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The goal of this work is to elaborate on new geometric methods ofconstructing exact and parametric quasiperiodic solutions for anamorphiccosmology models in modified gravity theories, MGTs, and general relativity,GR. There exist previously studied generic off-diagonal and diagonalizablecosmological metrics encoding gravitational and matter fields with quasicrystallike structures, QC, and holonomy corrections from loop quantum gravity, LQG.We apply the anholonomic frame deformation method, AFDM, in order to decouplethe (modified) gravitational and matter field equations in general form. Thisallows us to find integral varieties of cosmological solutions determined bygenerating functions, effective sources, integration functions and constants.The coefficients of metrics and connections for such cosmologicalconfigurations depend, in general, on all spacetime coordinates and can bechosen to generate observable (quasi)-periodic/ aperiodic/ fractal / stochastic/ (super) cluster / filament / polymer like (continuous, stochastic, fractaland/or discrete structures) in MGTs and/or GR. In this work, we study newclasses of solutions for anamorphic cosmology with LQG holonomy corrections.Such solutions are characterized by nonlinear symmetries of generatingfunctions for generic off--diagonal cosmological metrics and generalizedconnections, with possible nonholonomic constraints to Levi-Civitaconfigurations and diagonalizable metrics depending only on a time likecoordinate. We argue that anamorphic quasiperiodic cosmological modelsintegrate the concept of quantum discrete spacetime, with certain gravitationalQC-like vacuum and nonvacuum structures. And, that of a contracting universethat homogenizes, isotropizes and flattens without introducing initialconditions or multiverse problems.

Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections