For attractor basins it is best to try out small sizes first, especially for networks other than regular 1d CA. Much larger systems sizes may be run ``forward only`` for just space-time patterns, or ``backwards'' to generate a subtree. The maximum sizes DDLab can support are 9999 for 1d, and 255255 for 2d, but in practice smaller sizes are preferable. A good size for 1d space-time patterns for a clear view of other features on the screen is 150-200.
A small network size n is appropriate for attractor basins as these exist in a state-space that grows exponentially (though the program's upper limit for single basins or subtrees is as above, and n=32 for basin of attraction fields).
As an example, the time to generate the basin of attraction field of some 1d CA rules for a range of neighbourhood, k, and system size, n, is noted below. With some notable exceptions, the table shows the time doubling with increasing n, and by a factor of about 1.6 with increasing k (on my 66MHz 486),
n= 12 13 14 15 16 17 18
time= 2s 4.9s 8s 16s 32s 1m4s 2m13s k=3 rule (dec) 193
time= 3.8s 7s 13s 27s 50s 1m47s 3m37s k=4 rule (hex) e9 24
time= 5.4s 9.8s 30s 37s 1m18s 2m36s 8m46s k=5 rule (hex) b7 55 d3 d9
A similar exercise for random Boolean networks (wiring and rules selected at random) gave the following more erratic timings, especially sensitive to k.
n= 12 13 14 15 16
time= 12s 21s 40s 1m13s 3m21s k=2
time= 18s 50s 1m8s 2m43s 8m39ss k=3
time= 60s 2m8s 4m33s 34m32s 87m20s k=4
The timing depends on n, k, the rule, and the resulting topology of attractor basins (the greater the characteristic in degree, the longer the time). In the case of random Boolean networks, the timing also depends to the particular wiring and rule mix.
The system size that is appropriate for generating an attractor basin in a reasonable time can be inferred from the above. Large sizes may be tried, but may impose unacceptable time, memory and display constraints. Single basins, and especially sub-trees, may be generated for relatively much larger systems, especially for rules having a low in-degree.