# Launching the chaotic realm of iso-fractals: A short remark

## Abstract

In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit 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 iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics 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 Einstein-Galilei (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: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 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 iso-fractals: 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 iso-fractals: A short remark*. United States. doi:10.1063/1.4912722.

```
O'Schmidt, Nathan, Katebi, Reza, and Corda, Christian. Tue .
"Launching the chaotic realm of iso-fractals: A short remark". United States.
doi:10.1063/1.4912722.
```

```
@article{osti_22391107,
```

title = {Launching the chaotic realm of iso-fractals: A short remark},

author = {O'Schmidt, Nathan and Katebi, Reza and Corda, Christian},

abstractNote = {In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit 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 iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics 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 = {Tue Mar 10 00:00:00 EDT 2015},

month = {Tue Mar 10 00:00:00 EDT 2015}

}