AXELROD'S MODEL FOR DISSEMINATION OF CULTURE
    The java applet below visualizes the dynamics of Axelrod's model for dissemination of culture [1], including perturbations and noise [2], as well as the effect of network topology [3].

    [1] R. Axelrod, J. Conflict Res. 41, 203 (1997), Related material by R. Axelrod

    [2] Konstantin Klemm, Victor M. Eguiluz, Raul Toral, Maxi San Miguel, Global culture: A noise induced transition in finite systems, Phys. Rev. E 67, 045101(R) (2003).

    [3] Konstantin Klemm, Victor M. Eguiluz, Raul Toral, Maxi San Miguel, Nonequilibrium transitions in complex networks: a model of social interaction, Phys. Rev. E 67, 026120 (2003).

    [4] Globalization, Polarization, Cultural Drift and Social Networks. A presentation in pdf

    [5] An analysis of the dissemination of culture in a one-dimensional world can be found in Konstantin Klemm, Victor M. Eguiluz, Raul Toral, Maxi San Miguel, Globalization, Polarization and Cultural Drift, J. Economic Dynamics & Control 29, 321 (2005). See also Role of dimensionality in Axelrod's model for the dissemination of culture, Physica A 327, 1 (2003).

    [6] Review paper on Voter and Axelord's models: M. San Miguel et al., Binary and multivariate stochastic models of consensus formation, Computing in Science and Engineering 7, Issue 6, 67 (2005).

    [7] PDF Presentation of the effects of mass media in cultural dynamics, J.C. Gonzalez Avella et al, Physical Review E 73, 046119 (2006).


A guide for using the applet
     Here it is assumed that you are familiar with the dynamical rules of the model. If not, reference [2] above should be helpful.
  • + and - buttons increase/decrease the basic model parameters.
  • L is the linear size of the square lattice. Increasing/decreasing L fine/coarse grains the current configuration. However, the new larger/smaller lattice is generated independently of the old one (relevant in the case p>0).
  • F is the number of features. Changing F while the dynamics is running or between setting different kinds of initial configurations allows you to play many tricks. Try it out.
  • q is the number of traits used in the random initial configuration, for perturbations, and the ongoing noise (r>0).
  • r is the noise rate. When r is increased from zero the state of the applet is changed to "running" automatically.
  • p is the "small-world parameter", the probability of randomly rewiring a bond of the lattice. Any change made to p creates a new random lattice.
  • The time is the number of elementary epochs divided by the system size: In one time unit each site performs on average one update trial.
  • Stop/Go allows you to toggle the state of the applet between "running" and "paused". If r=0 and the current configuration is absorbing, no updates are possible and the state of the applet is displayed as "frozen".
  • Perturbation assigns a random new trait out of {1, ... q} to a randomly chosen feature at a randomly chosen site.
  • The homogeneous initial configuration assigns the same trait to all features in all sites.
  • The random initial configuration assigns an independent random trait out of {1, ... q} to each feature in each site.
  • The bubble initial configuration consists of two zones with cultures (0,0,...,0) and (0,1,...,1) with a circle-shaped interface.
  • The Colours display maps the culture (s1,s2,s3,...) of a site into a color (R,G,B) with R=f(s1), G=f(s2) and B=f(s3). So each of the first three features determines exactly one of the spectral intensities of red, green and blue. Further features (in case F>3) are ignored by the display. For F=2 the intensity of blue is a constant.
  • The Borders display draws a black line along the border between sites without common traits. Sites with at least one common are separated by a red line, except for those with agreement in all features. Between the latter pairs of sites no border is drawn.
  • The Lattice display shows the interaction network currently used, useful when working with the small world parameter p>0.
  • The fast option makes the dynamics run as fast as possible, medium and slow options reduce the speed. Note that system time is not necessarily proportional to real time. In particular with the fast option this ratio varies immensely.

Konstantin Klemm