A Minimal CA-Based Model Capturing Evolutionarily Relevant Features of Biological Development

Understanding how complex biological forms emerge and evolve remains a central question in evolutionary and developmental biology. To explore this complexity, we introduce a minimal two-dimensional, cellular automaton (CA)-based model that captures key features of biological development—such as spatial growth, self-organization, and differentiation—while remaining computationally tractable and evolvable. Unlike most abstract genotype–phenotype mapping models, our approach generates emergent morphological complexity through spatially explicit rule-based interactions governed by a simple genetic vector, resulting in self-organized patterns reminiscent of biological morphogenesis. Using simulations, we show that, as observed in empirical studies, the resulting phenotypic distribution is highly skewed: simple forms are common, while complex ones are rare. The model exhibits a strongly non-linear genotype-to-phenotype mapping in such a way that small genetic changes can lead to disproportionately large morphological shifts. Notably, transitions toward complexity are less frequent than regressions to simplicity, reflecting evolutionary asymmetries observed in natural systems. We further demonstrate that, by allowing for mutations in the generative rules, our model is capable of adaptive evolution and even reproducing generic features of tumoral growth. These findings suggest that even minimal developmental rules can give rise to rich, hierarchical patterns and complex evolutionary dynamics, positioning our CA-based model as a powerful tool for investigating how developmental constraints and biases shape morphological evolution.