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isomorphism

Isomorphism [Greek isos, equal; morphe, form, configuration] is a precise mathematical concept borrowed by systems theorists. Hofstadter (1979) notes that the word "applies when two complex structures can be mapped onto each other, in such a way that to each part of the structure there is a corresponding part in the other structure, where 'corresponding' means that the two play similar roes in their respective structures" (p. 49). The copy "preserves all the information in the original theme, in the sense that the theme is fully recoverable from any of the copies." Isomorphism, therefore, is "an information - preserving transformation" (p.9).
Credit

Definition extracted with permission from Simon, Fritz, et al, Family Process, Inc.: Language of Family Therapy: A Systemic Vocabulary and Source Book (Family Process Press Series)