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A continuity equation for information is presented, involving flows in both space and scale in chemical pattern formation systems. The flows are connected to thermodynamic properties of the system. Information leaves the system (or is destroyed) at the smallest length scales, which corresponds to entropy production. Information enters the system at the largest length scales when the system is open to an inflow of Gibb's free energy. The continuity equation describes how information can be aggregated at different scales and positions during the pattern formation process. The formalism is applied to the Gray-Scott model, exhibiting self-replicating spots in a spatially extended system.