Circuit and Level Sequence

Circuit levels are the areas of orbital movement. For n circuits, circuit levels are numbered 1 through n, beginning with the outermost circuit. Levels also include the exterior level 0 and center level n + 1.

Circuit Permutation records successive circuit levels by sector unit. Circuit Sequence records successive circuit levels by circuit section, combining units connected through direct crossings into a single entry. Circuit permutations and sequences do not fully specify connectivity and can therefore be shared by more than one type.

Level Sequence includes exterior, circuit, and center levels. Annotated Level Sequence also marks crossing transitions. Turning transitions are assumed where no crossing is annotated. An Annotated Level Sequence can uniquely represent a topological type when its annotations fully specify the required connections.

In some contexts, circuits may be numbered from inside to outside, but for analysis, and from the labyrinth user’s perspective, levels are numbered outside to inside. A single numbering  approach can also be expressed in multiple ways depending on the analysis or user context. For example:

• 3, 2, 1

• 3-2-1

• 321

• 0 3 2 1 4

• 0 | 3 2 1 (4)

Outside-in numbering:

• Typically used for pattern analysis

• Relates to the dynamic transformation of the path thread to or from its underlying mathematical topology

• Begins where the walker begins

Inside-out numbering:

• Sometimes used in design and construction contexts

• Relates to static expressions of a type and design/construction

• Begins where the builder begins