Article: Fractal past, fractal future. (fractal research of the past and future)(75th Anniversary Supplement)

On a clear, brisk morning, a child marvels at the frilled intricacy of frost splayed across a sunlit windowpane. In the laboratory, a scientist peers at the minutely branched structure of a cluster of gold particles.

A character in Tom Stoppard's 1993 play Arcadia asks, "If there is an equation for a curve like a bell, there must be an equation for one like a bluebell, and if a bluebell, why not a rose?" If you asked a mathematician how to characterize the shape of a flower or Jack Frost's handiwork or metallic sprays, the answer would probably refer to forms called fractals.

Fractals have invaded the popular imagination. Calendars, computer screens, and ...

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