  Collective motion provides a spectacular example of self-organization in
Nature. Visual information plays a crucial role among various types of
information in determining interactions. Recently, experiments have revealed
that organisms such as fish and insects selectively utilize a portion, rather
than the entirety, of visual information. Here, focusing on fish, we propose an
agent-based model where the direction of attention is guided by visual stimuli
received from the images of nearby fish. Our model reproduces a branching
phenomenon where a fish selectively follows a specific individual as the
distance between two or three nearby fish increases. Furthermore, our model
replicates various patterns of collective motion in a group of agents, such as
vortex, polarized school, swarm, and turning. We also discuss the topological
nature of the visual interaction, as well as the positional distribution of
nearby fish and the map of pairwise and three-body interactions induced by
them. Through a comprehensive comparison with existing experimental results, we
clarify the roles of visual interactions and issues to be resolved by other
forms of interactions.
