There are three different reverse algorithms for generating the pre-images of a network state. The first is specifically for ``local'' 1d wiring with a homogeneous neighbourhood, such as 1d CA, though the rules may be heterogeneous. This is the most efficient thus fastest algorithm, described in (Wuensche 1992). Furthermore, compression of 1d CA attractor basins by rotation symmetry (see #20.1) speeds up the process.
Any other network architecture, with non-local wiring, will be dealt with by a slower general reverse algorithm described in (Wuensche 1994a). A histogram revealing the inner workings of this algorithm can be displayed. Regular 2d CA will use this general reverse algorithm; however compression algorithms will come into play to take advantage of the many rotation symmetries on the torus (unless suppressed, and not for a neighbourhood of 7, the symmetries of a triangular grid on the torus have yet to be resolved).
Both these reverse algorithms generate the pre-images of a state directly; their speed is sensitive to neighbourhood size as well as system size. A neighbourhood of 9, such as the game of life, is slowest. A third reverse algorithm first sets up a list of ``exhaustive pairs'' of each state in state-space and its successor (this can be saved). The pre-images of states are generated by reference to this list. This method is efficient for basin of attraction fields, or large basins that use up a good proportion of state-space, and additionally is not sensitive to neighbourhood size (the basin of attraction field of the 4x4 ``game of life'' by this method takes about 30 minuets on my 66MHz 486 ).
The method used to generate pre-images will be chosen by default, which can be overridden. For example, a regular 1d CA can be made to use either of the two other algorithms for benchmark purposes. The time taken to generate attractor basins is displayed, and for the basin of attraction field, a progress bar indicates the proportion of states in state-space used up so far.
Finally, a ``random mapping'' can be set up which assigns a successor state at random to each state in state space (rules and wiring previously set are ignored)*. The attractor basins are reconstructed by reference to this random mapping. The space of such random mappings corresponds to the space of all possible basin of attraction fields and is the super-set of all other deterministic discrete dynamically systems.