Animals and fungi assemble a contractile ring of actin filaments and the motor protein myosin to separate into individual daughter cells during cytokinesis. We used fluorescence microscopy of live fission yeast cells to observe that membrane-bound nodes containing myosin were broadly distributed around the cell equator and assembled into a contractile ring through stochastic motions, after a meshwork of dynamic actin filaments appeared. Analysis of node motions and numerical simulations supported a mechanism whereby transient connections are established when myosins in one node capture and exert force on actin filaments growing from other nodes.