A Monte Carlo Approach for ɛ Placement in Fractal‐Dimension Calculations for Waveform Graphs

Abstract

Many diverse and complicated objects of nature and math possess the quality of self‐similarity, and algorithms which produce self‐similar shapes provide a way for computer graphics to represent natural structures. For a variety of studies in signal processing and shape‐characterization, it is useful to compare the structures of many different “objects”. Unfortunately, large amounts of computer time are needed as prerequisite for rigorous self‐similarity characterization and comparison. The present paper describes a fast computer technique for the characterization of self‐similar shapes and signals based upon Monte Carlo methods. The algorithm is specifically designed for digitized input (e.g. pictures, acoustic waveforms, analytic functions) where the self‐similarity is not obvious from visual inspection of just a few sample magnifications. A speech waveform graph is used as an example, and additional graphics are included as a visual aid for conceptualizing the Monte Carlo process when applied to speech waveforms. Copyright © 1986, Wiley Blackwell. All rights reserved