Various measures and data (also presented graphically) include the following:
Parameters on rules and network architecture:
The (or P*) parameter and the Z parameter measured on rule look-up tables.
The frequency of canalyzing ``genes'' and inputs. This can be set to any arbitrary level.
Various measures on forward dynamics (these may be spread over a number of generations) :
A rule-table lookup frequency histogram, which can be toggled between 2d and 3d to include a time dimension.
The entropy of the lookup frequency over time.
The variance of the entropy, which allows ordered, complex and chaotic rules to be discriminated automatically *.
A plot of mean entropy against the variance of the entropy for a set range of time steps (and initial conditions), for an arbitrarily large sample of CA rules. This plot can be redraw as a 3d frequency histogram. Ordered, complex and chaotic dynamics are located in different regions allowing a statistical measure of their frequency. In addition the rules can be sorted by entropy variance allowing complex rules to be found automatically*.
The pattern density over time.
Frozen islands, the fraction of ``genes`` that have not changed over the last n generations (and the fraction of frozen 0s and 1s*).
Pattern difference fraction between two networks, or damage spreading*.
The ``Derrida plot'' showing how the Hamming distance of network trajectories from sets of state pairs changes. This indicates if a network is in the ordered or chaotic regime*.
A plot of the Hamming distance between successive iterations*.
Various measures on global dynamics:
Garden-of-Eden density and more generally the in-degree frequency of attractor basins (or fragments).
A scatter-plot of state space (plotting the left half against the right half of each state bit string), using colour to identify different basins, or attractor cycle states.
(items marked * are not yet covered in the program reference #4)
Most of these ideas are explained in (Wuensche 1994b,1995).