Fractal and chaotic patterns in animal morphology

Abstract

In the review the spatial organization of cells, cell ensembles, tissues and metazoan body are considered using the concepts of fractal geometry, topology and dynamic chaos theory. We investigated both the scenario of transition from chaos into order during self-organization of cells in vitro and the reverse scenario of transition from order to chaos in the fractal morphogenesis of metazoan cell systems. Chaotic features in animal morphology were identified and quantified. Fractal morphogenesis was studied using epithelial branching channels of gastrovascular system in the scyphomeduse Aurelia aurita and tracheal gill system in the mayfly larvae Siphlonurus immanis and Parameletus chelifer, as well as structures of colonial interna in rhizocephalan crustaceans Peltogasterella gracilis and Polyascus polygenea. It was shown that completely identical fractal patterns do not occur even within a single animal body with radial or bilateral symmetric, functionally equivalent repetitive modules. Fractal dimension was used to quantify the spatial complexity of neuron morphology in central nervous system of the fishes Pholidapus dybowskii, Oncorhyhchus keta and Oncorhyhchus masou. During ontogenesis of Oncorhyhchus masou the values of fractal dimension and linear morphometric indicators were rising in studied neuron groups. Probably biological morphogenesis with chaotic fractal regime had an advantage in evolution, providing morphofunctional variability, plasticity and adaptability to unpredictable environmental changes.