\begin{definition}[Definition:Replicative Function]
A '''replicative function''' is a real function $f$ such that:
:$\ds \forall n \in \Z_{\ge 0}: \sum_{k \mathop = 0}^{n - 1} \map f {x + \frac k n} = \map f {n x}$
where $\sum$ denotes indexed summation.
\end{definition}