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|Title:||EXISTENCE OF 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 Elliot or E(t) functions, that allow for infinite number of exact replications of 12345abc structures, has been demonstrated. These E(t) functions are defined algorithmically and have no derivitive anywhere. One of these E(t) functions has the unexpected property of scaling like a random walk. This leads to speculation that it might be possible to construct a statistically self-affine E(t) function that would be a random walk forgery.|
|Appears in Collections:||Bradley, James|
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