I have a $\mathcal{C}^0(\mathbb{R})$ given implicitly as $\varphi(x)=\sum\limits_{k=-3}^{k=3}a_k\varphi(3x-k-\frac{1}{2})$, and I know the coefficients $a_k$ and the values of $\varphi$ in the points $\frac{k}{2}, \, k \in \mathbb{Z}, \, -3 \leq k \leq 3$.
How can I find the plot of such function? [For example using Matlab]