of computation [@berger1966undecidability]. As the simulation works by representing the space-time diagram of the execution, it is enough to restrict to Wang tiles over $\nat^2$ by considering machines with a single right-infinite tape (i.e. Turing’s original *a-machine* model [@turing1936computable]). As a consequence, we obtain the following theorem.

Stellar resolution can simulate Turing machines.

Wang tiles are very close to the abstract tile assembly models (aTAM) [@winfree1998algorithmic; @patitz2014introduction] which can be used as a model of computation with applications in DNA computing [@seeman1982nucleic]. Our model is able to represent aTAM, and even generalise it.

A tile $t = (g_w, g_e, g_s, g_n)$ in the aTAM is a Wang tile where the sides $g \in \mathcal{G}$ (called glues types instead of colours) are associated to an integer $\mathrm{str}(g) \geq 0$ called their strength. An additional model parameter is called the *temperature*, which we write $\mathtt{t}$. A tile can be attached to an assembly (i.e. a diagram in the stellar resolution terminology) if adjacent sides have matching glue type and strength, and the total strength of its connections is at least[^4] $\mathtt{t}$. To encode those we use colours $h,v$ of arity 3 as above but decline them in pairs $h_{-},h_{+}$ and $v_{-},v_{+}$, together 