Computing by nowhere increasing complexity

A cellular automaton is presented whose evolution rule is the following. A cell's value is changed from y to x if the Kolmogorov complexity of its present Moore neighborhood is smaller with x than with y. Using an approximation of this two-dimensional Kolmogorov complexity the underlying automaton is shown to be capable of simulating logic circuits. It is also shown to capture trianry logic described by a quandle, a non-associative algebraic structure. A similar automaton whose rule permits at times the increase of a cell's neighborhood complexity is shown to produce animated entities which can be used as information carriers akin to gliders in Conway's game of life.