Bi-asymptotic fractals: Fractals between lower and upper bounds

Autor:	Jürgen W Dollinger, Ralf Metzler, Theo F. Nonnenmacher
Rok vydání:	1998
Předmět:	Fractal Dimension (vector space) Mathematical analysis General Physics and Astronomy Biological cell Statistical and Nonlinear Physics Function (mathematics) Constant (mathematics) Value (mathematics) Mathematical Physics Analytic function Mathematics
Zdroj:	Journal of Physics A: Mathematical and General. 31:3839-3847
ISSN:	1361-6447 0305-4470
DOI:	10.1088/0305-4470/31/16/012
Popis:	Extending the idea of Rigaut's asymptotic fractals issuing a turnover from a constant to a power-law behaviour towards smaller scales, we extend this idea to asymptotic fractals with both lower and upper turnover points, i.e. the fractal region is terminated, towards larger scales, by another constant value. This behaviour is typical for natural fractals, such biological cell boundaries. Here, we present a new analytic function describing this bi-asymptotic behaviour. The introduced parameters can be directly interpreted. We show the advantage of this function in fitting processed images of natural and mathematical fractals, in comparison with standard procedures: the determined dimension is significantly more accurate. A program package with this new function is available.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::02fa914e7dd32cd73cefae5397f6ffa3 https://doi.org/10.1088/0305-4470/31/16/012 Zobrazit plný text záznamu