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Income inequality and fractal patterns

Posted by Christopher Shea  September 9, 2010 12:49 PM

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A fractal is a shape whose contours replicate themselves at every scale. If one were to zero in on the snowflake reproduced below, for example (known as a Koch snowflake), the same patterns of jaggedness would be evident however close you got. Mathematicians have long been enthralled by the beauty and elegance of fractals.


At Aidwatch, Bill Easterly makes the case that the concept of fractals sheds light on the distribution of poverty. Globally, there are pockets of wealth (the U.S., Western Europe) and pockets of desperation (sub-Saharan Africa). Ditto when you zoom in to explore the U.S. (greater Washington, DC, for example, in contrast with Appalachia). And even when you drill down and look at neighborhoods in a single city, similar patterns of abundance and want reveal themselves: Incomes in New York's Lower East Side are roughly 14 percent of what they are in the Lower West Side.\

"At each scale," Easterly writes--making his point with a series of noteworthy graphics-- "there is a remarkably high level of inequality across space." Of course, the social implications of these patterns are considerably less pleasing than are their geometrical representations.


A representation of income inequality in New York

Hat tip: Brad DeLong

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