The fundamental theories of physics are local theories, depending on local interactions of local variables. It is not clear if and how strictly local theories can produce non-local variables that have causal effectiveness. Yet, non-local effectiveness appears to exist, such as in the form of memory (non-locality through time) and causally effective spatial structures (non-locality through space). Here it is shown, by construction, how such non-locality can be produced from elementary components: non-isolated systems, multiplicative noise, self-replication, and elimination. A theory is derived that explains how causal non-locality can arise from strictly local interactions.