Physarum machines imitating a Roman road network: the 3D approach

The evolution of an experiment under the influence of landscape height is shown in Fig. 11. The evolution proceeds in a similar manner to the no-height condition but the pores in the virtual Plasmodium form predominantly at regions of greater landscape height (Fig. 11(b) and (c)). The network minimisation continues as with the no-height condition but the network adaptation is constrained by the influence of landscape height. Note that there were occasionally some spurious remnants of particle trails (for example in the bottom right corner of Fig. 11(d)). These were caused by the particle trails becoming ‘trapped’ by the terrain in enclosed regions and did not affect the network analysis as these regions were disconnected from region nodes.

Twenty experiments were performed for both no-height and landscape height conditions. Adjacency matrices were constructed from the network analysis results and the results are summarised in Fig. 12 where edge strength is proportional to edge thickness.

The connectivity of both no-height and landscape height conditions with increasing values of the edge weight parameter w can be seen in Fig. 13 and Fig. 14. Numerical values of mean degree connectivity for both conditions can be seen in Table 1 which shows the regions ranked in order of highest mean connectivity. In both conditions region 4 (Skopje) has the highest connectivity. However, in the networks where landscape height modulated the virtual Plasmodium behaviour there is a shift in connectivity to regions to the left of region 1 (Thessaloniki). This is most evident with an increase in the connectivity of region 6 (Dyrrachium). The shift in region influence under the landscape height condition can be observed in the visualisations denoted in Fig. 15 where the radius of the regions vary in proportion to their mean degree value.

As has been repeatedly proved in different experiments (eg. experiments where slime mould navigates a maze) the simple amoeboid organism P. Polycephalum has an innate heuristic shortest path ability that can solve decision making problems (especially multi source problems). This becomes possible mainly due to the fact that the oscillatory cytoplasm of the Plasmodium is a spatially extended nonlinear excitable medium which closely matches the dynamics of other reaction – diffusion systems. As shown in the previous experiment27 the method can actually be applied on the archaeological or historical research as means to recreate networks and the decision making strategies behind them.

However, in order for the technique to evolve to a real archaeological tool, it must clearly be able to allow the researcher to incorporate in the experiments these geographical features which influenced or constrained choices important in the development of a network. The recent developments in 3D printing and solid terrain modelling promise a relatively accessible platform so as to test different case scenarios with the use of Physarum machines while at the same time Geoarchaeology52 can provide solid evidence so as to recreate terrains that will resemble very closely to past physical landscapes. It is clear that the heuristic ability of P. Polycephalum (and probably of similar unconventional computing methods) can evolve to become a very dynamic way to explore these terrains. Concerning the Roman road network in the Balkans the slime mould experiments on a 3D terrain showed that once more the P. Polycephalum managed to create a network which resembled to a great extent not only the results of the previous experiment on a flat terrain but also physical reality.

In our previous article we gave special emphasis on the interdisciplinary character of the experiment, noticing at the same time the limitations but also the theoretical considerations concerning the application of such methods in archaeology. The greatest possibly advantage of P. Polycephalum experiments as other unconventional computing methods lies on the fact that it provides a non human-biased method of modelling the world or living phenomena. 3D terrain brings the analogous modelling closer to reality since P. polycephalum, due to its positive geotropism, navigates around and through elevations recreating successfully the network. Overcoming this limitation (and the practical difficulties of applying a new computational method) it becomes clear that now the issue lies on the way that the technique can become a viable archaeological method. This requires the existence of a strong theoretical underpinning combined with well planned archaeological case studies which will instigate new experiments. Issues of specialized interest (for instance to explore the route that Via Egnatia followed in Thrace) or more theoretical and general questions (for instance the relationship between water bodies, river valleys and the development of roads) can be potentially be the next step for Physarum machines in archaeology.

V.E., G.S. and A.A. conceived the experiments, J.J. conducted the modeling experiments, A.A. conducted the biological experiments, J.J., N.D., M.T., G.S. and A.A. analysed the results. All authors reviewed the manuscript.