The CA
This is the "MajorityLD" cellular automaton model,
i.e. "Majority with Long Distance interactions". You can think of it
as a model of peer pressure, genetic drift, or the spread of opinions
or ideas. The rules are that each cell tries to do
what the majority of its neighbors (peers) are doing, or a sample of
its neighbors.
If we have n states, labelled 0 through
n-1, each site looks at some set of neighbors. It then sets
its own state either to whatever the majority of its neighbors are
doing, or to copy a randomly-chosen neighbor.
The Controls
See the parent web page for
general controls.
Controls specific to this particular applet are:
- Number of states: You can change the number of states allowed
per cell, by typing in a number and then either hitting "Enter"
or clicking on the "Set numStates" button.
- Alpha: the proportion of long-distance interactions. E.g. if
alpha=0.01, it means that whenever a site looks at a given
neighbor to plug into the update-rule, there is a 1% chance
that it will actually use the value of a randomly-chosen site
from the entire lattice in place of that neighbor's value.
Alpha=0 means no long-distance interaction, and alpha=1 means
entirely long-distance interactions.
- Nbor method: method for deciding which neighbors to examine.
- Random: If set to "Random", each site randomly chooses one
of its neighbors to look at, and sets its own state to the
same as that of its neighbor.
- All: If nbor method is set to All, then each site looks at
all of the sites in its neighborhood, and then sets
its own state to whichever state is most common in the
neighborhood. If it's a tie, i.e. multiple states are
tied for first place, then the target site chooses one of
the tied majority states, at random.
- Nhood size: size of the neighborhood to use.
- vonNeumann: Each site only looks at its four adjacent
neighbors (north, south, east and west).
- Fixed radius: if the radius is set to r, the
neighborhood of a site is all sites within plus or minus
r units, horizontally and vertically. So
r=1 corresponds to a 3x3 block of sites (often
called the Moore neighborhod). r=2 corresponds
to a 5x5 block of sites. And in general, a given value
of r corresponds to a (2r+1)x(2r+1)
block of sites.
- Time method: whether to use a discrete- or continuous-time
model.
- Discrete: all sites are updated simultaneously, as in
traditional cellular automata models.
- Continuous: sites are updated asynchronously, one site
at a time. A single site is chosen at random to be
updated, then another site is chosen to be updated, and
so on. Sampling is done with replacement, i.e. one site
may be updated multiple times before another site is
updated at all. With an LxL lattice, a "time step" is
defined as L*L site updates, so during a time step, on
average each site gets updated once, although to be more
precise, each site will be updated N times, where N
follows a Poisson distribution with mean=1, and N is iid
(independent and identically distributed)
among the sites in the lattice.
Hiebeler's home page
Dave Hiebeler <hiebeler@math.zzz.edu> (change 'zzz' to 'umaine' to send e-mail -- sorry, but spam harvesters are out there)
Last modified: Fri May 18 10:28:23 EDT 2012