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|Title:||A COMPLETE L-SYSTEM SPECIFICATION FOR GENERATING AN EXACT SELF-AFFINE TIME FUNCTION WITH A RANDOM-WALK SCALING PROPERTY|
|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.|
|Appears in Collections:||Bradley, James|
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