  Simulators can realise novel phenomena by separating them from the
complexities of a full physical implementation. Here we put forward a scheme
that can simulate the exotic statistics of $D(S_3)$ non-Abelian anyons with
minimal resources. The qudit lattice representation of this planar code
supports local encoding of $D(S_3)$ anyons. As a proof-of-principle
demonstration we employ a photonic simulator to encode a single qutrit and
manipulate it to perform the fusion and braiding properties of non-Abelian
$D(S_3)$ anyons. The photonic technology allows us to perform the required
non-unitary operations with much higher fidelity than what can be achieved with
current quantum computers. Our approach can be directly generalised to larger
systems or to different anyonic models, thus enabling advances in the
exploration of quantum error correction and fundamental physics alike.
