COMBINATORIAL FRACTAL GEOMETRY WITH A BIOLOGICAL APPLICATION

Fractals ◽  
2006 ◽  
Vol 14 (02) ◽  
pp. 133-142 ◽  
Author(s):  
JOHN KONVALINA ◽  
IGOR KONFISAKHAR ◽  
JACK HEIDEL ◽  
JIM ROGERS
Keyword(s):  
Fractal Geometry ◽  
Boolean Network ◽  
Biological Systems ◽  
Sierpinski Gasket ◽  
Network Models ◽  
Combinatorial Problem ◽  
Higher Dimensions ◽  
Global Dynamics ◽  
Biological Application ◽  
Sierpiński Gasket

The solution to a deceptively simple combinatorial problem on bit strings results in the emergence of a fractal related to the Sierpinski Gasket. The result is generalized to higher dimensions and applied to the study of global dynamics in Boolean network models of complex biological systems.

scholarly journals Explicit Spectral Decimation for a Class of Self-Similar Fractals

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Sergio A. Hernández ◽  
Federico Menéndez-Conde
Keyword(s):  
Laplace Operator ◽  
Sierpinski Gasket ◽  
Higher Dimensions ◽  
Explicit Construction ◽  
Sierpiński Gasket ◽  
Infinite Collection ◽  
Self Similar ◽  
The Laplace Operator

The method of spectral decimation is applied to an infinite collection of self-similar fractals. The sets considered are a generalization of the Sierpinski Gasket to higher dimensions; they belong to the class of nested fractals and are thus very symmetric. An explicit construction is given to obtain formulas for the eigenvalues of the Laplace operator acting on these fractals.

scholarly journals Broadband 1–3 Piezoelectric Composite Transducer Design Using Sierpinski Gasket Fractal Geometry

2018 ◽  
Vol 65 (12) ◽  
pp. 2429-2439 ◽  
Author(s):  
Haoyu Fang ◽  
Zhen Qiu ◽  
Anthony J. Mulholland ◽  
Richard L. O'Leary ◽  
Anthony Gachagan
Keyword(s):  
Fractal Geometry ◽  
Sierpinski Gasket ◽  
Piezoelectric Composite ◽  
Sierpiński Gasket ◽  
Transducer Design

scholarly journals Dimer Coverings on the Sierpinski Gasket

2008 ◽  
Vol 131 (4) ◽  
pp. 631-650 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

2021 ◽  
Vol 385 ◽  
pp. 107771
Author(s):  
Therese-Marie Landry ◽  
Michel L. Lapidus ◽  
Frédéric Latrémolière
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Spectral Triples
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