Colonies of ants are remarkable interacting living systems in which the distribution of roles of ants and interactions among individuals with an environment produce a reliable performance of complex tasks. Particularly remarkable is the process of formation of narrow paths between nests and food sources that is essential for successful foraging. I will present a simple mathematical off-grid model of ant foraging in the absence of direct communication. The motion of ants is governed by two components - a random change in direction of motion that improves ability to explore the environment and to find food, and a non-random global indirect interaction component based on pheromone signalling. The main goals are to show how are essential real-ant-world problems solved within the system and how the system acquires a partial synchrony, that is very similar and yet quite different to behaviour observed for seemingly unrelated neuronal networks. This is a joint work with my student, Miriam Malickova (Comenius University).