The fifteen transformations provide the base transformations from which, in practice, all structure-preserving transformation are made.

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

• Each of the fifteen transformations designates one way in which a structure may be transformed into another structure, while increasing its life.quote0.865
  Defines the role of the transformations in generating living structure.
• The fifteen transformations provide us with a natural 'alphabet' of living process.claim0.851
  Asserts that the fifteen structure-preserving transformations can serve as elementary units for generating living form.
• The unfolding of wholeness through structure-preserving transformations must inevitably create the fifteen properties.hypothesis0.849
• All eleven principles are, of course, embodiments of the fifteen transformations.claim0.842
  States that the teaching principles directly instantiate the underpinning theory.
• The fifteen properties come into existence naturally as a result of the structure-preserving process.claim0.833
  Claim that the properties are not applied artificially but are consequences of correct unfolding.
• Structure-Preserving Transformationsconcept0.832
  Chapter 2 of Volume 2 of The Nature of Order, introducing structure-preserving transformations as the mechanism by which living structure arises naturally through unfolding wholeness.
• Structure-preserving transformations govern the emergence of all structure in nature, not just in buildings and art.hypothesis0.831
  Alexander's conjecture extending the unfolding framework from architecture to natural phenomena generally.
• The fifteen transformations guarantee the appearance of orderly large and larger wholes with beautiful internal geometry; this is the secret of all living process.claim0.829
  Strong assertion that the entire generative capacity of life in space reduces to repeated application of the fifteen transformations.