Contents
glider
as a "localised propagating structure" -- example of
self-organisation search looks at variance of input entropy over
time measures: maps of attractor basins -- bushy sub-trees with
high in-degree => high convergence and order, sparse sub-trees =>
low convergence and chaos; G density (Garden-of-Eden state
density), ratio of increase of G density with size: order is
high, chaos is low; distribution of in-degree size; Z parameter
-- statistical predictor of convergence: Z=0 => order, Z=1
=> chaos; local measures (on trajectory), global measures (on
attractor basin), static measures (Z) 1D CA, binary
state, neighbourhood k=3, can represent using state value (2
colours) or neighbourhood lookup value (8 colours); with 2nd repn, if
background (commonly looked up values) is filtered, gliders can show up
better (especially if transformed to equivalent rule using larger
neighbourhood) attractor basins diagrammed as state transition
relations [picture], by repeatedly calculating pre-image of states
ordered rules become rarer at higher k, complex rules are rare
gliders can have a large diameter, and a large period compound
gliders formed from sub-gliders colliding periodically -- hierarchy
could continue without limit classify rules using entropy of "lookup
frequency" -- order: low entropy, low variance -- complex: medium
entropy, high variance -- chaos: high entropy, low variance
glider collision table: description of behaviour allowing some
prediction of future evolution -- neighbourhood rule table: accounts for
origin of gliders, emergence by self-organisation
Contents
Contents
Contents
Contents