The Science Book

316

See also: Robert FitzRoy 150–55 ■ Edward Lorenz 296–97

B

elgian mathematician Benoît

Mandelbrot used computers

to model the patterns in

nature in the 1970s. In doing so, he

launched a new field of mathematics

—fractal geometry—which has

since found uses in many fields.

Fractional dimensions

Whereas conventional geometry

uses whole-number dimensions,

fractal geometry employs fractional

dimensions, which can be thought

of as a “roughness measure.” To

understand what this means, think

of measuring Britain’s coastline

with a stick. The longer the stick,

the shorter the measurement, as

it will smooth out any roughness

along its length. The British coast

has a fractional dimension of 1.28,

which is an index of how much the

measurement increases as the

length of the stick decreases.

A characteristic of fractals is

self-similarity—meaning that there

is an equal amount of detail at all

scales of magnification. The fractal

nature of clouds, for example,

makes it impossible to tell how

close they are to us without

external clues—clouds look the

same from all distances. Our

bodies contain many examples

of fractals, such as the way the

lungs branch out to fill space

efficiently. Like chaotic functions,

fractals show sensitivity to small

changes in initial conditions, and

they are used to analyze chaotic

systems such as the weather. ■

A CLOUD IS MADE

OF BILLOWS

UPON BILLOWS

BENOÎT MANDELBROT (1924–2010)

IN CONTEXT

BRANCH

Mathematics

BEFORE

1917–20 In France, Pierre

Fatou and Gaston Julia build

mathematical sets using

complex numbers—that is,

combinations of real and

imaginary numbers (multiples

of the square root of –1). The

resulting sets are either

“regular” (Fatou sets) or

“chaotic” (Julia sets) and are

the precursors of fractals.

1926 British mathematician

and meteorologist Lewis Fry

Richardson publishes Does

the Wind Possess a Velocity,

pioneering mathematical

models for chaotic systems.

AFTER

Present-day Fractals form

part of the field of complexity

science. They are used in

marine biology, earthquake

modeling, population studies,

and oil and fluid mechanics.

The Mandlebrot set is a fractal

generated using a set of complex

numbers, and conceals limitless

representations of itself at every scale.

When visualized graphically, it produces

the distinctive shape shown here.