Route 20, autobahn 7 and Physarum polycephalum: Approximating longest roads in USA and Germany with slime mould on 3D terrains (1211.0519v1)

Abstract: Acellular slime mould Physarum polycephalum is a monstrously large single cell visible by an unaided eye. It shows sophisticated behavioural traits in foraging for nutrients and developing an optimal transport network of protoplasmic tubes spanning sources of nutrients. The slime mould sufficiently approximates man-made transport networks on a flat substrate. Does slime mould imitate man-made transport networks on three-dimensional terrain as well as it does on a flat substrate? We simplified the problem to approximation of a single transport route. In laboratory experiments with 3D Nylon terrains of USA and Germany we imitated development of route 20, the longest road in USA, and autobahn 7, the longest national motorway in Europe. We found that slime mould builds longer transport routes on 3D terrains, comparing to flat agar plates yet sufficiently approximates man-made transport routes studied. We discuss how nutrients placed in destination sites affect performance of slime mould, how the mould navigates around elevations, and offer an automaton model of slime mould which might explain variability of the protoplasmic routes constructed. We also display results of scoping experiments with slime mould on 3D terrains of Russia and United Kingdom.

• The paper investigates the ability of Physarum polycephalum slime mold to approximate lengthy transport routes like USA's Route 20 and Germany's Autobahn 7 on 3D terrain models.
• Experiments on 3D-printed topographies showed that the slime mold's paths were surprisingly longer than the actual routes on 3D terrains compared to flatter surfaces, averaging 1.095x (USA) and 1.158x (Germany) the length.
• Topographical features significantly influenced the mold's navigation, causing it to deviate around natural obstacles, highlighting limitations compared to human-engineered infrastructure like tunnels or bridges.

Analyzing Physarum Polycephalum's Path Optimization on 3D Terrains

The research paper investigates the ability of the acellular slime mold, Physarum polycephalum, to approximate the longest transport routes in the USA (Route 20) and Germany (Autobahn 7) using 3D terrain models. The paper explores whether the slime mold can replicate human-constructed transport networks on non-flat surfaces, simulating a single transport route through simplified experimental setups with 3D Nylon terrains representing the designated countries.

The paper involves evaluating the path-finding capabilities of P. polycephalum in laboratory experiments, where the slime mold was allowed to grow over models mimicking the terrains of the USA and Germany. The experiment aimed to discern if the mold's behavior changed on 3D terrains compared to traditional flat agar substrates. Physarum's path creations were analyzed to determine their correspondence to the real-world Route 20 and Autobahn 7.

Methodology and Experimentation

Physarum polycephalum was inoculated and allowed to propagate towards nutrient sources both in 3D and flat agar terrains. On 3D models, nutrients were strategically placed at one end of the route, simulating a nutrient gradient that influences the mold's growth direction. Critical measurements involved comparing the lengths and trajectories of the slime mold-created paths to the actual highways in both the USA and Germany.

The experiments utilized 3D-printed topographies from elevation data, representing these nations' significant geographical reliefs. The slime mold’s paths were observed and recorded over several days to analyze their alignment and deviation from the designated transport routes.

Findings

1. Approximation Efficiency: Surprisingly, on 3D terrains, P. polycephalum was found to create paths that were on average 1.095 times longer than Route 20 in the USA and 1.158 times longer than the Autobahn 7 in Germany. On flat agar, the paths created were 1.046 and 1.005 times the lengths of Route 20 and Autobahn 7, respectively. This suggests better approximation on simpler, flat substrates likely due to the absence of terrain-induced deviation.
2. Topographical Influence: The experiments highlighted that the mold's pathfinding was affected by the topography. The slime mold navigated around major geographical barriers such as mountains, indicating a physical sensitivity that impacts its growth on 3D terrains. These deviations underscored the mold's inability to emulate infrastructures designed to penetrate through or bypass such natural obstacles efficiently, as human-engineered solutions like tunnels and bridges do.
3. Route Variability: Slime mold showed significant variability in the routes it created, which could be attributed to its inherent biological variability and response to environmental stimuli.
4. Computational Model Validity: A computational cellular automaton model was developed to mimic the slime mold's growth patterns. This model also indicated that path lengths decreased with increased excitation levels, paralleling the mold’s behavior in physical experiments, thus supporting certain theoretical aspects of the mold's navigation capabilities, albeit in a simulated environment.

Implications and Future Directions

The research enhances our understanding of biological computation and its potential application in network optimization. The paper illustrates how the biological processes of P. polycephalum can inspire and potentially lead to alternative methods for designing transport networks, particularly in consideration of complex geographical factors.

Future work could focus on refining computational models to better predict slime mold behavior, as well as testing on varied and more complex terrains to further explore the mold's adaptive mechanisms. There is also potential for examining the mold's behavior when presented with multi-criteria pathfinding challenges, such as cost-optimal paths that balance distance with other factors like elevation change and resource availability.

This paper's insights may serve as a stepping stone for further integration of biological strategies in computational and engineering problems, particularly in enhancing the adaptability and efficiency of transport network designs in challenging terrains.