01 December 1997

Lightning calculations make fractals practical

Lovelace’s memory was jogged by Babbage’s recollection last month of their inventor friend Mr Andrew Crosse. She remembers fondly her visits to his Somerset home, Fyne Court, with its orchards festooned with wires to harness atmospheric electricity: one of the experiments that earned him the epithet ‘Wizard of the Quantocks’. Mr Crosse, she feels, would have approved of the contribution of Analytical Engines to the study of aerial phenomena, from everyday lightning to the ‘sprites’ and ‘jets’ newly observed in the upper atmosphere above thunderstorms.

This subject engaged Lovelace’s mathematical curiosity recently, when she read of the work of Juan Alejandro Valdivia at NASA's Goddard Space Flight Center; his computed models of the electromagnetic disturbance of lightning bolts assume a conductor with the spiky branching form known as a Diffusion Limited Aggregate fractal.

Ever a devotee of arithmetical beauty, Lovelace admits to a fascination with such engine-generated shapes; indeed, she feels that she is due some recognition for having anticipated fractals. The sight of a program creating the opium-dream arabesques of the Mandelbrot soundly confirms her prediction that the Analytical Engine would weave algebraical patterns just as the Jacquard loom weaves flowers and leaves.

While Lovelace’s interest in fractals derives largely from aesthetics, she expects that Babbage will find more sympathy with their growing practical use. Until recently, fractal theory was largely directed toward mathematical explanations of natural forms: for instance, tree branches and roots; blood vessel and bronchial networks; geological folds and cracks; or the surface of abraded materials at microscopic level.

Now, however, they are finding application in generating tangible and useful structures. Amalgamated Research Inc. of Idaho, USA, manufactures space-filling fractal conduits, similar in shape to the branches of the cardiovascular system. Designed to minimise turbulence, the many rootlike outlets of such an ‘engineered fractal cascade’ (EFC) can draw or inject fluid simultaneously throughout a mixing vessel.

Another company, Fractal Antenna Systems Inc., is developing a branching ‘Fractenna’(tm) for hand-held telephony or for networks of portable Engines. The details are as yet concealed by commercial considerations, but, its makers tell us, this highly efficient sender and receiver of electrical waves will be no bigger than a small coin, tiny even compared to the conventional wand antennae that would have so amazed Mr Crosse.