A geometric model for non-uniform processes of morphogenesis

TL;DR

This paper introduces a geometric groupoid-based model for understanding non-uniform morphogenesis processes, providing a unified framework and explicit equations for material evolution in morphogenesis.

Contribution

It applies groupoid theory to morphogenesis, offering a novel, simple mathematical framework and explicit equations for modeling material distribution during morphogenetic processes.

Findings

Develops the morphogenesis equation for material distributions

Provides a unifying geometric framework for morphogenesis phenomena

Simplifies the mathematical modeling of material evolution

Abstract

In this paper we present an application of the groupoid theory to the study of relevant case of material evolution phenomena, the \textit{process of morphogenesis}. Our theory is inspired by Walter Noll's theories of continuous distributions and provides a unifying and very simple framework of these phenomena. We present the explicit equation, the \textit{morphogenesis equation}, to calculate the \textit{material distributions} associated to this phenomenon.