|From a visual standpoint it is often easy to point out whether a system is considered to be
self-organizing or not, though a quantitative approach would be more helpful. Information
theory, as introduced by Shannon, provides the right tools not only quantify self-organization,
but also to investigate it in relation to the information processing performed by
individual agents within a collective.
This thesis sets out to introduce methods to quantify spatial self-organization in collective
systems in the continuous domain as a means to investigate morphogenetic processes.
In biology, morphogenesis denotes the development of shapes and form, for example
embryos, organs or limbs. Here, I will introduce methods to quantitatively investigate
shape formation in stochastic particle systems.
In living organisms, self-organization, like the development of an embryo, is a guided
process, predetermined by the genetic code, but executed in an autonomous decentralized
fashion. Information is processed by the individual agents (e.g. cells) engaged in this
process. Hence, information theory can be deployed to study such processes and connect
self-organization and information processing. The existing concepts of observer based
self-organization and relevant information will be used to devise a framework for the
investigation of guided spatial self-organization.
Furthermore, local information transfer plays an important role for processes of self-organization.
In this context, the concept of synergy has been getting a lot attention lately.
Synergy is a formalization of the idea that for some systems the whole is more than the sum
of its parts and it is assumed that it plays an important role in self-organization, learning and
decision making processes. In this thesis, a novel measure of synergy will be introduced,
that addresses some of the theoretical problems that earlier approaches posed.