The fifteen properties appear again and again throughout nature at all scales, from subatomic particles to galaxies.

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

• The fifteen properties appear in nature as a direct result of repeated structure-preserving transformations unfolding the wholeness.claim0.881
  Interpretation that the geometric properties of living structure are not arbitrary but arise inevitably from the smooth unfolding process.
• The fifteen properties appear in nature because they are structural complements to the formation of stable and semistable systems, contributing to coherence and stability.hypothesis0.869
• Why do the fifteen properties occur in nature?question0.849
• The fifteen properties are fundamental to the existence of wholeness and thus to all physical structures, not merely visual features of artifacts.claim0.826
  The chapter's central thesis, arguing that the properties are necessary manifestations of wholeness in any generated system.
• The fifteen properties are the ways centers sustain each other's coherence, thereby contributing to the stability and robustness of natural systems.claim0.824
  Proposed as the reason the properties appear in functionally stable or semistable systems.
• The fifteen properties emerge directly and inevitably from the unfolding of the whole; it is these fifteen properties that guide all differentiations during development.claim0.821
  Alexander's claim that living structure properties are not incidental but are the operative mechanisms of wholeness-preserving transformation
• The fifteen properties are not merely visual features which appear in works of art. ... they must be fundamental to the appearance of life in all centers that are generated or created in any system.quote0.819
  Foundation of the chapter's argument that the properties transcend aesthetics and are fundamental to all physical reality.
• The fifteen properties are attributes of wholeness and appear naturally when one focuses on enhancing the whole through structure-preserving transformations.claim0.818
  Linking the fifteen properties to the process of seeking wholeness.