A COMPLETE L-SYSTEM SPECIFICATION FOR GENERATING AN EXACT SELF-AFFINE TIME FUNCTION WITH A RANDOM-WALK SCALING PROPERTY
Date
1992-12-01
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Abstract
An exact self-affine time
function, unlike a fractal in two-dimensional space, replicates
exactly when scaled by differing ratios in the amplitude and time
axes. A statistical self affine time function replicates only
statistically when scaled by differing ratios in the amplitude and
time axis, the best known example being a random walk, where the time
scaling factor is the square of the amplitude scaling factor. The
existence of at least four exact self affine time functions, called
E53 functions, that allow for an infinite number of exact replications
of 12345abc structures, is demonstrated. These E53 functions are
defined by algorithms and have no derivitive anywhere. One of these
E53 functions, called the standard E53 function, has the property of
scaling like a random walk. A complete L-System specification for
generating the standard E53 function is presented.
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Computer Science