The goal of this Thesis is to investigate spatial self-organization. The cellular coherence
is the mechanism of local actioning units ensembled over a network to generate
organization. The cells are modeled as computational machines acting through their
regulatory networks with di erent types being the attractors of such automata. The
self-organized cell types across the tissue is the emergent organism.
The work consists of two building blocks: Cellular dynamics and gene regulation.
In cellular dynamics, we cellularize continuous space-time dynamics on a general
manifold into discrete dynamics on a mesh. Singular attractor is proposed as a novel
dynamics that generates tissue-wide symmetry breaking which is key for generating
form in an organism. Extending the model to dipolar attractor, it is shown that
animal body plans can self-organize by self-generated positional information.
In gene regulation, we develop the computron as a generalized computational
model of genetic regulatory networks where each gene is a node of the machine and
the attractor con gurations are the cell types. We provide a formal set-theoretic
framework for embedding the gene regulatory network into a novel metric space,
called the diversity space. A measure for complexity of regulation is proposed using
entanglement complexity of basin partitioning. Combining cellular dynamics and
gene regulation, a model for morphogenesis is presented.
In this Thesis, we invented a mechanism for developing fully
edged organism
forms through self-organization, contributing a mathematical basis to biological theory
of development. Whether Nature does it the same way remains to be seen. On
the practical front, our work can be used for building self-organizing nano-machinery,
and can nd applications in soft robotics and biomimetic architecture.