Launching the chaotic realm of isofractals: A short remark
Abstract
In this brief note, we introduce the new, emerging subdiscipline of isofractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, nonlinear, and selfsimilar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the isofractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot isosets. Third, we present the cuttingedge notion of dynamic isospaces and explain how a mathematical space can be isotopically lifted with isounit functions that (continuously or discretely) change; in the discrete case examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of isounits to construct an ordered series of (magnified and/or demagnified) isospaces that are locally isomorphic. Fourth, we consider the initiation of isofractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D isospaces. In total, the reviewed isofractal results are a significant improvement over traditional fractals because the application of Santilli’s isomathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas formore »
 Authors:
 Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725 (United States)
 Department of Physics, California State University in Fullerton, 800 North State College Boulevard, Fullerton, CA 92831 (United States)
 Institute for Theoretical Physics and Advanced Mathematics EinsteinGalilei (IFM), Via Santa Gonda 14, 59100 Prato (Italy)
 Publication Date:
 OSTI Identifier:
 22391107
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: AIP Conference Proceedings; Journal Volume: 1648; Journal Issue: 1; Conference: ICNAAM2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 2228 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; DEGREES OF FREEDOM; FRACTALS; HOLOGRAPHY; ITERATIVE METHODS; MATHEMATICAL SPACE; NONLINEAR PROBLEMS; STATISTICS; TOPOLOGY
Citation Formats
O'Schmidt, Nathan, Katebi, Reza, and Corda, Christian. Launching the chaotic realm of isofractals: A short remark. United States: N. p., 2015.
Web. doi:10.1063/1.4912722.
O'Schmidt, Nathan, Katebi, Reza, & Corda, Christian. Launching the chaotic realm of isofractals: A short remark. United States. doi:10.1063/1.4912722.
O'Schmidt, Nathan, Katebi, Reza, and Corda, Christian. 2015.
"Launching the chaotic realm of isofractals: A short remark". United States.
doi:10.1063/1.4912722.
@article{osti_22391107,
title = {Launching the chaotic realm of isofractals: A short remark},
author = {O'Schmidt, Nathan and Katebi, Reza and Corda, Christian},
abstractNote = {In this brief note, we introduce the new, emerging subdiscipline of isofractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, nonlinear, and selfsimilar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the isofractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot isosets. Third, we present the cuttingedge notion of dynamic isospaces and explain how a mathematical space can be isotopically lifted with isounit functions that (continuously or discretely) change; in the discrete case examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of isounits to construct an ordered series of (magnified and/or demagnified) isospaces that are locally isomorphic. Fourth, we consider the initiation of isofractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D isospaces. In total, the reviewed isofractal results are a significant improvement over traditional fractals because the application of Santilli’s isomathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.},
doi = {10.1063/1.4912722},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1648,
place = {United States},
year = 2015,
month = 3
}

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