On relations between arrays of processing elements of different dimensionality

We are examining the power of $d$-dimensional arrays of
processing elements in view of a special kind of structural
complexity. In particular simulation techniques are shown, which
allow to reduce the dimension at an increased cost of time
only. Conversely, it is not possible to regain the speed by
increasing the dimension. Moreover, we demonstrate that increasing
the computation time (just by a constant factor) can have a more
favorable effect than increasing the dimension (arbitraril