Abstract
Most studies of pattern formation place particular emphasis on its role in the development of complex multicellular body plans. In simpler organisms, however, pattern formation is intrinsic to growth and behavior. Inspired by one such organism, the true slime mold Physarum polycephalum, we present examples of complex emergent pattern formation and evolution formed by a population of simple particle-like agents. Using simple local behaviors based on chemotaxis, the mobile agent population spontaneously forms complex and dynamic transport networks. By adjusting simple model parameters, maps of characteristic patterning are obtained. Certain areas of the parameter mapping yield particularly complex long term behaviors, including the circular contraction of network lacunae and bifurcation of network paths to maintain network connectivity. We demonstrate the formation of irregular spots and labyrinthine and reticulated patterns by chemoattraction. Other Turing-like patterning schemes were obtained by using chemorepulsion behaviors, including the self-organization of regular periodic arrays of spots, and striped patterns. We show that complex pattern types can be produced without resorting to the hierarchical coupling of reaction-diffusion mechanisms. We also present network behaviors arising from simple pre-patterning cues, giving simple examples of how the emergent pattern formation processes evolve into networks with functional and quasi-physical properties including tensionlike effects, network minimization behavior, and repair to network damage. The results are interpreted in relation to classical theories of biological pattern formation in natural systems, and we suggest mechanisms by which emergent pattern formation processes may be used as a method for spatially represented unconventional computation.
Highlights
Pattern Formation, Background, Mechanisms, and ModelingPattern formation mechanisms play a critical role in organism development and survival, from embryonic development to the growth and maintenance of the organism
We have presented a particle-based approach to complex pattern formation and evolution by emergent transport networks inspired by the behaviors of Physarum polycephalum—an organism whose very existence is based on mobile pattern formation and pattern evolution
The results presented in this article are in the spirit of chemotaxis-based cell migration approaches to pattern formation
Summary
The model uses a multi-agent approach that was introduced in [24] as a means of constructing synthetic and bottom-up dynamical transport networks. A layered approach is used: As well as the data landscape layer where the environment configuration is stored and the agents reside, other data structures, identical in size and corresponding to the coordinate system of the data layer, may be used (Figure 2) These separate layers are used to represent the projection of hazardous stimuli to the population (not described in this article) and to store the chemotactic stimuli that the agents both deposit and follow (the trail layer). Agents are selected from the population randomly in the motor and sensory stages to avoid the possibility of long term bias by sequential ordering The agent both deposits to and senses from the trail map, resulting in an autocrine mode of stimulus/response. Video recordings are referred to below with names beginning “VR F”
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