On the topological Billingsley dimension of self-similar Sierpiński carpet

2021 ◽  
Author(s):  
Anouar Ben Mabrouk ◽  
Bilel Selmi
Keyword(s):  
Sierpinski Carpet ◽  
Self Similar ◽  
Sierpiński Carpet

scholarly journals Sierpinski carpet fractal monopole antenna for ultra-wideband applications

2022 ◽  
Vol 12 (1) ◽  
pp. 983
Author(s):  
Medhal Bharathraj Kumar ◽  
Praveen Jayappa
Keyword(s):  
Microstrip Antenna ◽  
Monopole Antenna ◽  
Ultra Wideband ◽  
Base Case ◽  
Fractal Antenna ◽  
Sierpinski Carpet ◽  
Low Profile ◽  
Self Similar ◽  
Fractal Antennas ◽  
Sierpiński Carpet

Microstrip antenna is broadly used in the modern communication system due to its significant features such as light weight, inexpensive, low profile, and ease of integration with radio frequency devices. The fractal shape is applied in antenna geometry to obtain the ultra-wideband antennas. In this paper, the sierpinski carpet fractal monopole antenna (SCFMA) is developed for base case, first iteration and second iteration to obtain the wideband based on its space filling and self-similar characteristics. The dimension of the monopole patch size is optimized to minimize the overall dimension of the fractal antenna. Moreover, the optimized planar structure is proposed using the microstrip line feed. The monopole antenna is mounted on the FR4 substrate with the thickness of 1.6 mm with loss tangent of 0.02 and relative permittivity of 4.4. The performance of this SCFMA is analyzed in terms of area, bandwidth, return loss, voltage standing wave ratio, radiation pattern and gain. The proposed fractal antenna achieves three different bandwidth ranges such as 2.6-4.0 GHz, 2.5-4.3 GHz and 2.4-4.4 GHz for base case, first and second iteration respectively. The proposed SCFMA is compared with existing fractal antennas to prove the efficiency of the SCFMA design. The area of the SCFMA is 25×20 mm<sup>2</sup>, which is less when compared to the existing fractal antennas.

SCALE-FREE AND SMALL-WORLD PROPERTIES OF VAF FRACTAL NETWORKS

Fractals ◽  
2016 ◽  
Vol 24 (03) ◽  
pp. 1650033 ◽  
Author(s):  
HAO LI ◽  
JIAN HUANG ◽  
ANBO LE ◽  
QIN WANG ◽  
LIFENG XI
Keyword(s):  
Small World ◽  
The Self ◽  
Sierpinski Carpet ◽  
Scale Free ◽  
Evolving Networks ◽  
Self Similar ◽  
Sierpiński Carpet

In this paper, we investigate the vertical-affiliation-free (VAF) evolving networks whose node set is the basic squares in the process of generating the Sierpinski carpet and edge exists between any two nodes if and only if the corresponding basic squares intersect just on their boundary. Although the VAF networks gets rid of the hierarchial organizations produced naturally by the self-similar structures of fractals, we still prove that they are scale-free and have the small-world effect.

scholarly journals Sierpinski Carpet and Chaos in the Periodic Table of the Elements

2021 ◽  
pp. 1-14
Author(s):  
Leila Hojatkashani
Keyword(s):  
Linear System ◽  
Periodic Table ◽  
Chaotic Systems ◽  
Chemical Elements ◽  
Fibonacci Numbers ◽  
Geometric Pattern ◽  
Sierpinski Carpet ◽  
Fractal Sets ◽  
Self Similar ◽  
Sierpiński Carpet

Fractals are self-similar geometric pattern which can be found in nature. They have applications in mathematic, electronic, architecture. Fractal sets also can be used to create chaotic systems. This work is about applying Sierpinski carpet order on the periodic table of the elements to create a new pattern for the chemical elements. Fibonacci numbers and Math lab software are used to transform a linear system to three spiral systems. This new pattern which is consisted of three layers shows that the flows among chemical elements are based on Archimedes spiral equation The purpose of this study is to show Sierpinski carpet order in the periodic table of the chemical elements and also there can be a chaos even in chemical elements.

AVERAGE GEODESIC DISTANCE OF SIERPINSKI CARPET

Fractals ◽  
2017 ◽  
Vol 25 (06) ◽  
pp. 1750061 ◽  
Author(s):  
LUMING ZHAO ◽  
SONGJING WANG ◽  
LIFENG Xi
Keyword(s):  
Finite Type ◽  
Geodesic Distance ◽  
Sierpinski Carpet ◽  
Similar Measure ◽  
Self Similar ◽  
Sierpiński Carpet

We obtain the average geodesic distance on the Sierpinski carpet in terms of the integral of geodesic distance on self-similar measure. We find out the finite pattern phenomenon of integral inspired by the notion of finite type on self-similar sets with overlaps.

Thermal Performance of Sierpinski Carpet Fractal Fins in a Forced Convection Environment

2016 ◽  
Author(s):  
David Calamas ◽  
Daniel Dannelley ◽  
Gyunay Keten
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Forced Convection ◽  
Thermal Performance ◽  
Reynolds Numbers ◽  
Unit Mass ◽  
Thermal Testing ◽  
Sierpinski Carpet ◽  
Fractal Pattern ◽  
Sierpiński Carpet

When certain fractal geometries are used in the design of fins or heat sinks the surface area available for heat transfer can be increased while system mass can be simultaneously decreased. The Sierpinski carpet fractal pattern, when utilized in the design of an extended surface, can provide more effective heat dissipation while simultaneously reducing mass. In order to assess the thermal performance of fractal fins for application in the thermal management of electronic devices an experimental investigation was performed. The first four fractal iterations of the Sierpinski carpet pattern, used in the design of extended surfaces, were examined in a forced convection environment. The thermal performance of the Sierpinski carpet fractal fins was quantified by the following performance metrics: efficiency, effectiveness, and effectiveness per unit mass. The fractal fins were experimentally examined in a thermal testing tunnel for a range of Reynolds numbers. As the Reynolds number increased, the fin efficiency, effectiveness and effectiveness per unit mass were found to decrease. However, as the Reynolds number increased the Nusselt number was found to similarly increase due to higher average heat transfer coefficients. The fourth iteration of the fractal pattern resulted in a 6.73% and 70.97% increase in fin effectiveness and fin effectiveness per unit mass when compared with the zeroth iteration for a Reynolds number of 6.5E3. However, the fourth iteration of the fractal pattern resulted in a 1.93% decrease in fin effectiveness and 57.09% increase in fin effectiveness per unit mass when compared with the zeroth iteration for a Reynolds number of 1.3E4. The contribution of thermal radiation to the rate of heat transfer was as high as 62.90% and 33.69% for Reynolds numbers of 6.5E3 and 1.3E4 respectively.

scholarly journals Antena UHF multifuncional del tipo fractal microstrip basada en la alfombra de Sierpinski

2021 ◽  
Vol 9 (17) ◽  
pp. 4-16
Author(s):  
Pablo Lupera Morillo ◽  
Gary Flores ◽  
Amanda Montaluisa
Keyword(s):  
Wireless Local Area Network ◽  
Local Area Network ◽  
Local Area ◽  
Digital Tv ◽  
Area Network ◽  
Fractal Antenna ◽  
Sierpinski Carpet ◽  
Broadband Wireless ◽  
Rectangular Patch ◽  
Sierpiński Carpet

The use of multifunctional devices increases day by day. Mentioned devices, as smart tv, need appropriate and unified antennas which can meet required frequencies. Therefore, in this paper, a Sierpinski carpet microstrip fractal antenna in the second iteration is designed and fabricated for Digital Tv in UHF band and wireless wideband networks. It was verified that that the design of a fractal antenna based on the Sierpinski carpet is possible from a rectangular patch on iteration 0; however, it must be taken into account that the patch design must be carried out at a specific resonance frequency. Simulation is carried out using ADS simulator, and it was verified using a vector network analyzer. The proposed fractal antenna operates in the UHF digital TV range from 470 MHz to 683 MHz and in the 2.45 GHz to 2.4835 GHz range of broadband wireless local area network.

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