In the Spring of 2001, I did some research on applying catastrophe theory to real-data on language variation. You can read it here in "Portable Document Format" (PDF). If you don't already have it, you'll need to get the Adobe Acrobat Reader.

• Applied catastrophe theory in dialectology — evidence from Canada (term paper, April 2001)
• Catastrophic Variation around the Golden Horseshoe (handout from the Dialect Topography conference, March 2002)

The graph on the left deals with Ottawa Valley residents who regularly use a language other than English.

It shows a correlation in jump behaviour between people preferring asphalt with [sh] and people preferring "the cat wants out" (vs. the cat wants to go out). The jumps (up and down) are nearly identical for these two seemingly unrelated variables.

It would seems that whatever forces are acting differently on every second age group in the graph are doing the same action on both these variables.

Cellular Automata Dialect Simulations

Here are some cellular automata animations of a dialect variation simulation. Unstable situations can result in every cell converting to one or the other variant, but few types of essentially stable results are possible:

• Totally black and totally white results
• Horizontal and vertical stripes
• Diagonals

Expect more commentary on these items soon.