### Winter 2013

# Urban Jungle

The changing natural world at our doorsteps | Illustration and text by Patterson Clark

January 22, 2013

### Spacing out: Plotting the distance between individuals

Stark winter landscapes bring into sharp contrast the flocks of pigeons and starlings gathered on power lines. On a crowded wire, the **distance between individuals** seems fairly regular, yet with some variation. Surprisingly, a statistical plot of the distances between birds shows the same pattern as do the spaces separating parked cars, bunched-up pedestrians, freeway traffic and moving flocks of sheep.

Unlike the symmetrical **bell curve**, below, which works well for plotting random datapoints, such

as IQ scores

and shoe sizes,

the graph

depicting spaces

between **units that are aware of each other**

makes a curve resembling a cracking whip. The pattern was described in 2009 by Czech mathematical physicist Petr Seba.

On **Seba's curve**, snuggling birds or kissing bumpers would register at the left-hand extreme of the curve, where space between birds or cars is absent. The curve's peak, or mode, signals the distance most likely to occur between parties, which turns out to be a little more than half of the average distance.

On this curve, the average, or mean, has a larger value than the mode because of a broad range of increasingly wide gaps between individuals, created perhaps by birds needing a little extra room, pedestrians who appear threatening to others — or parallel parkers feeling timid.

Spacing between individuals is a result of numerous variables, including speed, body size, available space and social interaction. But a common denominator is what Seba describes as a "universal distance-controlling mechanism" hard-wired into each animal's eye and brain.

NASCAR drivers and house flies share a very similar response to a psychophysical **time-to-collision estimate** triggered by

the rate that an image expands on the retina of the animal's or person's eye.

That internal calculation of impending impact kicks in and helps carve a comfortable space every time a starling swoops in to negotiate a spot on a wire and every time you pull up behind another car at a stop light.

Sources: Petr Seba, University of Hradec Kralove; Perception; Journal of Statistical Mechanics:

Theory and Experiment

*On Seba's curve, the mean (average) distance between individuals is given the unit value of 1. Spaces between perched starlings and between parallel-parked* cars tightly conform to this curve. *

*

In unmarked spaces

PROBABILITY DENSITY

RELATIVE DISTANCE BETWEEN INDIVIDUALS

Mean

Mode

Mean,

mode

SHOE SIZES