2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80048We show mathematical structure of the function dynamics, i.e., the dynamics of interval maps $f_{n+1} = (1-\e)f_n + \e f_n\circ f_n$ and clarify the types of fixed points, the self-referential structure and the hierarchical structure.16 pages, 14 figuresAdaptation and Self-Organizing Systemstext