Logo IMG


E Pluribus Unum

Brian Hayes


The StarLogo model I have found most provocative is one that Resnick presents as a fable about frogs and turtles living together in a pond. Initially the two species occupy lily pads in a checkerboard pattern, so that each animal's eight neighbors include an equal number of frogs and turtles. Then one night a storm overturns all the lily pads, and in the morning the animals find themselves randomly rearranged. Frogs and turtles are tolerant of each other, but neither wants to be entirely isolated from their own species. So the unhappy frogs—those that happen to have too few frog neighbors—abandon their lily pads and choose a new home at random. The unhappy turtles do the same. After this migration, there may still be unhappy animals, and so the procedure is repeated until all find an acceptable neighborhood.

Figure 2. Frogs and turtlesClick to Enlarge Image

The social implications of this model are easier to see than the zoological ones. And the most interesting observation to come out of it is that even a moderate preference for living among your own kind can give rise to a dramatic pattern of segregation. What starts out as a salt-and-pepper mixture gradually evolves, over a few hundred iterations, into large blobs of almost uniform composition. Even though none of the individuals insist on racial purity, most of them wind up living with a very high percentage of neighbors like themselves.

It's an intriguing result, but as I watched the model evolving, with the frogs and turtles slowly withdrawing into their own territories, I began to have misgivings. In the first place, the patterns looked suspiciously familiar. I had seen them before in models that depict the onset of magnetization in ferromagnets and the separation of oil and water. What these latter processes have in common is that they tend to minimize surface area (or the area of interface between phases). It's not implausible that racial segregation also shares this tendency, and the discovery of a connection between a social process and certain physical systems would be illuminating. On the other hand, seeing the frogs-and-turtles model in that context turns it into a more generic bit of mathematics. The gears and levers of the underlying differential equations are showing through.

The model has some other curious features as well. As the desired fraction of like neighbors increases from 30 to 60 percent, the pattern of segregation grows more extreme, as one might expect. But what happens in a population of more radical segregationists, who won't be content unless at least 80 percent of their neighbors are of their own kind? Paradoxically, the system remains thoroughly integrated. Except at low population density, the proportion of like neighbors seldom departs far from 50 percent. The reason, of course, is that everybody is unhappy. Very few of the participants ever achieve their 80-percent target, and so most of the population is randomly rearranged on every trial. I think this is an unlikely outcome in a city of bigots.

comments powered by Disqus


Of Possible Interest

Feature Article: In Defense of Pure Mathematics

Spotlight: First Person: Jim Smith

Computing Science: Clarity in Climate Modeling

Subscribe to American Scientist