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A6. Quantitative, statistical and analytical measures

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).


next up previous
Next: A7. Reverse algorithms Up: Overview. Previous: A5. Mutations