Rate of Modeling of Computing Media on a Grid with a Reduction of Dimensionality

This article considers computing media on a grid having elements with a limited number of states and a limited neighborhood for the sorting of information. Consideration is given to the possibility of modeling such media by media of the same form but having lesser dimensionality. It is shown that with a reduction of dimensionality from $n$ to $m\leq n$ it is possible to provide an information processing slowdown $c\cdot t^{[n/m]}$ and that for each $n$ there is a medium of dimensionality n which cannot be modeled more rapidly than with a slowdown $ct^{n/m}$ ($c>0$, $t$ is time).