✦ LIBER ✦

Dimensional characterization of singular fractal functions

✍ Scribed by G.S. Bhattacharya; B.K. Raghuprasad

Book ID: 104363666
Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 398 KB
Volume: 8
Category: Article
ISSN: 0960-0779
DOI: 10.1016/s0960-0779(96)00161-0

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✦ Synopsis

Construction of singular fractal functions which are monotonically increasing functions, differentiable almost everywhere and possess nearly zero derivative, is explained based on an iterative technique of distribution of mass onto a line segment, and their graphs are generated using different values of the two relevant parameters. The fractal dimension of the set of points, called the measure's concentrate (where almost the entire mass to be distributed gradually becomes accumulated in successive generations) is found using the result of curdling. The multifractal nature of the measure's concentrate, keeping one parameter unchanged and varying another parameter, is pointed out.

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