Information Properties of Cellular Structures

The article considers $n$-dimensional cellular structures with an arbitrary definition of neighbor cells. It is shown that the existence of “gardens of Eden” in the structure is equivalent to the existence of erasable configurations. It is shown that almost all structures are structures with information losses (solution of Moore's problem [Proc. Symp. Appl. Math., vol. 14, AMS, Providence, 1962, pp. 17–33]).