1 Introduction

Bio-inspired computing focuses on extracting computational models for problem solving from in-depth understanding of behaviour and mechanisms of biological systems. In recent years, cellular computational models based on the structure and the processes of living cells, such as bacterial colonies (Kim et al. 2007) and viral models (Cortés et al. 2008) have become an important line of research in bio-inspired computing. Physarum-computing, as an example of cellular computing model, has attracted the attention of many researchers (Tero et al. 2010). Physarum polycephalum (Physarum for short) is an example of plasmodial slime moulds that are classified as a fungus "Myxomycetes" Cavender (1995). In recent years, research on Physarum-inspired computing has become more popular since (Nakagaki et al. (2000)) performed their well-known experiments showing that Physarum was able to find the shortest route through a maze (Nakagaki et al. 2000). Recent research has confirmed the ability of Physarum-inspired algorithms to solve a wide range of problems (Zhang et al. 2016b; Sun 2014) designed a real biological experiment where they measured the electrical activity of Physarum in the presence of stimuli (one food source) (Traversa et al. 2013; Whiting et al. 2014). The goal of the experiment was to show how the Physarum changes patterns of its electrical activity when exposed to attractants and repellents. Based on the fact that Physarum learn and adapt to periodic changes in its environment (Liu et al. 2015a; Reid et al. 2012). Gale et al. (2014) demonstrated that the protoplasmic tubes of the Physarum showed current versus voltage characteristics that is consistent with ideal memristor-systems (Gale et al. 2014). Memristor has been previously used in oscillation-based circuits and systems able to solve computationally hard problems (Ntinas et al. 2017b, a) and emerge neuron-like behaviour (Ntinas et al. 2018). For reviewing the foundations of memristor theory and applications, refer to Erokhin (2014) (Erokhin 2014).

Ntinas et al. (2017b) designed a real experiment similar to that of Whiting et al. (2014); where they presented a bio-inspired memristor-based circuit maze-solving approach. They measured the oscillatory electrical activity of Physarum in a maze structure, the goal of the experiment is to develop a memristor-based circuit models based on the fact that Physarum learn and adapt to periodic changes in its environment. Based on the wave-propagation information processing in the reaction-diffusion media, Fyrigos et al. (2019) Fyrigos et al. (2019) utilised the nano-electronic element memristor to design innovative circuits of electronic excitable medium to perform both classical (Boolean) calculations and to model neuromorphic computations in the same Memristor-RLC (M-RLC) re-configurable network (Fyrigos et al. 2019).

7.6 Physarum solving the two-armed bandit problem experiment

The two-armed bandit problem has previously only been used to study organisms with brains. Yet Physarum, a brainless unicellular organism, showed the ability of decision-making and solved the two-armed bandit problem. In this experiment, Physarum was challenged with a choice between two deferentially rewarding environments, where the arm with the greater number of food resources or higher quality was designated as the high-quality (HQ) arm, and the other arm with fewer food resources or low quality was designated as the low-quality (LQ) arm (Reid et al. 2016). The outcome of this experiment was to demonstrate the Physarum decision-making abilities. Physarum always chose the high-quality arm, and it can make multi-objective foraging decisions. It compares the relative qualities of multiple options and combines the information on reward (frequency and magnitude) in order to make correct and adaptive decisions. This experiment provides insight into the fundamental principles of Physarum decision-making and information processing.

7.7 Physarum foraging behaviour in competition settings experiment

In a biological experiment by Schumann et al. (2015), two strains were cultured in the same petri dish, the first was the usual Physarum Polycephalum plasmodium, and the second was another species called a Badhamiautricularis. Physarum Polycephalum definitely grows faster than Badhamiautricularis and overtakes more food resources, and could even grow into the branches of Badhamiautricularis, only if the Physarum inoculum was fatter (Schumann et al. 2015). Furthermore, if the invasive growth in front of Badhamiautricularis is well nourished by oat, it would easily overgrow the opposing tube system of Physarum Polycephalum. Thus, competitions between Physarum Polycephalum and Badhamiautricularis is based on Physarum power (type), mass, and the availability of nearby food resources.

A recent study by Masui et al. (2018), five geographical strains of Physarum with different genotypes were collected. In each experiment, two individual plasmodia on oat flakes were placed on \(2\%\) agar in a round petri dish and were allowed to behave freely. Whether the individuals avoided or fused was recorded for all encounter cases. Allorecognition was defined as the time when the plasmodium came into contact with the other individual. Completion of allorecognition was defined as a change in behaviour (continuing straight, changing direction, or starting to fuse at the point of contact). The study has revealed that Physarum strictly identifies allogeneic individuals when encountering different individuals. The Allorecognition system in Physarum prioritises the avoidance and severely restricts fusion when encountering different individuals (Masui et al. 2018).

Another biological experiment by Stirrup and Lusseau (2019), they have designed a biological experiment to study the behaviour of Physarum under competition settings (Stirrup and Lusseau 2019). The experiment intercalated two Physarum in a common environment (petri dish) where there was only one food resource available. The experimental results showed that the time taken by Physarum to find food depends on their hunger motivation. However, the time taken for a Physarum to start looking for food depended on its motivation and the motivation of its competitor. Physarum always initiates foraging behaviour quicker in the presence of competitors.

8 Mathematical models for simulating Physarum foraging behaviour

Physarum biological experiments are extremely slow and time-consuming to be applied in real-world network design problems. It is rather better to use the meta-heuristic algorithms inspired by Physarum intelligent behaviour (as conducted in real biological experiments) to construct mathematical models. However, rare work has been done to theoretically explain why these models work well experimentally. It is interesting to understand the theoretical analyses of Physarum models. Nevertheless, it is suggested that the protoplasmic flow through tubular veins plays an important role in explaining the observed Physarum’s intelligence. The tubes that transport the nutrients will grow bigger while the tubes which do not transport enough nutrients will vanish and disappear (Nakagaki et al. 2001; Tero et al. 2005; Werner 2019). The simulation and reproduction of this protoplasmic flow is the basis of many successful Physarum-inspired networking models (Sun 2017). For more details revise Section 3.

The existing models are simulating the intelligent behaviour of single Physarum, and have overlooked foraging behaviour of multiple Physarum under competitive settings. For this reason, we have presented our new model to simulate Physarum in competition, where multiple Physarum interact with each other and with their environments. We have summarised some of these existing mathematical models in Table 2.

Table 2 Physarum mathematical models
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8.1 The flow-conductivity model

The flow conductivity model is the most successful model that has been proposed to simulate the protoplasmic flow through Physarum’s tubular veins This model was first proposed by Tero et al. (2006) to solve the shortest path problem (Tero et al. 2006). Experiments on Physarum led by Nakagaki and Guy (2008) have proposed the mechanism of protoplasmic flow through Physarum’s tubular veins, which is believed to account for Physarum’s intelligence (Nakagaki and Guy 2008). The model illustrates the feedback between the flux and the thick of protoplasmic tubes; first, open-ended tubes, which are not connected between the two food sources, are likely to disappear. Second, when two or more tubes connect the same two food sources, the longer tube is likely to disappear. The flow-conductivity model is based on Hagen-Poiseuille Law and Kirchhoff Law to describe the adaptive feature of path finding and the feedback between flux and conductivity of the protoplasm tubes (Tero et al. 2007; Nakagaki and Guy 2008; Tero et al. 2008).

In this model, two terminals are representing Physarum (source/node), and the other terminal is food resource (sink/node). The protoplasm flows in every edge from the source node to the sink node. There is a pressure at each vertex, and the quantity of flux in each edge is proportional to the pressure difference between the two ends of these edges. Specifically, the flux \(Q_{ij}\) in edge (i, j) is given by the Hagen-Poiseuille equation below.

$$\begin{aligned} Q_{ij}=\frac{D_{ij}}{c_{ij}}(p_i-p_j) \end{aligned}$$
(1)
$$\begin{aligned} D_{ij}=\frac{\pi r^4_{ij}}{8\xi } \end{aligned}$$
(2)

where \(D_{ij}\) is the edge conductivity, \(c_{ij}\) is the edge length, \(p_i\) and \(p_j\) are pressures at vertices i and j, \(r_{ij}\) is the edge radius, and \(\xi\) is the viscosity coefficient.

Physarum solver based on the flow-conductivity model (Tero et al. 2006) is probably the most famous one. Many of the Physarum-inspired algorithms suffer from a low convergence speed. Recent researches have proposed methods to accelerate the original path-finding model. Zhang et al. (2014b) accelerated the search by reducing the number of iterations by combining the original Physarum-solver model with a new parameter, called energy Zhang et al. (2014b). Huang et al. (2021) innovatively proposed the concept of the dominant path that could distinguish the shortest path from other paths, and the exact transition point when the shortest path can be identified (Huang et al. 2021). These two novel termination criteria led to a fast algorithm outperforming other baseline algorithms. Still more theoretical work is needed to improve the performance of these models and to prove its ability in solving real world applications.

8.2 Reaction-diffusion model

Adamatzky (2009a, 2007) regards the Physarum as an encapsulated reaction-diffusion computer, and utilises a two-variable Oregonator equation to simulate the Physarum spanning tree construction (Adamatzky 2009a, 2007). In this model, the wavefront is used to simulate the motion of Physarum, whose trajectory is steered by the gradient of chemo-attractants. It was treated as a bio-realised unconventional computer called "Physarum Machine" to solve maze problems, graph problems and design logical gates (Adamatzky 2010).

8.3 The cellular model

The cellular model was proposed by Gunji et al. (2008). Given a planar lattice, and every lattice site has various states: the inside (state 1) is surrounded by a boundary (state 2) in a lattice outside (state 0). In the foraging phase, there is cell invasion of the outside with softening of the membrane of Physarum. The protoplasmic flow toward the softened area, which leads to a re-organisation of the distribution of the cytoskeleton. This model was applied to simulate the amoebic motion and solve the classical Steiner tree problem in planes (Gunji et al. 2008, 2011). Moreover, other researchers have developed a cellular automata model based on reaction diffusion to simulate the behaviour of Physarum (Tsompanas and Sirakoulis 2012; Tsompanas et al. 2016; Liu et al. 2013).

8.4 The multi-agent model

Jones (2009) has been proposed a multi-agent, where Physarum is thought to consist of a population of particle-like agents (Jones 2009). Each agent senses and deposits trails as it moves towards the nearby stimulus within a 2D diffusive lattice. In this model, the structure of the Physarum network is indicated by the collective pattern of the positions of agents, and the protoplasmic flow is represented by the collective movement of agents. Furthermore, Wu et al. (2012) improved the initial multi-agent model by adding a memory module to each agent (Wu et al. 2012). This improved model is more flexible and adaptive, and it approximates the behaviours of Physarum more closely.

Liu et al. (2017b) proposed a self-organised system modelling approach in which two types of agents are used for simulating both the search (exploration) and the contraction (exploitation) of Physarum in foraging behaviours (Liu et al. 2017b). In this model, the body comprises a synthesis module and a motion module, and each sensor is armed with a trail sampling module and a chemo-nutrient sampling module.

8.5 Physarum competition model

Awad et al. (2019b) proposed a novel model to imitate the complex patterns observed in Physarum polycephalum generated in competition settings (Awad et al. 2019b). This new model is based on hexagonal Cellular Automata (CA) and Reaction-Diffusion (RD) systems. This is the first time Physarum has been simulated in a 2-D hexagonal grid that is more applicable to Physarum natural diffusion in a circular pattern to equidistant cells (Figs. 1, 2). All other models considered either Von-Neumann (4 adjacent neighbours) (Shirakawa et al. 2015) or Moore neighbourhoods (8 adjacent neighbours) (Tsompanas et al. 2016). However, in Von-Neumann model, diagonal diffusion of Physarum can still occur, while in Moore model the neighbourhoods are not equidistant. In this competition model multiple Physarum interact with each other and with their environment, each Physarum has its autonomous behaviour: it compares information on reward determined by food resources’mass and quality, negative effects of competing neighbours according to their mass, and hunger motivation in order to make correct and adaptive decisions. They believe that competition among different Physarum individuals can lead to the emergence of a complex global behaviour, far beyond the capability of individual Physarum. The individual skills of competition are more efficient to achieve an optimal balance between exploration and exploitation and maintain population diversity.

Fig. 1
figure 1

The structure of the cellular automaton and how diffusion process is executed over time

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Fig. 2
figure 2

An example of a grid of four Physarum competing for two food resources, some obstacles and empty cells

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9 Physarum-inspired applications

In this section, we will address the most important question "What Physarum can offer to computing?". Many Physarum-inspired algorithms have been developed and proved to have great potential to solve various optimisation problems using simple heuristics. In this context we will not be restricted to graph optimisation problems as previous reviews (Zhang et al. 2016b; Sun 2017; Adamatzky 2010; Gao et al. 2019), we will open the horizon and through light to more recent applications. We will address this issue by briefly reviewing some of the existing researches on these Physarum-inspired applications.

9.1 Physarum-inspired algorithms for graph-optimisation problems

Physarum protoplasmic flux is changing continuously with the change of environment in its foraging process. This characteristic allows Physarum to have great potentials in dealing with graph-optimisation problems which are considered the main application. The Physarum solver constructs networks by making some nodes in the network "sources" and cytoplasmic streaming as edges to others "sinks". Physarum network design has attracted the attention of many researchers as it demonstrated excellent performance in network construction without central consciousness during the process of foraging. For a detailed discussion on the existing methods and applications refer to (Zhang et al. 2016b; Sun 2017).

As the previous work by Sun (2017) has indicated, these network graph-optimisation problems are typically based on the following four strategies:

  • One source node and one sink node: It was first proposed by Nakagaki et al. (2000) after performing his famous experiments showing that Physarum was able to find the shortest route through a maze (Nakagaki et al. 2000). Qian et al. (2013) solved the travelling salesman problem Qian et al. (2013). Zhang et al. (2016b) accelerated its optimisation process by intentionally removing the edges with a stable decreasing flow Zhang et al. (2016b).

  • Multiple source nodes and one sink node: this strategy is to select one terminal to be the sink node and then select the other terminals to be source nodes. It has been applied by Liu et al. (2015b) to solve the classical Steiner tree problem in graphs (Liu et al. 2015b). It has also been used to solve the prize-collecting Steiner tree problem and the node-weighted Steiner tree problem (Sun and Halgamuge 2016).

  • One source node and multiple sink nodes: this strategy is to select one terminal to be the source node and then select the other terminals to be sink nodes. It was first used by Watanabe and Takamatsu (2014) to design transportation networks with fluctuating traffic distributions (Watanabe and Takamatsu 2014).

  • Multiple source nodes and multiple sink nodes: this strategy is to select multiple terminals to be the source nodes and multiple terminals to be the sink nodes. It was recently proposed by Zhang et al. (2016b) to solve the supply chain network design problem (Zhang et al. 2016b).

The Physarum-inspired Graph-Optimisation applications can be categorised as follows:

9.1.1 Finding the shortest path in directed and undirected networks

Nakagaki et al. (2000) were the first to show how this simple organism has the ability to find the shortest path between two points in a labyrinth (Nakagaki et al. 2000). Subsequent research has confirmed and broadened the range of its computation abilities to spatial representations of various graph problems (Zhang et al. 2016b). It showed that the Physarum’s network geometry met the requirements of a smart network: short tubes, close connections among all the branches, and tolerance to dynamic changes. A lot of Physarum-inspired algorithms (PAs) have been proposed to solve challenging network optimisation problems, such as the travelling salesman problem (Masi and Vasile 2014), spanning tree approximation (Adamatzky 2009b), vehicle routing problems Liu et al. (2016), designing supply chain networks (Zhang et al. 2016a), and community detection (Gao et al. 2018).

9.1.2 Designing transport networks

Adamatzky (2012a) presented a bioevaluation of world transport networks (Adamatzky 2012a). This work showed that man-made transport networks and their design are closely related to the shortest path problem. Tero et al. (2010) carried their designed well-known real experiment to design a Physarum bio-inspired networks similar to the Tokyo rail system (Tero et al. 2010). The resulting networks are both efficient and robust. Some other real-world transportation networks have also been approximated by Physarum since then, such as Mexican highway (Adamatzky et al. 2011), Iberian highway (Adamatzky and Alonso-Sanz 2011), Route 20 in USA Adamatzky (2014) and Autobahn 7 in Germany (Adamatzky 2014). Tsompanas et al. (2015) presented a cellular automaton-based, Physarum-inspired, transport network designing model (Tsompanas et al. 2015).

9.1.3 Solving steiner tree problem and applications

The classical geometric Steiner tree problem is to find the shortest network to connect multiple terminals. Several algorithms have been proposed to solve this problem such as flow-conductivity based model (Tero et al. 2006) and cellular model (Gunji et al. 2008). Inspired by the path-finding and network formation capability of Physarum, Liu et al. (2015b) explored a cellular computing model to solve the Steiner tree problem, especially in network design (Liu et al. 2015b).

In the prize-collecting Steiner tree problem, we not only have edge costs, but also have none-negative node weights. Recently, Sun et al. (2016) proposed a flow-conductivity model to solve this problem for drug re-positioning (Sun et al. 2016). The node-weighted Steiner tree problem is a more general version of the prize-collecting Steiner tree problem, and the node weight can be positive, negative, or zero. It has been applied to various areas, such as communication network design (Sun and Halgamuge 2016) and biomedical data analytics (Sun et al. 2017). These Physarum algorithms compute Steiner trees by iteratively calculating pressures, updating edge conductivities, and cutting edges.

Recently Sun et al. (2020) have conducted theoretical analyses on some Physarum-inspired algorithms to reveal their potential of computing Steiner trees (Sun et al. 2020). It was concluded that Physarum-inspired algorithms can find low-cost networks to connect multiple compulsory vertices together, and have the potential to compute Steiner trees. However, it is observed that using such iterations are computationally too expensive for large graphs. To overcome this point they have proposed a hybrid algorithm by incorporating Steiner tree techniques into the Physarum-inspired optimisation process. They formulated the Node-Weighted Partial Terminal Steiner Tree Problem for minimum-cost relay node placement in two-tiered wireless sensor networks. The objective is to minimise the sum of heterogeneous production and placement costs of relay nodes and the sum of outage probabilities of transmission routes in a routing tree simultaneously.

9.2 Evolutionary algorithm optimisation (Hybrid Models)

Prior knowledge plays a vital role in the computational efficiency of evolutionary algorithms (e.g., Genetic Algorithm, and Ant Colony). Taking advantage of Physarum powerful computational capabilities, such as morphological diversity (Gunji et al. 2008) and positive feedback loop (Tero et al. 2005), these characteristics have been used to optimise some evolutionary algorithms to improve its efficiency and robustness (Zhang et al. 2014a; Gao et al. 2018).

Ant colony optimisation (ACO) algorithms have been shown to provide an approximate solution for NP-hard problems existing in many real-world applications. However, premature convergence has significantly reduced the performance of these algorithms. Zhang et al. (2014a) proposed an optimisation strategy for updating the pheromone matrix in ant colony algorithms based on a Physarum mathematical model (Zhang et al. 2014a). This strategy has accelerated the positive feedback process in ACO, for solving NP-hard problems such as travelling salesman problem (TSP) and 0/1 knapsack problem, which contributed to the quick convergence of the optimal solution (Liu et al. 2017a). Later on Gao et al. (2018) has incorporated Physarum-inspired initialisation to optimise the genetic algorithm, ant colony optimisation algorithm and Markov clustering algorithm for solving community detection problems (Gao et al. 2018).

9.3 Biological computing and physarum logic gates

Boolean logic which describes binary arithmetic is fundamental to computer science as electronic logic gates form the basis of digital operations in computers. Organism based Bio-Logic gates have been attempted using cell constituent (bacteria) as transducers (Wang et al. 2005). Bacteria have many drawbacks, mainly due to the fragility, short life, limited temperature, and pH conditions. Also, bacteria will often not grow on specific substrates which would be ideal for the cell-transducer interface. Yeast and wild fungi are offering the advantage of high growth rate and the ability to grow on a broad range of surface substrates used for cell-transducer interface (Baronian 2004). Moreover, yeast can survive for over a long time after dehydration and could be re-hydrated when required.

Like other fungi and yeast, Physarum is accessible to culture on moist filter paper or agar and resist dehydration for a long time. This is why it can be considered as a prospective experimental prototype of biological computers which does not require sophisticated support. In standard electric devices, we deal with electrical signals to code information. However, in a Physarum biological device instead of electrical signals, the calculation process is performed by using the Physarum chemotaxis to food (Adamatzky 2010; Umedachi et al. 2011).

Physarum as a method of biological computing has been extensively studied in the PhyChip project that ran between 2013 and 2016 "Physarum chip: growing computers from slime mould" (Adamatzky et al. 2012). A Physarum chip is formed of a living network of protoplasmic tubes that acts as an active non-linear transducer of information, while templates of tubes coated with conductor act as fast information channels. The symbolic-logical, mathematical and programming aspects of the Physarum chip have been studied by Schumann et al. (2015) Schumann et al. (2015). Schumann (2019) studied the logics of swarm behaviours, where each unicellular organism can be regarded as a logic gate, and all behaviours can be controlled by stimuli in the environment: attractants (motivational reinforcement) and repellents (motivational punishment). The reactions to stimuli can be regarded as: sensing stage (perceiving input signals) and motoring (appropriate direct reactions output signals) Schumann (2019). Physarum was also used as a Boolean gate, where the presence and absence of Physarum in a given locus of space is equivalent to logic values 1 and 0, respectively (Schumann and Adamatzky 2011). The Physarum chip is expected to solve a wide range of computation tasks, including graph optimisation, logic and arithmetical computing (Andrew and Krzysztof 2016).

The EU-funded PhySense project "Physarum Sensor: Biosensor for Citizen Scientists" is an extension of the PhyChip project. This project showed that Physarum is an ideal biological substrate that could be used as a biosensor that converts a biological response into an electrical signal, providing a unique fusion of living and digital technology. The PhySense software calculates any changes in the frequency and amplitude of oscillations in the tubular structures of Physarum. The aim of this project is develo** marketable low-cost biosensors for various applications, including environmental monitoring and health (CORDIS 2019)Footnote 1.

9.4 Physarum competition algorithm applications

The Physarum competition model (Awad et al. 2019b) has a great potentials to be customised to formulate new algorithms to solve the real-world problems that have heuristic similarity to Physarum foraging behaviour in competition settings. Thus we are inspiring from biology to advance computational solution. Graph-optimisation problems in a dynamic environment as in Mobile Wireless Sensor Networks, and Discrete Multi-Objective Optimisation problems are examples of these applications.

9.4.1 Physarum competition algorithm for wireless sensor networks

The popular Physarum-inspired Algorithms (PAs) have proven its potential in solving challenging network optimisation problems (Reid and Beekman 2013; Zhang et al. 2016b). However, some network optimisation problems remain unsolved. New techniques are required to address the large scale of the next-generation networks, where centralised control of communication becomes impractical. Physarum distributed intelligence may inform the design of an adaptive, robust and spatial infrastructure networks with decentralised control systems (Sun 2017). We have proposed a Physarum competition model (Awad et al. 2019b), where multiple Physarum with autonomous behaviours react to each other and with their environment without central control to achieve efficient exploration of the whole system evolving to an optimal global network, this has allowed us to deal with the increasingly proposed networks scenarios with multiple sources and multiple sinks. In our previous work, we have presented a Physarum-inspired competition algorithms for mobile wireless sensor networks, where multiple Physarum (as represented by sensors) will sense the surrounding environment, and compete over multiple food resources (as represented by interest points). These algorithms have demonstrated their promising performance in solving node deployment (Awad et al. 2018) and connectivity restoration even in harsh environment (Awad et al. 2019a).

9.4.2 Physarum competition Algorithm (PCA) for discrete multiobjective optimisation problems

Many real-world problems can be naturally formulated as discrete multi-objective optimisation problems. Physarum competition algorithm has been proposed to solve this problem (Awad et al. 2019c). This algorithm is based on Physarum motility over hexagonal cellular automaton (problem search space). Each cell is considered a food resource (objective functions) to attract Physarum. The PCA has achieved similar performance results compared to the state-of-the-art multi-objective evolutionary algorithms and even outperformed other well-established algorithms.

10 Conclusion

By studying Physarum foraging behaviour and translating that behaviour into mathematical models, we increase our understanding of how to inspire from biology to develop Physarum bio-inspired algorithms can solve many challenging real world problems. Physarum polycephalum is an example of plasmodial slime moulds. The primitive intelligence of Physarum polycephalum is mostly demonstrated during its plasmodium stage (a large multi-nucleated single cell) that consists of a single cell amoeba-like organism. Physarum senses gradients of chemo-attractants and repellents and forms a yellowish vascular network in search of nutrition. A stimulus triggers the release of a signalling molecule cyclic adenosine monophosphate (cAMP) which starts cytoplasmic streaming. This generates a feedback loop; the higher the rate of cytoplasmic streaming is, the thicker the vein becomes. The Physarum foraging behaviour consists of two simultaneous self-organised processes of expansion (exploration) and shrinkage (exploitation). Just like social insects and animals, Physarum too exhibits swarm intelligence; it shares many features of collective behaviour such as synchronisation, communication, positive feedback, leadership, and response thresholds. There is increasing evidence that a simple organism like Physarum has complex social behaviours including cooperation and competition. Physarum is capable of making complex foraging decisions based on trade-offs between risks, hunger level and food patch quality. The skills of individual competitors are effective methods for inspiration to develop intelligent systems and to provide solutions for decision-making problems.

Physarum may not have brains, but the advantages of Physarum unconventional computational capabilities, as morphological diversity and positive feedback loop, have great potentials for solving many real-world applications. Physarum, as a simple organism, has the ability to find the minimum-length between two points in solving the maze problem and discover the shortest path in real-world networks such as the Tokyo railway network using simple heuristics. Much research has confirmed and broadened the range of its computation abilities to spatial representations of various graph optimisation problems. Physarum-inspired initialisation of other bio-inspired techniques has the ability to accelerate convergence and improve the searching capability of evolutionary algorithms (e.g., Genetic Algorithm, and Ant Colony) in terms of accuracy and computational cost. Physarum as a biological model has been studied in the PhyChip and PhySense projects to develop marketable and low-cost biosensors for various applications including environmental monitoring and health.Physarum can be considered one of the biological models of unconventional computation capable of making a programmable Physarum machine.