Fractals: An Eclectic Survey, Part-I

Husain, Akhlaq; Nanda, Manikyala Navaneeth; Chowdary, Movva Sitaram; Sajid, Mohammad

doi:10.3390/fractalfract6020089

Cited by 27 publications

(15 citation statements)

References 53 publications

(75 reference statements)

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“…For instance, Neves et al [99] pioneered the usage of computer generated fractals for printed textile patterns. The term fractal refers to geometric motifs that can replicate their shapes at smaller, or larger, scales due to inherent self-similarity [100]. By the usage of fractal geometry it is possible to generate visual attracting motifs that resemble the shape of nature, that found many applications in the fashion industry [101].…”

Section: Mathematics-inspired Fashion Stylementioning

confidence: 99%

Mathematics meets the fashion industry on path to product innovation and sustainability

Magri

Ciarletta

2023

Proc. R. Soc. A.

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Mathematics remains an endless source of inspiration for both the conception and the fabrication of clothes and fashion products. Over the last century, the prominent role of mathematics in the fashion industry has evolved together with the progress in computational resources and fabrication technologies. Nowadays, mathematics not only provides useful theoretical and computational tools to assist design and fabrication, but also acts as a catalyst of creativeness. This survey discusses the latest advances on mathematical models and methods in the fashion industry, restricting our attention to clothing design and multi-scale modelling, and their applications for digital manufacturing of textiles and garments. Particular focus is given to the usage of mathematics to drive product innovation and to reduce the environmental impact of the fashion industry in order to meet the Sustainable Development Goals of the United Nations.

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Section: Mathematics-inspired Fashion Stylementioning

confidence: 99%

Mathematics meets the fashion industry on path to product innovation and sustainability

Magri

Ciarletta

2023

Proc. R. Soc. A.

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“…The Julia set (J-set) secured an indistinguishable place in the field of dynamical systems and fractal geometry due to its useful characteristics, applications in various fields, and amazing beauty ( [3,5,[36][37][38][39]). In this section, we utilize the escape time algorithm to generate Julia sets for different input parameters by taking a maximum of 30 iterations.…”

Section: Generation Of Julia Setsmentioning

confidence: 99%

A Brief Study on Julia Sets in the Dynamics of Entire Transcendental Function Using Mann Iterative Scheme

Prajapati¹,

Rawat

Tomar

et al. 2022

Fractal Fract

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In this research, we look at the Julia set patterns that are linked to the entire transcendental function f(z)=aezn+bz+c, where a,b,c∈C and n≥2, using the Mann iterative scheme, and discuss their dynamical behavior. The sophisticated orbit structure of this function, whose Julia set encompasses the entire complex plane, is described using symbolic dynamics. We also present bifurcation diagrams of Julia sets generated using the proposed iteration and function, which altogether contain four parameters, and discuss the graphical analysis of bifurcation occurring in the family of this function.

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“…In today's communication systems, multiband antennas are required. A major issue for contemporary transmitters and receivers is to expand the capability of many functions in tiny volume sizes [1][2][3]. Today's antennas are integrated with other circuit components and serve as more than just a receiving and transmitting device [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Study of Diminutive Antenna employing identical elliptical notch in Elliptical Microstrip patch for multiband applications

Jat,

Gupta

2023

Preprint

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The focus of discussion in this paper is an acceptable small configuration for an elliptical microstrip patch antenna. This is featured with planer geometry embedded mirror ellipse with elliptical notch layout. It can be used for multiband application in wireless communication. The chosen antenna produces seven echoing frequencies that operate across the frequency range of 5 to 18 GHz, including 5.9 GHz (use in WiMAX), 8.2 GHz, 9.99 GHz (use in X- band), 12.63 GHz (use in space services and within rise-data-rate), 13.97 GHz (land portable spacecraft, broadcast navigating implementation), 16.24 GHz and 17.57 GHz (use in Ku- band). The proposed antenna has mirror-imaged elliptical slots with embedded ellipse in slots having the microstrip signal line feed without any defects in the ground structure. A simulation tool that uses the finite element modelling set up (ex. CST) created the potential antenna. On a dual-sided FR-4 substrate (ɛᵣ = 4.3) with a layer thickness ‘h’ of 1.6 mm and a surface size (Ls× Ws) of 20 x 24 mm², the recommended antenna is modelled. The outcomes of the simulations show the fact that our presented antenna has satisfactory gain and S11 ≤ -10 dB input impedance bandwidths across seven working frequencies. This offered antenna design concept is a major contender for multiple purposes in wireless communication and is backed by resonant frequency regions spread throughout a broad spectrum.

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Fractals: An Eclectic Survey, Part-I

Cited by 27 publications

References 53 publications

Mathematics meets the fashion industry on path to product innovation and sustainability

Mathematics meets the fashion industry on path to product innovation and sustainability

A Brief Study on Julia Sets in the Dynamics of Entire Transcendental Function Using Mann Iterative Scheme

Study of Diminutive Antenna employing identical elliptical notch in Elliptical Microstrip patch for multiband applications

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