This paper addresses the multi-agent patrolling problem, which consists for a set of autonomous agents to visit all the places of an unknown environment as regularly as possible. The proposed approach is based on the ant paradigm. Each agent can only mark and move according to its local perception of the environment. We study EVAW, a pheromone-based variant of the EVAP [Chu07] and VAW [Wagner99]. The main novelty of the paper is the proof of some emergent spatial properties of the proposed algorithm. In particular we show that obtained cycles are necessarily of same length, which ensures an efficient spatial distribution of the agents. We also report some experimental results and discuss open questions concerning the proposed algorithm.