Recent work in the area of coordination models and collective adaptive systems promotes a view of distributed computations as functions manipulating computational fields (data structures spread over space and evolving over time), and introduces the field calculus as a formal foundation for field computations. With the field calculus, evolution (time) and neighbor interaction (space) are handled by separate functional operators: however, this intrinsically limits the speed of information propagation that can be achieved by their combined use. In this paper, we propose a new field-based coordination operator called share, which captures the space-time nature of field computations in a single operator that declaratively achieves: (i) observation of neighbors’ values; (ii) reduction to a single local value; and (iii) update and converse sharing to neighbors of a local variable. In addition to conceptual economy, use of the share operator also allows many prior field calculus algorithms to be greatly accelerated, which we validate empirically with simulations of a number of frequently used network propagation and collection algorithms.