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Unmanned Aerial Vehicles (UAVs) dynamic encirclement is an emerging field with great potential. Researchers often get inspiration from biological systems, either from macro-world like fish schools or bird flocks etc, or from micro-world like gene regulatory networks (GRN). However, most swarm control algorithms rely on centralized control, global information acquisition, and communications among neighboring agents. In this work, we propose a distributed swarm control method based purely on vision and GRN without any direct communications, in which swarm agents of e.g. UAVs can generate an entrapping pattern to encircle an escaping target of UAV based purely on their installed omnidirectional vision sensors. A finite-state-machine (FSM) describing the behavioral model of each drone is also designed so that a swarm of drones can accomplish searching and entrapping of the target collectively in an integrated way. We verify the effectiveness and efficiency of the proposed method in various simulation and real-world experiments.