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Visualizing multifractal scaling behavior: a simple scaling heuristic
Citation key GWF-VMSB-98
Author Gilbert, Anna C. and Willinger, Walter and Feldmann, Anja
Title of Book Conference Record of the Thirty-Second Asilomar Conference on Signals, Systems & Computers
Pages 715–722
Year 1998
ISBN 0-7803-5148-7
DOI http://dx.doi.org/10.1109/ACSSC.1998.750955
Location Pacific Grove, CA, USA
Volume 1
Month November
Abstract The self-similar or monofractal scaling behavior of a signal can be readily visualized in the time domain by plotting and comparing the signal at many different levels of resolution (i.e., time scales). No comparable visualization techniques appear to be available for qualitatively assessing the presence of multifractal scaling in a given signal. To help in developing an intuitive understanding of multifractals, we propose in this paper a simple coloring heuristic that gives rise to an effective, time domain-based visualization technique for multifractals. Our approach combines wavelet-based statistical denoising techniques with wavelet characterizations of local regularity for functions. We illustrate our heuristic with a number of examples, including the binomial measure, a simple and well-studied multifractal, and measured traces of actual data network traffic.
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