.

Three States Example

The source set S_n contains the quantum potential state of all Simple Labyrinths. It is the complete symmetric set of permutations given a particular number of circuits (n). The numbers are rearranged without consideration of any connections to other circuits or to the additional levels (0 and in some cases n + 1) that give context for the subsets.*

For example, when n = 3, S_3 contains six permutations: 123, 132, 213, 231, 312, and 321. We can take these permutations and apply the conditions of each subset to move from the quantum potential state to the dynamic thread state and identify the viable types:

SAT_3 = {0|123|4, 0|321|4}
SXT_3 = {0|123|4, 0|1x23|4, 0|1x2x3|4, 0|12x3|4}
SZT_3 = { } = ∅
SYP_3 = {0|12(3)|0, 0|1y(3)2|0, 0|2(3)y1|0, 0|(3)21|0}

Processional types are a special case. These four SYP_3 level sequences represent only two types which each have a base approach and a transpose approach:

B: 0|12(3)|0, T: 0|(3)21|0
B: 0|1y(3)2|0, T: 0|2(3)y1|0

Continuing on to the static expression state, we can choose one of these eight viable 3-circuit types and make decisions about size, shape, style, orientation, chiral reflection (right- or left-hand entrance), materials, and decorative embellishments to create a realized labyrinth.

* The Simple subsets are Simple Alternating Transit (SAT), Simple Spiral Crossing Transit (SXT), Simple Bayonet Crossing Transit (SZT), and Simple Crossing Processional (SYP).

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