A cell is a minimal self-sustaining system that can move and compute. Previous work has shown that a unicellular slime mold, Physarum, can be utilized as a biological computer based on cytoplasmic flow encapsulated by a membrane. Although the interplay between the modification of the boundary of a cell and the cytoplasmic flow surrounded by the boundary plays a key role in Physarum computing, no model of a cell has been developed to describe this interplay. Here we propose a toy model of a cell that shows amoebic motion and can solve a maze, Steiner minimum tree problem and a spanning tree problem. Only by assuming that cytoplasm is hardened after passing external matter (or softened part) through a cell, the shape of the cell and the cytoplasmic flow can be changed. Without cytoplasm hardening, a cell is easily destroyed. This suggests that cytoplasmic hardening and/or sol-gel transformation caused by external perturbation can keep a cell in a critical state leading to a wide variety of shapes and motion.

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Recent experimental and observational data have revealed that the internal structures of collective animal groups are not fixed in time. Rather, individuals can produce noise continuously within their group. These individuals’ movements on the inside of the group, which appear to collapse the global order and information transfer, can enable interactions with various neighbors. In this study, we show that noise generated inherently in a school of ayus (Plecoglossus altivelis) is characterized by various power-law behaviors. First, we show that individual fish move faster than Brownian walkers with respect to the center of the mass of the school as a super-diffusive behavior, as seen in starling flocks. Second, we assess neighbor shuffling by measuring the duration of pair-wise contact and find that this distribution obeys the power law. Finally, we show that an individual’s movement in the center of a mass reference frame displays a Lévy walk pattern. Our findings suggest that inherent noise (i.e., movements and changes in the relations between neighbors in a directed group) is dynamically self-organized in both time and space. In particular, Lévy walk in schools can be regarded as a well-balanced movement to facilitate dynamic collective motion and information transfer throughout the group.

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Collective behaviour is known to be the result of diverse dynamics and is sometimes likened to a living system. Although many studies have revealed the dynamics of various collective behaviours, their main focus was on the information process inside the collective, not on the whole system itself. For example, the qualitative difference between two elements and three elements as a system has rarely been investigated. Tononi et al. have proposed Integrated Information Theory (IIT) to measure the degree of consciousness Φ. IIT postulates that the amount of information loss caused by certain partitions is equivalent to the degree of information integration in the system. This measure is not only useful for estimating the degree of consciousness but can also be applied to more general network systems. Here we applied IIT (in particular, IIT 3.0 using PyPhi) to analyse real fish schools (Plecoglossus altivelis). Our hypothesis in this study is a very simple one: a living system evolves to raise its Φ value. If we accept this hypothesis, IIT reveals the existence of continuous and discontinuous properties as group size varies. For example, leadership in the fish school emerged for a school size of four or above; but not below three. Furthermore, this transition was not observed by measuring mutual information or in a simple Boids model. This result suggests that integrated information Φ can reveal some inherent properties which cannot be observed using other measures. We also discuss how the fish recognition of the figure-ground relation, that is, what determines the relevant ON and OFF states, may reveal various optimal paths for obtaining the functional evolution of collective behaviour.

Collective behavior emerging out of self-organization is one of the most striking properties of an animal group. Typically, it is hypothesized that each individual in an animal group tends to align its direction of motion with those of its neighbors. Most previous models for collective behavior assume an explicit alignment rule, by which an agent matches its velocity with that of neighbors in a certain neighborhood, to reproduce a collective order pattern by simple interactions. Recent empirical studies, however, suggest that there is no evidence for explicit matching of velocity, and that collective polarization arises from interactions other than those that follow the explicit alignment rule. We here propose a new lattice-based computational model that does not incorporate the explicit alignment rule but is based instead on mutual anticipation and asynchronous updating. Moreover, we show that this model can realize densely collective motion with high polarity. Furthermore, we focus on the behavior of a pair of individuals, and find that the turning response is drastically changed depending on the distance between two individuals rather than the relative heading, and is consistent with the empirical observations. Therefore, the present results suggest that our approach provides an alternative model for collective behavior.

Emergent behavior that arises from a mass effect is one of the most striking aspects of collective animal groups. Investigating such behavior would be important in order to understand how individuals interact with their neighbors. Although there are many experiments that have used collective animals to investigate social learning or conflict between individuals and society such as that between a fish and a school, reports on mass effects are rare. In this study, we show that a swarm of soldier crabs could spontaneously enter a water pool, which are usually avoided, by forming densely populated part of a swarm at the edge of the water pool. Moreover, we show that the observed behavior can be explained by the model of collective behavior based on inherent noise that is individuals’ different velocities in a directed group. Our results suggest that inherent noise, which is widely seen in collective animals, can contribute to formation and/or maintenance of a swarm and that the dense swarm can enter the pool by means of enhanced inherent noise.

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