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Fractal Dimensions in Circular and Spiral Phenomena

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posted on 2022-12-24, 06:06 authored by Subhash KakSubhash Kak

 In many natural and engineered systems, the circle and the spiral are the appropriate primitives. As example, rotating motion of fluid around a common centerline constitutes a vortex. In many of these situations, the associated fractal dimension is of analytical interest. The box counting approach to determining this dimension is not appropriate for such cases, because unlike squares and boxes that span 2- and 3-dimensional spaces, circles and spheres don’t. Since self-similarity or scale invariance is not an exact property, we propose the computation of the dimension is such cases based on the number of circles or spheres in the mapping process. This is illustrated by a few examples. How this may apply to spiral patterns that are repeated across scale is indicated. 

History

Email Address of Submitting Author

subhash.kak@okstate.edu

ORCID of Submitting Author

https://orcid.org/0000-0001-5426-9759

Submitting Author's Institution

Oklahoma State University

Submitting Author's Country

  • United States of America