4.  Computational universality

The first principle of DM, dating from 1958, was that the model had to be computation uni­versal. If microscopic physics (assuming finite na­ture) was not universal, then it would be tauto­logically true that the macroscopic construction of an ordinary computer would not be possible; but nature allows us to construct computers! Univer­sality is the most important property. Strangely enough, it is not only necessary, but as previously mentioned, it is sufficient. It is even feasible to use a non-reversible model to model a reversible process; it is just aesthetically obnoxious. When we say that any UCA can model the behavior of any target CA, we are normally thinking of those cases where the UCA doing the modelling has the same dimensionality as the target system. In that case tiles made up of compact and tile-able (such as a triangle or square in 2D or a cube in 3D) sets of cells, set to initial patterns of states, can mimic the behavior of any particular kind of cell. To mimic the behavior of a particular cellular au­tomaton, one would have to wallpaper the entire space with states that correspond to the appropri­ate tile patterns, as part of the initial conditions. Of course, the simulation would proceed slowly, use more space, and require the identification of the particular cells within the tiles that at certain time steps (such as "at every 1296th time step") represent the state of the simulated cellular au­tomaton.