\(R^*\)-transformers and fractal curves
type: Item
instance of: scholarly article
title: \(R^*\)-transformers and fractal curves
zbMATH Open document ID: 0948.28005
DOI: 10.1007/BF02733431
author: L. P. Lisovik
author: D. A. Koval'
author: S. V. Martines
published in: Cybernetics and Systems Analysis
publication date: 2000-05-07T00:00:00Z
review text: \(R\)-transformers process binary representation of real numbers and, as it has been already shown by \textit{L. P. Lisovik} [Kibern. Sist. Anal. 3, No. 3, 11-22 (1994; Zbl 0868.28004)], make it possible to specify a continuous nowhere-differentiable function, a Peano curve, a singular strictly increasing function, and some fractal curves. In the current paper the authors define pseudo-synchronous \(R\)-transformers and \(R^*\)-transformers. It is shown that the class of functions defined by finite pseudo-synchronous \(R\)-transformers is closed with respect to the operations of addition, multiplication by a rational number, and modulus taking. The authors argue that \(R^*\)-transformers (allowing both digits themselves and the radix of the numeration system to be fractional numbers in representations of real numbers appearing on the output tape) are more convenient in representing continuous real functions and fractal curves than the \(R\)-transformers. The authors do not compare their approach with conventional approaches widely used to define fractal sets and based on iterated function systems.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 03D80
Mathematics Subject Classification ID: 26A27
zbMATH DE Number: 1439546
zbMATH Keywords: transformer
zbMATH Keywords: fractal curves
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
cites work: Operations on R-numbers
cites work: Axiomatic theory of partial continuous functions and the Peano curve
cites work: Finite transformers for construction of fractal curves
cites work: One-to-one mappings defined by finite transformers
cites work: Q5752571
cites work: Q5537518
full work available at URL: https://doi.org/10.1007/bf02733431
OpenAlex ID: W1970974905
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description: scientific article; zbMATH DE number 1439546