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Fractal Fract
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Fractals in Biophysics and Their Applications
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Fractals in Biophysics and Their Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Life Science, Biophysics".

Deadline for manuscript submissions: 28 February 2025 | Viewed by 3614

Special Issue Editor

Dr. Anirban Bandyopadhyay

E-Mail Website
Guest Editor
International Center for Materials and Nanoarchitectronics (MANA), Research Center for Advanced Measurement and Characterization (RCAMC), National Institute for Materials Science (NIMS), 1-2-1 Sengen, Main Bldg, Tsukuba 815, Japan
Interests: fractals; quantum biology; condensed matter physics; computing; quantum optics; nanoelectronics; cancer biology; neuroscience

Special Issue Information

Dear Colleagues,

Welcome to the thrilling world of "Biophysics and Fractal"—an extraordinary Special Issue that delves into the mesmerizing intersection of two fascinating fields! This cutting-edge collection aims to captivate readers and researchers alike, enticing them to embark on a groundbreaking journey that explores the intricate relationship between biophysics and fractals.

In this Special Issue, we invite authors to explore a wide array of captivating topics that have already garnered immense popularity in the media. From unraveling the hidden fractal patterns within biological systems to deciphering the biophysical principles underlying the emergence of fractal structures, contributors have the opportunity to shed light on the dynamic interplay between nature's complexity and its underlying mathematical elegance.

Emphasizing the relevance for the future, this Special Issue will also be an avenue to showcase visionary research. Pioneering investigations that investigate the application of fractals in biophysical modeling, such as utilizing fractal dimension analysis for characterizing biomolecules' spatial organization, hold tremendous promise for revolutionizing our understanding of life's fundamental processes.

Moreover, we are particularly interested in the innovative fusion of biophysics and fractals in emerging fields. Be it the integration of fractal-based algorithms for deciphering the human brain's intricate networks or exploring the role of fractal geometry in understanding and designing novel drug delivery systems, this Special Issue aims to encompass a diverse range of cutting-edge applications that will shape the future of both disciplines.

We welcome researchers to submit their most radical proposals and visionary insights, taking inspiration from the latest breakthroughs and envisioning the uncharted territories that biophysics and fractals are poised to conquer. By fostering interdisciplinary collaboration and encouraging a forward-looking perspective, this Special Issue seeks to ignite excitement and inspire a new wave of research that will undoubtedly propel our understanding of life's complexity to unprecedented heights.

Join us on this extraordinary expedition into the captivating realm of "Biophysics and Fractal," where curiosity knows no bounds, and the possibilities are as infinite as the fractals themselves. Together, we shall unravel the mysteries of life through the mesmerizing lens of fractal geometry!

Dr. Anirban Bandyopadhyay
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum mechanics
  • quantum biology
  • biophysics, biophotonics, bioelectronics
  • neuroscience
  • brain dynamics
  • fractal analysis in medicine
  • water network in biology

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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11 pages, 1749 KiB  
Article
Artificial Intelligence in Chromatin Analysis: A Random Forest Model Enhanced by Fractal and Wavelet Features
by Igor Pantic and Jovana Paunovic Pantic
Fractal Fract. 2024, 8(8), 490; https://doi.org/10.3390/fractalfract8080490 - 21 Aug 2024
Cited by 1 | Viewed by 792
Abstract
In this study, we propose an innovative concept that applies an AI-based approach using the random forest algorithm integrated with fractal and discrete wavelet transform features of nuclear chromatin. This strategy could be employed to identify subtle structural changes in cells that are [...] Read more.
In this study, we propose an innovative concept that applies an AI-based approach using the random forest algorithm integrated with fractal and discrete wavelet transform features of nuclear chromatin. This strategy could be employed to identify subtle structural changes in cells that are in the early stages of programmed cell death. The code for the random forest model is developed using the Scikit-learn library in Python and includes hyperparameter tuning and cross-validation to optimize performance. The suggested input data for the model are chromatin fractal dimension, fractal lacunarity, and three wavelet coefficient energies obtained through high-pass and low-pass filtering. Additionally, the code contains several methods to assess the performance metrics of the model. This model holds potential as a starting point for designing simple yet advanced AI biosensors capable of detecting apoptotic cells that are not discernible through conventional microscopy techniques. Full article
(This article belongs to the Special Issue Fractals in Biophysics and Their Applications)
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25 pages, 3191 KiB  
Article
Fractal Operators Abstracted from Arterial Blood Flow
by Tianyi Zhou, Yajun Yin, Gang Peng, Chaoqian Luo and Zhimo Jian
Fractal Fract. 2024, 8(7), 420; https://doi.org/10.3390/fractalfract8070420 - 18 Jul 2024
Cited by 1 | Viewed by 581
Abstract
In this paper, we present a re-established functional fractal circuit model of arterial blood flow that incorporates the shunt effect of the branch vessels. Under the background of hemodynamics, we abstracted a family of fractal operators and investigate the kernel function and properties [...] Read more.
In this paper, we present a re-established functional fractal circuit model of arterial blood flow that incorporates the shunt effect of the branch vessels. Under the background of hemodynamics, we abstracted a family of fractal operators and investigate the kernel function and properties thereof. Based on fractal operators, the intrinsic relation between Bessel function and Struve function was revealed, and some new special functions were found. The results provide mathematical tools for biomechanics and automatic control. Full article
(This article belongs to the Special Issue Fractals in Biophysics and Their Applications)
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20 pages, 3143 KiB  
Article
On the Application of Mann-Iterative Scheme with h-Convexity in the Generation of Fractals
by Asifa Tassaddiq, Muhammad Tanveer, Muhammad Zubair, Muhammad Arshad and Carlo Cattani
Fractal Fract. 2024, 8(7), 414; https://doi.org/10.3390/fractalfract8070414 - 15 Jul 2024
Cited by 1 | Viewed by 929
Abstract
Self-similarity is a common feature among mathematical fractals and various objects of our natural environment. Therefore, escape criteria are used to determine the dynamics of fractal patterns through various iterative techniques. Taking motivation from this fact, we generate and analyze fractals as an [...] Read more.
Self-similarity is a common feature among mathematical fractals and various objects of our natural environment. Therefore, escape criteria are used to determine the dynamics of fractal patterns through various iterative techniques. Taking motivation from this fact, we generate and analyze fractals as an application of the proposed Mann iterative technique with h-convexity. By doing so, we develop an escape criterion for it. Using this established criterion, we set the algorithm for fractal generation. We use the complex function f(x)=xn+ct, with n≥2,c∈C and t∈R to generate and compare fractals using both the Mann iteration and Mann iteration with h-convexity. We generalize the Mann iterative scheme using the convexity parameter h(α)=α2 and provide the detailed representations of quadratic and cubic fractals. Our comparative analysis consistently proved that the Mann iteration with h-convexity significantly outperforms the standard Mann iteration scheme regarding speed and efficiency. It is noticeable that the average number of iterations required to perform the task using Mann iteration with h-convexity is significantly less than the classical Mann iteration scheme. Moreover, the relationship between the fractal patterns and the input parameters of the proposed iteration is extremely intricate. Full article
(This article belongs to the Special Issue Fractals in Biophysics and Their Applications)
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23 pages, 6551 KiB  
Perspective
Fractal Calculus Facilitates Rethinking ‘Hard Problems’: A New Research Paradigm
by Bruce J. West
Fractal Fract. 2024, 8(11), 620; https://doi.org/10.3390/fractalfract8110620 - 23 Oct 2024
Viewed by 569
Abstract
This paper introduces a non-standard research technique to clarify how complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using fractal dynamical models with and without stochastic forces. This method for conducting research involves tracing the [...] Read more.
This paper introduces a non-standard research technique to clarify how complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using fractal dynamical models with and without stochastic forces. This method for conducting research involves tracing the historical evolution of understanding an empirical medical process facilitated by the fractal-order calculus perspective. Herein, we trace the analysis of the time series for heart rate variability (HRV) developed for diagnosing the cardiovascular health of a patient. This is performed herein by introducing four (one empirical, which entails three theoretical fractal models) distinct but related fractal models, each one introduced to solve a particular problem arising from a fundamental defect in the previous model, but in generalizing a model at one stage to resolve the problem associated with the defect, another is invariably introduced by the replacement model. It is through the utilization of the fractal-order calculus that the necessity for rethinking how to systematically incorporate additional layers of complexity is revealed, ultimately resulting in a ‘complete’ description of its empirical dynamics in fractal terms. Full article
(This article belongs to the Special Issue Fractals in Biophysics and Their Applications)
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