We are going to study finite lattice systems in the context of simple rewriting rules: based on discrete manifolds and Cayley graphs, in this project we look for the set and taxonomy of simple rewriting rules that preserve certain properties that can later be understood as conserved measurable magnitudes of a physical system, like the Brouwer degree or winding number. By investigating those toy models about field configurations of discrete fiber bundles, we will later apply local perturbations to a field configuration, looking for discrete analogs to Noether's theorem. Furthermore, via coloured graphs, with this approach we will aim to characterise (energetically stable) physicalinspired systems in the context of manyparticle quantum finite distributions in highly symmetric arrays or lowdimensional spinlike states as domain wall in magnetization theory, being local solutions of minimal information configurations. Even mesoscopic scale is responsible for exotic topological defects; with this discretization, we will try to understand the computational firstprinciple mechanism that allows nontrivial winding numbers and the material and geometries to host pseudoparticle structures like skyrmions, bubbles or merons. We think that this inductive reasoning here would offer a valuable approach for finding new phenomena or even reinterpreting old ones.