  The goal of this work is to elaborate on new geometric methods of
constructing exact and parametric quasiperiodic solutions for anamorphic
cosmology models in modified gravity theories, MGTs, and general relativity,
GR. There exist previously studied generic off-diagonal and diagonalizable
cosmological metrics encoding gravitational and matter fields with quasicrystal
like structures, QC, and holonomy corrections from loop quantum gravity, LQG.
We apply the anholonomic frame deformation method, AFDM, in order to decouple
the (modified) gravitational and matter field equations in general form. This
allows us to find integral varieties of cosmological solutions determined by
generating functions, effective sources, integration functions and constants.
The coefficients of metrics and connections for such cosmological
configurations depend, in general, on all spacetime coordinates and can be
chosen to generate observable (quasi)-periodic/ aperiodic/ fractal / stochastic
/ (super) cluster / filament / polymer like (continuous, stochastic, fractal
and/or discrete structures) in MGTs and/or GR. In this work, we study new
classes of solutions for anamorphic cosmology with LQG holonomy corrections.
Such solutions are characterized by nonlinear symmetries of generating
functions for generic off--diagonal cosmological metrics and generalized
connections, with possible nonholonomic constraints to Levi-Civita
configurations and diagonalizable metrics depending only on a time like
coordinate. We argue that anamorphic quasiperiodic cosmological models
integrate the concept of quantum discrete spacetime, with certain gravitational
QC-like vacuum and nonvacuum structures. And, that of a contracting universe
that homogenizes, isotropizes and flattens without introducing initial
conditions or multiverse problems.
