# Exploration of Swarm Dynamics Emerging from Asymmetry
## 7 Conclusions  
The present study has been motivated by the practical needs to the potential of the emergence of interesting patterns in SC has not been totally revealed and leveraged. It is better to be able to detect measure the interestingness of the static structures of the swarms or the dynamic changes in them, in an objective manner, e.g., by GA. This paper has studied an effective way of quantifying the interestingness of swarm patterns that emerge in SC and then to detect such interesting patterns automatically. We have defined several quantitative measures, focusing particularly on the asymmetry of some kinds. While swarms tend to result in a segregating pattern, which is not interesting, several notable dynamical patterns have been yielded from the proposed FFs. FFs-D and E have delivered some motion like a pulsation, and FF-F has delivered a gradually changing structure. It is also interesting that the a type could experience different roles in the same transient history. The contributions of this paper are summarized as follows. 1. We have constructed a framework to search higher-scoring swarms using a genetic algorithm. Experimental results showed the possibility of detecting several characteristic and attractive patterns using the proposed quantitative measures and optimization framework. 2. Discussing the relationship between the fitness functions and the corresponding swarm behaviors or structures gained by them, we have derived some key points of designing a good function to detect interesting patterns. The results provide some clue to what kind of fitness function should be used to obtain a specific type of structure or motion. Numerical study using seven different fitness functions has given a brief overview and general knowledge about the quantification of interestingness. As a general conclusion on how we can define the interestingness, the geometrical (positional) asymmetry of structures and topological asymmetry of information transfer have possibilities to let interesting swarm patterns emerge. Major findings are summarized as below. 1. A swarm tends to result in a segregating pattern, which is frequently observed but uninteresting, when one or more type has a too small perception range and a too high speed. Therefore, it is better to choose values for a recipe with a large perception range, a speed which does not overwhelm the perception range. Introducing some terms of limiting into the fitness functions may be effective to prevent an easy breaking of structure. 2. Another possibility of avoiding a segregating patterns is making the cohesion force large and the separation force small. 3. The asymmetry of information transfer, which is represented by the topological connectivity (used in FFs-D, E and F), is an effective way to characterize the interestingness of heterogeneous swarm patterns. 4. The usage of derivative function can help detect a pulsating motion (finding from FFs-D and E). The differential operation is believed to be facilitating quick transitions between high-degree and low-degree states over two successive time steps to be sustained, while preventing from tendency of breaking off. The fitness value would have been low if the degree monotonically increased or decreased. The same discussion might be applied only to the case of using the degrees, but also to some other measuring indices representing the state of system. 5. A gradual deformation, which looks lively or like an organism, can be captured by a function form like FF-F, in combination with a long evaluation period which starts at a sufficiently time-elapsed point, because a swarm with quick segregation occurring in the early time steps will not have so large min-max difference at the period of evaluation and eventually its fitness score will be low. Recently, [PERSON] and others have presented a minimal model of swarming behavior, inspired from friendship formation in human society [25]. Simulation results showed that emerged patterns can be classified into 6 categories by introducing two macroscopic variables.