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Weierstrass functions

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Weierstrass functions

[′vī·ər‚shträs ‚fəŋk·shənz]
(mathematics)
Used in the calculus of variations, these determine functions satisfying the Euler-Lagrange equation and Jacobi's condition while maximizing a given definite integral.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive
Regarding the modeling of the 3D rough fractal surface, we introduce here a bandlimited Weierstrass function of two variables, (1) below, as a straightforward extension of similar Weierstrass functions provided in the past by Jaggard [8] (function of one variable) and by Zaleski [10] (function of two variables).
Furthermore, a variant of 2D self--similar fractal surface representation, namely a 'one-dimensional bandlimited Weierstrass function', was introduced in [8], which will be generalized in this paper for 3D fractal surface.
Therefore, the equation proposed here, which describes the modified two-dimensional bandlimited fractal Weierstrass function for modeling 3D rough fractal surfaces is given by
Characterization of three-dimensional rough fractal surfaces from backscattered radar data
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