Possible states for a group of ants. (j) Complexity analysis for different states compared to the first identified state with lowest energy level for a group of ants. the group formation. These stable states have lower energy level compared to others. On the other hand, if it is not probable for the group to stay in the same state, we consider that as transient state. Because of the difference in the energy level, the group prefers to stay for a relatively longer time in stable states compared to transition states. Meanwhile, the group may shape the transition states while evolving between two different stable states. Figure 5a and 5c demonstrate that adding chemoattractant to the environment, decreases the number of possible states for the group dynamics and the free energy landscape is more smooth compared to the case without chemoattractant. The existence of chemoattractant in the environment contributes to the preferable alignment of the bacteria motion with each other and causes the group to get more organized with less oscillatory and scattered motions. Based on our analysis, we observe that the missing information of the first local equilibrium state is the lowest (Fig. 5b and 5d). Accordingly, for the transient state the missing information is higher compared to the stable states (see missing information section in Methods). Figure 5 shows the level of change in missing information when the collective group leaves any of the identified states to evolve to a new state (Note S1 in Supplementary Documents explains this in more details). We define emergence for a collective group as being proportional to the structural order gained by the system and quantified in statistical terms with respect to ambiguity of the Decumbin site initial state49. Based on this definition, changing the system dynamics from one state to another can be interpreted as a way to transform or propagate the information. Figure 5b and 5d show the SIS3 manufacturer relative emergence of all possible states with respect to the most probable state, which has the lowest amount of missing information (see emergence section in Methods). Based on our analysis, high emergence means more dependencies in the group as a result of stronger interactions. This indicates that the group has more interdependent components in stable states with lower level of missing information compared to transition states. On the other hand, low emergence shows the group has more independent components, which represents the group in transition states. We define a group to be self-organized when the internal dynamics of the group increases its organization over time. This could be a measure for collective group intelligence and we plan to investigate further in our future work. Our proposed free energy landscape analysis shows that the group is naturally attracted to be in stable states with lower energy compared to transitioning states with higher energy level. By considering these attractor stable states as organized states, the group will be self-organized through time (see self-organization section in Methods). Figure 5b and 5d show the level of increase in self-organization of the swarm going from any possible state to the first stable state with lower energy level (i.e., each point shows the amount of increase in group self-organization evolving from the corresponding state to the first stable one). The figure shows that the group gets more self-organized when it evolves from any possible state to the first and most pr.Possible states for a group of ants. (j) Complexity analysis for different states compared to the first identified state with lowest energy level for a group of ants. the group formation. These stable states have lower energy level compared to others. On the other hand, if it is not probable for the group to stay in the same state, we consider that as transient state. Because of the difference in the energy level, the group prefers to stay for a relatively longer time in stable states compared to transition states. Meanwhile, the group may shape the transition states while evolving between two different stable states. Figure 5a and 5c demonstrate that adding chemoattractant to the environment, decreases the number of possible states for the group dynamics and the free energy landscape is more smooth compared to the case without chemoattractant. The existence of chemoattractant in the environment contributes to the preferable alignment of the bacteria motion with each other and causes the group to get more organized with less oscillatory and scattered motions. Based on our analysis, we observe that the missing information of the first local equilibrium state is the lowest (Fig. 5b and 5d). Accordingly, for the transient state the missing information is higher compared to the stable states (see missing information section in Methods). Figure 5 shows the level of change in missing information when the collective group leaves any of the identified states to evolve to a new state (Note S1 in Supplementary Documents explains this in more details). We define emergence for a collective group as being proportional to the structural order gained by the system and quantified in statistical terms with respect to ambiguity of the initial state49. Based on this definition, changing the system dynamics from one state to another can be interpreted as a way to transform or propagate the information. Figure 5b and 5d show the relative emergence of all possible states with respect to the most probable state, which has the lowest amount of missing information (see emergence section in Methods). Based on our analysis, high emergence means more dependencies in the group as a result of stronger interactions. This indicates that the group has more interdependent components in stable states with lower level of missing information compared to transition states. On the other hand, low emergence shows the group has more independent components, which represents the group in transition states. We define a group to be self-organized when the internal dynamics of the group increases its organization over time. This could be a measure for collective group intelligence and we plan to investigate further in our future work. Our proposed free energy landscape analysis shows that the group is naturally attracted to be in stable states with lower energy compared to transitioning states with higher energy level. By considering these attractor stable states as organized states, the group will be self-organized through time (see self-organization section in Methods). Figure 5b and 5d show the level of increase in self-organization of the swarm going from any possible state to the first stable state with lower energy level (i.e., each point shows the amount of increase in group self-organization evolving from the corresponding state to the first stable one). The figure shows that the group gets more self-organized when it evolves from any possible state to the first and most pr.
