The manner in which nucleosomes stack to form higher order chromatin is critical to biological regulation of gene expression, but remains poorly understood. Throughout this work, we utilize multiple coarse-grained models to characterize chromatin structure across length-scales, and lend physical interpretation to experimental results. Our simulations reveal that classical, ideal models for chromatin structure are not thermodynamically stable, and that chromatin displays a wide range of heteromorphic structures at equilibrium which span the range between these ideal models. We combine these simulation results with Bayesian maximum a-posteriori estimation to augment the interpretability of related cryo-electron microscopy techniques which have heretofore been used to characterize chromatin fiber structure. We further extend these simulations to fibers of chromatin bearing H4K16 acylations, which are epigenetic marks understood to drive increases in gene expression in vivo. Our results demonstrate that, although all H4K16 acylations significantly alter chromatin fiber structure, the resulting structural variation is small compared to the natural heterogeneity present in each fiber at equilibrium.Lastly, we develop and validate a novel method to directly compare and contrast chromatin structural measurements obtained by complementary Hi-C and IF-sSMLM measurements, and demonstrate this method's utility on simulated chromatin structures. In total, our work both adds considerable detail to the field of chromatin folding, and provides clear avenues for future developments of combined computational and experimental techniques.