Axelrod's model of Cultural Diversity



This implements a version of Axelrod's simple model of how
cultures maintain diversity, despite presures on agents
(e.g., interpreted as villages) to become more alike
when they interact with each other.
See Axelrod's chapter 7 book, The Complexity of Cooperation,
(Princeton Univ Press, 1996).  An allignment and replication
of this model, in which the ktour algorithm was used, is 
described in ``Alligning Simulation Models: A Case Study and Results,''
Axtell, Robert, Axelrod, Robert, Epstein, Joshua, and Cohen, Michael.
SFI Working Paper 95-07-065.  (This also appeared in volume 1 of
The Journal of Computational and Mathematical Organization Theory.

The key parameters:

worldSize    size of world (i.e., length of sides of square world).
             settable only at the start.

numFeatures  number of features each agent has values for,
             e.g., for religion, language, etc.
             settable only at the start.

numTraits    number of possible values for each feature.
             settable only at the start.

Each step (ie click of the top level clock) we do one
of two ways of activity agents, depending on the value of
  actMethod    Mechanism
  ---------    ---------
  axelrod      pick worldSize^2 agents to be activated
               pick them uniform randomly, with replacement.

  ktour        knight's tour, as done by Axtell etal, i.e.
               shuffle the list of agents, and activate each
               one in that (now random) order, once per step. 

When an agent is activated, the basic mechanism is:
- it picks one of its NEWS neighbors at random.
- the probability that the two agents actually interact 
  is set to  numFeaturesInCommon / numFeatures.
- when they interact, a feature is picked at random,
  and the value of that feature for the agent is set to
  the value it has for the other.  Note if they happen to
  be the same on that feature, no change will occur.

The sim continues until there are no possible changes left,
i.e, each agent is either completely the same or completely
different from its neighbors.

There is 2D display of the agents in the world, as well as of
the differences between neighbors.  By default, one sees only
the differences between the agents, with grey-scale varying
from white for completely different neighbors, to black for 
identical neighbors.  

This display can also show the values of single features in the
agents by setting the drawAgents variable to values in
[1,numFeatures].   Different colors are shown for each trait
value at the selected feature.

Note: For the display of agents, only works for 15 numTraits max.
  0 grey                  8 some green
  1 red                   9 some other green
  2 light green          10
  3 dark blue            11
  4 light blue           12
  5 magenta              13
  6 yellow               14
  7 dark orange          15

There are also display graphs.
One graph shows
  numberInteractions    - number of times / t that an agent is able
      to interact with another (note there may be no change).
  numberChanges         - actual number of feature changes / t
  numberPossibleChanges - number of edges (agent pairs) that
      would allow a change (i.e., the agent's have at least
      one feature but not all features in common).
When the number of possible change-interactions is 0, it stops.

Another graph shows the number of regions and zones vs time.
A region is defined as a contiguous set of cells (agents) who
have the exact same culture, i.e., have the same traits for
all features. (see p156 of The Complexity Of Cooperation.)
A zone is a continguous set of cells that have at least
one feature in common with their neighbors (see p 164).

You can also probe agents, and see what their feature values
are with time, etc., by pressing MB3 (usually the right button)
with the mouse over the agent to be probed.
The probe shows the instance variables (state) of the agent,
including an arbitrary ID value, its traits in binary and ascii,
its x,y location and the region and zone numbers it is in.
(These numbers have no particular meaning, they are just assigned
in order as the number of regions and zones are counted.)

Notes: 
0. numAgents currently has no effect, as the world is
   completely filled.

1. It would be nice to have a display of the traits of 
   of all agents in a rectangular grid, as shown in an example
   in Axelrod's paper.  This could be used as an alternative to colors,
   or it could be printed in the terminal window by pressing a button.

2. It might be nice to display zones and regions, maybe
   as shades of gray.

Ack: This is based on an early version written at SFI
     (by Nelson Minar and/or Manor Askenazi).

Examples:

These assume you have a copy of the axelcult program in your
working directory.   If you do not, you can always run the
shared version by replacing "./axelcult" in the examples below with:

   /users/rlr/SwarmStuff/CSCS-Demos/Axelcult/axelcult 

To avoid typing all that over and over, remember you can use
the arrows in the keypad area of your keyboard to "recall"
command you have entered and then change/add to them 
before re-entering them.  (See the intro-To-Unix web page
off the CSCS main lab documentation page for more information
about command re-entry and other useful tricks.)

To run with worldSize=30, numFeatures=10, numTraits=15,
and all other parameters at defaults:
   ./axelcult -DworldSize=30 -Dnf=10 -Dnt=15
After you run it, there will be a file
   report
which contains the initial parameter values,
any changes you made, and lines of output data.
You can have it write to files of different names, e.g.
   ./axelcult -DRFN=output -DRN=00
will write to a file
  output.00
(The RNF is report file name, the RN is report file name suffix).

To get a list of all run-time settable parameters
and their aliases:
 ./axelcult -Dh


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Updates: July, 1999; July 2000;