LOCAL SYMMETRY

One of Alexander's fifteen properties; appears in birthday table, handshake, and namaste examples

Neighborhood — ranked by edge-count

framework

Fifteen Properties of Living Centers
extends
Alexander's structural framework for identifying living centers; referenced as analytical tool for comparing artworks

concept

Local Symmetries
related_to
The property that living wholes contain many interlocking and overlapping local symmetries rather than overall symmetry; local symmetries act as glue holding space together, and their number predicts cognitive coherence
Local Symmetries Transformation
related_to
A structure-preserving transformation: introducing symmetries within a center, not globally, to strengthen local order.
Local-Symmetry Transformation
related_to
A transformation that strengthens a center by giving it an internal axis of symmetry, local to the center.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Local Hamiltonianconcept0.782
Sum of windowed Hamiltonians with same window length; a key construct introduced in the paper to model local interactions on graphs
Translation Symmetryconcept0.777
Movement in a given direction through a given distance; all frieze patterns possess this symmetry by definition.
rotation symmetryconcept0.775
Rotation about a point by an angle 360°/n leaving the pattern invariant
Reflection Symmetryconcept0.768
One of four key isometries; reflection across a line (mirror line or axis of reflection).
Local symmetries are pervasive in nature (sun, trees, crystals, bodies) and are associated with minimum energy and least-action principles.claim0.764
Local symmetries act as a kind of glue which holds space together; the more glue there is, the more the space is one, solid, unified, coherent—and the symmetrical segments must overlap for the glue to be effectiveclaim0.760
Interpretation of the experimental finding: overlapping local symmetries are the hidden structural feature that creates perceived wholeness
Symmetry Groupsconcept0.756
Rotational Symmetryconcept0.746
One of four key isometries; rotation about a point through a given angle, with n-fold variants based on 360°/n invariance.