  The true slime mould Physarum polycephalum is a recent well studied example
of how complex transport networks emerge from simple auto-catalytic and self-
organising local interactions, adapting structure and function against changing
environmental conditions and external perturbation. Physarum networks also
exhibit computationally desirable measures of transport efficiency in terms of
overall path length, minimal connectivity and network resilience. Although
significant progress has been made in mathematically modelling the behaviour of
Physarum networks (and other biological transport networks) based on observed
features in experimental settings, their initial emergence - and in particular
their long-term persistence and evolution - is still poorly understood. We
present a low-level, bottom-up, approach to the modelling of emergent transport
networks. A population of simple particle-like agents coupled with paracrine
chemotaxis behaviours in a dissipative environment results in the spontaneous
emergence of persistent, complex structures. Second order emergent behaviours,
in the form of network surface minimisation, are also observed contributing to
the long term evolution and dynamics of the networks. The framework is extended
to allow data presentation and the population is used to perform a direct
(spatial) approximation of network minimisation problems. Three methods are
employed, loosely relating to behaviours of Physarum under different
environmental conditions. Finally, the low-level approach is summarised with a
view to further research.
