TITLE

# Symmetries of fractals

AUTHOR(S)
Xiang Sheng; Spurr, Michael J.
PUB. DATE
January 1996
SOURCE
Mathematical Intelligencer;Winter96, Vol. 18 Issue 1, p35
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Presents a discussion on the symmetries of fractals. Apparent reflective symmetry through the center of each snowflake-like Generalized Mandelbrot set; Symmetry of motions; Symmetries of Mandelbar sets; Julia sets.
ACCESSION #
9603142880

## Related Articles

• General theory of fractal path integrals with applications to many-body theories and statistical physics. Suzuki, Masuo // Journal of Mathematical Physics;Feb91, Vol. 32 Issue 2, p400

A general scheme of fractal decomposition of exponential operators is presented in any order m. Namely, exp[x(A+B)]=Sm(x)+O(xm+1) for any positive integer m, where Sm(x)=et1A et2B et3A et4BÂ·Â·Â·etMA with finite M depending on m. A general recursive scheme of construction of {tj} is given...

• Microscopic model of a non-Debye dielectric relaxation: The Cole-Cole law and its generalization. Khamzin, A.; Nigmatullin, R.; Popov, I. // Theoretical & Mathematical Physics;Nov2012, Vol. 173 Issue 2, p1604

Based on a self-similar spatial-temporal structure of the relaxation process, we construct a microscopic model for a non-Debye (nonexponential) dielectric relaxation in complex systems. In this model, we derive the Cole-Cole expression for the complex dielectric permittivity and show that the...

• Fractal geometry and topology abstracted from hair fibers. Ya-jun Yin; Fan Yang; Ying Li; Qin-shan Fan // Applied Mathematics & Mechanics;Aug2009, Vol. 30 Issue 8, p983

Based on the concepts of fractal super fibers, the (3, 9+2)-circle and (9+2,3)-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the (3)-circle and the (9+2)-circle fractal sets as subsets. As far as the (9+2) topological patterns are concerned,...

• Revisiting random walks in fractal media: On the occurrence of time discrete scale invariance. Bab, M. A.; Fabricius, G.; Albano, Ezequiel V. // Journal of Chemical Physics;1/28/2008, Vol. 128 Issue 4, p044911

This paper addresses the kinetic behavior of random walks in fractal media. We perform extensive numerical simulations of both single and annihilating random walkers on several Sierpinski carpets, in order to study the time behavior of three observables: the average number of distinct sites...

• Fractal dimension of the interatomic distance histogram: New 3D descriptor of molecular structure. Grigor'ev, V. A.; Raevskii, O. A. // Russian Journal of General Chemistry;Mar2011, Vol. 81 Issue 3, p449

method is developed for the calculation of a new 3D descriptor of molecular structure, which is the fractal dimension of the histogram of interatomic distances serving as a measure of the structure complexity in the geometric aspect. The new descriptor was found to depend mainly on three...

• Discrete Scale Relativity. Oldershaw, Robert L. // Astrophysics & Space Science;Oct2007, Vol. 311 Issue 4, p431

The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored. If the discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened in order to accommodate this form of discrete conformal...

• The self-organizing fractal theory as a universal discovery method: the phenomenon of life. Kurakin, Alexei // Theoretical Biology & Medical Modelling;2011, Vol. 8 Issue 1, p4

A universal discovery method potentially applicable to all disciplines studying organizational phenomena has been developed. This method takes advantage of a new form of global symmetry, namely, scale-invariance of self-organizational dynamics of energy/matter at all levels of organizational...

• Explicit Spectral Decimation for a Class of Self-Similar Fractals. Hernández, Sergio A.; Menéndez-Conde, Federico // Abstract & Applied Analysis;2013, p1

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...

• On Measures Driven by Markov Chains. Heurteaux, Yanick; Stos, Andrzej // Journal of Statistical Physics;Dec2014, Vol. 157 Issue 6, p1046

We study measures on $$[0,1]$$ which are driven by a finite Markov chain and which generalize the famous Bernoulli products.We propose a hands-on approach to determine the structure function $$\tau$$ and to prove that the multifractal formalism is satisfied. Formulas for the dimension of the...

Share

## Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library