Convolution of 2D objects into an invariant and probabilistic “genetic code”

We developed an algorithm for convolving two-dimensional images into a compact, linear, and probabilistic “genetic code” inspired by biological mechanisms of storing and transmitting hereditary information. Our approach simulated processes of cell division, differentiation, and mutation by treating each pixel of a two-dimensional image as a conditional cell and its color as a cell type. The algorithm implemented a probabilistic image traversal with random direction selection, which ensured invariance to processing order and reproduced the stochasticity of biological systems. Each element was encoded as a rule containing a color identifier, links to neighboring elements, and special markers indicating dead ends.
We proposed an optimization method that removed zero values, switched to relative links, and fixed string length to improve access efficiency. We also introduced two types of mutations: parametric (color changes) and structural (topology violations), which allowed us to model structural evolution. The algorithm produced a text file containing division rules, a color palette, and meta-information sufficient to reconstruct the original image. Experiments with images of varying complexity confirmed the correctness of the convolution and demonstrated the possibility of modeling mutations. This method creates prospects for applications in bioinformatics, robotics, and adaptive systems, including the development of self-organizing and self-reproducing structures.