| The Cellular Automata of John von Neumann
The topology of the cell lattice
In this WJVN.EXE version, the cellular automaton space is a rectangle of 640x480 cells. The topology of the lattice, however, depends on how the transition rules link the cell states at the opposite sides of the rectangle boundary.
The lattice topology is set automatically when an automaton is loaded from a file, but it can be changed in any moment by selecting Set topology from the menu Settings or clicking button . The topology associated with a given automaton can be changed also during file saving by clicking on the Save dialog button Set file content description.
The cell lattice admits four qualitatively different topologies:
- Open rectangle. Cells on the cell-lattice boundary "see" the external space as permanently filled with vacuum cells. This topologicy has the effect of stopping any local process that might continue beyond the boundary. Of this kind is, for instance, the elongation of a constructing arm or of a reading/writing arm. The following non-open topologies allow you to circumvent these limits by some extent.
- Vertical cylinder. Cells on the top and the bottom of the 640x480 cell area "see" the external space as permanently filled by vacuum cells. In contrast, each cell on the right boundary "sees" on its right a cell of the left boundary. In general, the positions of corresponding cells on the opposite boundaries are vertically shifted by a small number of cells. This vertical shift can be positive or negative (modulo cell-lattice height). Therefore, the continuation of a horizontal row of cell states beyond a vertical boundary will behave as a spiral wound around a vertical cylinder.
- Horizontal cylinder. Cells on the right and the left of the 640x480 cell area "see" the external space as permanently filled by vacuum cells. In contrast, each cell on the bottom boundary "sees" sees as on the down side a cell of the top boundary side. In general, the positions of corresponding cells on the opposite boundaries are horizontally shifted by a small number of cells. This horizontal shift can be positive or negative (modulo cell-lattice width). Therefore, the continuation of a vertical line beyond a horizontal boundary will behave as a spiral wound around a horizontal cylinder.
- Torus. This is a combination of the vertical and horizontal cylinder topology. Thus, in general, the continuation of line in any direction behaves as a spiral wound around the surface of a torus with a drift depending on the torus-topology shifts.