Scroll down for a description of the simulation and suggestions of things to try!
The applet requires Java 1.4.1 or higher. It will not run on Windows 95 or Mac OS 8 or 9. Mac users must have OS X 10.2.6 or higher and use a browser that supports Java 1.4. (Safari works, IE does not. Mac OS X comes with Safari. Open Safari and set it as your default web browser under Safari/Preferences/General.) On other operating systems, you may obtain the latest Java plugin from Sun's Java site.
created with NetLogo
view/download model file: CategoryRegularity3.nlogo
This simple program demonstrates how a similarity-bias at a local scale can result in large-scale categorical behavior. When the 'setup' button is clicked, the field is populated with a random distribution of yellow and blue squares. In each round of the simulation, each square looks at its eight immediate neighbors, and if there are more of the other color, may switch to match. Because squares change color less often within uniform areas than at the boundaries between areas, uniform areas tend to expand at the expense of mixed areas. As a consequence, this simple, local 'similarity bias' results in the rapid formation of long-rage uniformity, with sharp boundaries between distinct regions.
This simulation is meant as a companion to the paper 'Feedback and Regularity in the Lexicon' (2007, Phonology 24: 147-185). This paper argues that local similarity biases on variation/error in production and perception can drive the development of regular patterns in the lexicon over many 'cycles' of communication and language acquisition.
Click on 'setup', and then click 'go once' a few times. Each time you click 'go once', all squares check their local neighborhood and change accordingly. You can see that regions of long-range uniformity rapidly emerge from the originally random distribution. If you click on 'go forever', you can see the program proceed rapidly toward uniformity. Depending on the initial distribution, the final state will either be a single color, or two stable regions. The existence of the latter stable state in this simulation is an artifact of the simple orthogonal, two dimensional shape of the space; a more realistically dimensional space would not support the permanent coexistence of multiple regions. For an account of how multiple categories can coexist stably despite similarity biases, see the Category Competition simulations on this page, and the draft paper 'Modeling sublexical contrast maintenance as an emergent effect of lexical category competition' on my publications page.
To see how random noise and the stregth of the bias interact, you can modify these variables using the relevant sliders. Try setting the bias at some intermediate level, and then seeing how high you can set the noise before the field seems to lose all tendency to long-range pattern formation.