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This paper presents an experimental and computational study of dipolar ordering phenomena in ion-beam patterned Co/Pt multilayers. The fabrication and the patterning of the layers were chosen to achieve single-domain dots, which show strong magnetic coupling and are uniform in their magnetic properties. We find that antiferromagnetic-like ordering can extend to as many as several hundred adjacent dots. Micromagnetic simulations reproduce the experimentally observed ordering and suggest that such multilayers are promising candidates for field-coupled computing devices.