Fractal Design Research Articles

The Effect of Multiple Rotations on Mobius Transformations in Generating IFS Fractals

Iterating two pairs of Mobius transformations as attractors generates fractals that are known as Mobius fractals. In the present paper one studies the effect of multiple rotations on Mobius transformations, that frequently lead to more wellrounded as well as original fractal designs. General Terms Fractal, Algorithm, Turbo C++, Program.

Construction of a patterned hydrogel-fibrous mat bilayer structure to mimic choroid and Bruch's membrane layers of retina.

Deterioration of retina and death of the retinal cells due to age, diabetes, or occlusion can cause retinal degeneration which leads to loss of vision. In this study, it is aimed to design a bilayered matrix to mimic the choroid and the Bruch's membrane of the retinal tissue. As choroid, a microchanneled network resembling a fractal tree design was fabricated by photolithography over photo-cross-linkable methacrylated hyaluronic acid hydrogel. Gelatin or collagen was immobilized into the microchannels to enhance adherence of Human Umbilical Vein Endothelial Cells (HUVEC). At late culture periods (2 weeks), formation of tubular structures due to proliferation of the attached cells was observed. As Bruch's membrane, an electrospun fibroin nanofiber mat was produced to grow retinal pigment epithelium (RPE) cells on. Cellular interactions between RPE and HUVEC in the microchannels were investigated in a coculture model in a noncontact mode. It was deduced that by combining the RPE layer on the highly permeable Bruch's membrane with the choroid layer populated by HUVECs, a retinal substitute which might have a potential for use in the treatment of retinal diseases is possible. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 104A: 2166-2177, 2016.

Fractal detector design and analysis for multi‐input multi‐output radar system

The fractal dimension has been used in the monostatic radar to improve the target detection performance, especially in non-homogeneous clutter environments. In this study, the application of fractal dimension is extended to multi-input multi-output (MIMO) radar. A target detection method for MIMO radar using the fractal dimension measurements is developed. Two types of fractal dimension definitions, i.e. Hausdorf dimension and box-counting dimension are explained and the characteristics of the box-counting dimension are analysed in detail. Then, a fractal dimension estimation-based detector is presented and its performance is analysed for colocated MIMO and statistical MIMO. The simulations results verify the theoretical founding of the proposed target detector for MIMO radar based on the fractal dimension estimation.

The Effect of Multiple Rotations on a Unified System of Affine Transformations with related Trigonometric Coefficients

IFS fractals generated by affine transformations with arbitrary coefficients often there is a lot of chaotic noise. In the present paper the author studies the effect of multiple rotations on affine transformations with related trigonometric coefficients in terms of the IFS fractals generated by them. In the process a unified set of equations for generating both the Highway Dragon and the C curve have been developed. The effect of multiple rotations is to lend additional depth to the generated fractal as well as create new fractal designs..

Koch fractal inductors printed on flexible substrate

Performance analysis of Koch fractal inductors, printed in ink-jet technology, is presented. Koch fractal inductors are printed on a flexible polyimide film in two, three, four and eight layers, using silver nanoparticle ink as the conductor. It was shown that inductors performance improved with increasing the number of conductive layers. In addition, a coreless flexible transformer based on Koch fractal design is presented. The inductance and quality factor of the inductors and transformer windings were measured by impedance analyser in the frequency range from 1 to 250 MHz.

Quasi quarter SIW‐mode resonator and its application to sierpinski fractal filter design

ABSTRACTIn this letter, a new kind of quasi quarter SIW resonator (QQSIWR) using Sierpinski fractal defected structure is presented first. Comparing with SIW resonator, this novel resonator has lower resonant frequency (f0) and acceptable unloaded quality (Qu) value, while maintaining almost unchanged electromagnetic fields distributions. The frequency characteristics and Qu of this resonator is investigated under different fractal sizes. To validate the properties of QQSIWR, a miniature cross‐coupled bandpass filter (BPF) with a size reduction over 88% is proposed and optimized using Sierpinski fractal structure and cross coupling technology. It can produce asymmetrical frequency response by generating a transmission zero (TZ) on the high side of passband. A prototype of the filter is fabricated and measured, and the measured results are in good agreement well with the simulated ones. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:1176–1179, 2016

Boundary Element Modelling of a Novel Simple Enhanced Bandwidth Schroeder Diffuser Offering Comparable Performance to a Fractal Design

It is well established that Schroeder diffusers may be used as surface treatment to promote diffuse sound fields in auditoria over a target frequency range. Quadratic Residue Diffusers are very effective within a design frequency bandwidth, and this frequency bandwidth may be significantly extended by a nested or fractal design. Publicly available data typically publish diffusion coefficients separately for the parent diffuser and the child diffuser, with some ambiguity surrounding the effect the two levels have on each other, and the performance at ‘crossover’ frequencies. This paper uses an optimised 2D boundary element method to investigate the differences in results when the parent and child diffusers are modelled separately, and as an integrated design. It is found that the scattering properties of the child diffuser are significantly modified by the well of the parent diffuser in which it is placed. More interestingly, the excellent scattering properties of the fractal design may be achieved with only a minor loss of bandwidth using a far simpler and more robust geometry in which the child diffuser is replaced by a concave surface at the base of the well in the parent diffuser. The paper outlines the optimisation of the boundary element code for this task, and compares results for a variety of well bottom shapes with the fractal design.

Introduction to Fractal Antenna

In this article, the most recent improvements in the field of fractal antenna designing are theoretically and additionally basically checked on and its future extension is talked about. Fractal design is a geometric example that is rehashed at each design and in this way can't be spoken to by exemplary geometry. The method of considering the fractal geometry in designing various attributes related to the performance of the antenna becomes advantageous when it improves the some parameters such as low VSWR, high radiation efficiency, high gain, wide bandwidth and reduced size etc. Fractal has exceptional property that it can make duplicates of itself at various scales. Fractal antenna basically centered around two fields: one is the utilizations of fractal antenna and second is the design and investigation of fractal antenna. As of late there has been a lot of enthusiasm for the design of antenna for remote correspondence on account of continuously growing scope of remote telecom benefits and related applications for voice and information transmission. The motivation behind this paper is to audit various inventive configuration ideas of Fractal antenna for remote applications.

Construction of Electrical Performance Model for Geometric Characteristic of Combined Fractal Antenn

The application of fractal geometry in the antenna can greatly improve the performance of the antenna, and make it continue to be small, to meet the growing communication needs of the people. From birth of fractal geometry to the present application in various fields of science, because of its complex image with high self-similarity, when applied to antenna design, it can be well integrated with the electromagnetic theory, so as to solve the disadvantages and shortcomings of traditional antenna design. The combined fractal antenna based on fractal geometry design can further realize the miniaturization and gain of the antenna. Though the analysis of the relevant theoretical basis of the antenna, the model of the ring oscillator combined fractal antenna was constructed. In order to verify the performance of the combined fractal antenna structure, through the comparative analysis of physical measurement and simulation data, we can see that all the direction map, gain and bandwidth of combined fractal antenna have good effects, to better achieve the miniaturization of the antenna. Therefore, the combined fractal antenna can be used in practice, and it can be used for reference for the design of similar antennas

Can massive communities of teachers facilitate collaborative reflection? Fractal design as a possible answer

ABSTRACTThis paper explores the possibility that virtual communities of teachers with large numbers of members (referred to as massive communities of teachers) can offer support to novice teachers by means of collaborative reflection. The paper examines and conceptualises some problems found in professional massive communities and proposes that massification can dilute what some authors have called social presence or engagement. It is argued that this dilution, among other problems, very much hinders collaborative reflection among members of the community. Collaborative reflection is argued to be a crucial part of the support that novice teachers need in their first years in the profession. Therefore, a challenge is envisioned for massive communities of teachers to avoid the dilution of social presence or engagement. The authors argue that this dilution can be overcome by the use of multiple layers within a platform, referred to as fractal design.

Hybrid stent device of flow-diverting effect and stent-assisted coil embolization formed by fractal structure.

This paper presents a novel hybrid medical stent device. This hybrid stent device formed by fractal mesh structures provides a flow-diverting effect and stent-assisted coil embolization. Flow-diverter stents decrease blood flow into an aneurysm to prevent its rupture. In general, the mesh size of a flow-diverter stent needs to be small enough to prevent blood flow into the aneurysm. Conventional flow-diverter stents are not available for stent-assisted coil embolization, which is an effective method for aneurysm occlusion, because the mesh size is too small to insert a micro-catheter for coil embolization. The proposed hybrid stent device is capable of stent-assisted coil embolization while simultaneously providing a flow-diverting effect. The fractal stent device is composed of mesh structures with fine and rough mesh areas. The rough mesh area can be used to insert a micro-catheter for stent-assisted coil embolization. Flow-diverting effects of two fractal stent designs were composed to three commercially available stent designs. Flow-diverting effects were analyzed using computational fluid dynamics (CFD) analysis and particle image velocimetry (PIV) experiment. Based on the CFD and PIV results, the fractal stent devices reduce the flow velocity inside an aneurism just as much as the commercially available flow-diverting stents while allowing stent-assisted coil embolization.

Different-scale distribution of collembola in homogenous ground vegetation: Stability of parameters in space and time

We have tested the hypothesis about the existence of species-specific patterns of local spatial distribution of Collembola, i.e., combinations of differently sized aggregations or the absence of distinct aggregations. The presence of such patterns was previously demonstrated for some abundant collembolan species in the sphagnum pine forests of Karelia using the special fractal design of surveys, with groups of core samples taken at different distances. The aim of the present work was to find out whether the patterns observed in sphagnum pine forests were preserved in the mesophytic and xerophytic variants, namely green moss and lichen pine forests. As a rule, the parameters of local spatial distribution of species were quite similar in different seasons, in drier habitats as well as in humid ones. Some characteristics of collembolan aggregations at different levels, such as their size, density, and strength relative to the background, were described, and the occurrence of individual species in differently sized plots was estimated. On the whole, the typical traits of local spatial distribution of collembolan species were preserved not only within each biotope but also in different habitats. However, these species-specific patterns were not absolutely constant, as some species became more clumped under xerophytic conditions. The types of spatial redistribution of springtails accompanying an increase in their population density are discussed.

Effect of Porosity on Circle Grid Perforated Plate Performance as a Static Mixer in Laminar Flow

Mixing is one of the important processes to the many industries. Fluid mixing process typically involves three phases of fluid in the form of liquids, gases and solids. To obtain a desired type of mixing, one of the devices that can be use is a static mixer. In this study, a perforated plate static mixer with circle grid fractal design with two grades of porosity which are 50% and 75% will introduce. The purpose of implementing the two grades porosity of perforated plate in this study is to determine a performance of the two static mixers. In order to achieve the objective, the simulations of mixing fluid were carried out by using ANSYS CFX software. The simulation was carrying out primarily in cylindrical pipe with insertions of circle grid perforated plate. Three levels of laminar flow had been used which is Reynolds numbers (Re) equal to 100, 200 and 400. The performance of circle grid perforated plate static mixer will be evaluated by determining the Coefficient of Variation (COV). The simulation results also were compared in term of homogeneity level of mixing fluids to the Kenics static mixer. Based on the simulation results, the value of COV at selected plane in pipeline simulated for Kenics static mixer and the two grades porosity of perforated plate at Re = 400 are 0.000703, 0.0247and 0.00427 respectively. Since the values of COV between 0.01 and 0.05 are a reasonable target for many industry applications, the results for new approach of static mixer represent completely homogeneous mixing fluid for this application. Definitely this new approach of circle grid perforated plate with fractal design gave better results because of lower number of inserts and simple design of static mixer.

Different-scale distribution of Collembola in homogenous ground vegetation: Sphagnum moss

Patterns of spatial distribution of Collembola were studied in sphagnum pine forests (Karelia, northwest of European Russia) in habitats of the same type using plots varying in area from 1 dm2 to 100 m2. The fractal design of counts with groups of samples taken from 5 cm to 10 m apart was used. The mosaic distribution and density of aggregations were assessed on different scales. Based on four model species, the patterns of spatial distribution were shown to be species-specific and constant in time and space. Two main types of species distribution (“continuous” and “spotty”) were distinguished. Such factors as relative humidity, mass of moss cover, and litter thickness only insignificantly affected the collembolan distribution within humid biotopes.

ChemInform Abstract: From 1 → 3 Dendritic Designs to Fractal Supramacromolecular Constructs: Understanding the Pathway to the Sierpinski gasket

AbstractReview: 76 refs.

CFD Analysis of Industrial Multi-Stage Impeller in Stirred Tank with Fractal Pattern Baffled and Impeller

This paper presents tool for analysis of CFD adapted for flows in multi-staged stirred vessels with fractal pattern baffled for industrial. In order to develop a good mixing process model for stirred tanks, several way have been investigated by using the computational fluid dynamic. Implementing fractal design into stirred tank’s baffle and impeller are believed to influence the flow characteristic inside the stirred tank. The mixing process will be conduct by using multi-stage stirred tanks. Hence, the study is to simulate a fractal pattern baffled stirred vessels with fractal base of impeller. Four models with a new concept and different design of stirred tank have been introduced and studied. The multi-stages stirred tanks will adapted with fractal base pattern concept. The simulation is carry out by using the standard k-ε turbulence model. The results have been analysis in order to prove that which one of that model is the most effective in mixing. The flows produced in stirred tank are different and relevant with each model. The velocity profiles also give a relevant and quite impressive result by each model. At the end, the results will be examined and compared with each data that use a common type of baffle and impeller design.

A finite element approach to modelling fractal ultrasonic transducers

Piezoelectric ultrasonic transducers usually employ composite structures to improve their transmission and reception sensitivities. The geometry of the composite is regular with one dominant length scale and, since these are resonant devices, this dictates the central operating frequency of the device. In order to construct a wide bandwidth device it would seem natural therefore to utilize resonators that span a range of length scales. In this article, we derive a mathematical model to predict the dynamics of a fractal ultrasound transducer; the fractal in this case being the Sierpinski gasket. Expressions for the electrical and mechanical fields that are contained within this structure are expressed in terms of a finite element basis. The propagation of an ultrasonic wave in this transducer is then analysed and used to derive expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities as a function of the driving frequency. Comparing these key performance measures to an equivalent standard (Euclidean) design shows some benefits of these fractal designs.

(Invited) Design and Characterization of a New Low Cost Thick Film Copper Metallization Transfer Process Onto PDMS Enabling Stretchable Electronics

We present a new low cost microfabrication technology that utilizes a sacrificial conductive paint transfer method to realize thick film copper microstructures that are embedded in polydimethylsiloxane (PDMS). Several example structures are fabricated and characterized that demonstrate the potential application of this process in flexible electronics, wearable electronics, and novel microsensor and actuator designs. This process has reduced fabrication complexity and cost compared to existing metal-on-PDMS techniques, and enables large scale rapid prototyping of designs using minimal laboratory equipment. This technology differs from others in its use of a conductive copper paint seed layer and a unique transfer process that results in copper microstuctures embedded in PDMS rather than on top of the PDMS surface. The fabrication process begins with the deposition of the seed layer onto a flexible substrate via airbrushing. A dry film photoresist layer is laminated on top and patterned using standard techniques. Electroplated copper is grown on the seed layer through the photoresist mask and transferred to PDMS through a unique baking procedure. This baking transfer process releases the electroplated copper from the seed layer, permanently embedding it into the cured PDMS. The characterization of the copper microstructures is given in terms of feature size, film thickness, surface roughness, and resistivity. The resistivity is measured under static conditions as well as under conditions of flexing and stretching using various linear and 1-dimensional Peano curve structures [1]. To quantify the stability of a structure’s conductivity under flexing, linear structures are bent over curves having various radii and the response of the resistivity is measured against the number of iterations. To measure the response under stretching, 1-dimensional Peano curve structures are fabricated and stretched until failure, while the resistivity is measured against the strain. Results show that we can achieve films 25-75 micrometers in thickness, with reliable feature sizes down to 100 micrometers and a film resistivity of approximately 7.15 micro-Ω-cm [2]. Results from current experiments will be presented that characterize the resistivity response under flexing and stretching. Process variants and future work are discussed, as well as large scale adaptations and rapid prototyping. Finally, we outline the potential uses of this technology in flexible electronics and novel sensor and actuator designs. [1] J.A. Fan, W.-H. Yeo, Y. Su, Y. Hattori, W. Lee, S.-Y. Jung, Y. Zhang, Z. Liu, H. Cheng, L. Falgout, M. Bajema, T. Coleman, D. Gregoire, R. J. Larsen, Y. Huang, J. A. Rogers, “Fractal design concepts for stretchable electronics,” Nature Communications 5 (3266), 2014. [2] D. Hilbich, A. Khosla, L. Shannon, B. L. Gray, “A new low-cost, thick-film metallization transfer process onto PDMS using a sacrificial copper seed,” SPIE 9060, Nanosensors, Biosensors, and Info-Tech Sensors and Systems (906007), 2014

Performance comparison of bio-inspired optimization algorithms for Sierpinski gasket fractal antenna design

The Sierpinski gasket fractal antenna is most popular structure in the domain of fractal antennas. This fractal antenna has multi-band performance, and hence, the design of this antenna for the desired frequencies is a challenging problem. The artificial intelligence tools like artificial neural networks, fuzzy logic systems, bio-inspired optimization techniques are appropriate to provide accurate design solution in such cases. In this paper, three most popular bio-inspired optimization algorithms: genetic algorithms, particle swarm optimization (PSO), and bacterial foraging optimization, have been proposed to solve the design issues of Sierpinski gasket pre-fractal antenna. Their performances are analyzed and are compared with the experimental results. A simplified expression for calculation of resonant frequency of Sierpinski gasket pre-fractal antenna is proposed and is used as the objective function. Finally, the effectiveness is compared on the basis of three different measures: mean absolute percentage error, the average time taken by the models to evaluate the results, and the coefficient of correlation. The results indicate that the PSO algorithm is most suitable for this type of antenna.

A Study of Palm Oil-Methanol Mixing in a Stirred Tank Equipped with a Fractal Baffles

Palm oil and methanol do not form a single phase mixture in transesterification process in stirred tank due to a poor surface contact between them; hence give a relatively slow mixing process of the mixing. Introduction of new baffles in the stirred tank with a fractal pattern due to the fractal shape can give a high turbulent level when a fluid flow through the fractal pattern is the new idea in optimizing the using of the fractal pattern in engineering especially in mixing industries. Hence, in the present study, a new concept of baffles with a fractal design was proposed to enhance a palm oil-methanol mixing in stirred tank. In order to achieve the objective, the simulation of palm oil-methanol mixing was carried out by using ANSYS Fluent software. The simulation was carrying out primarily in the stirred tank equipped with the fractal baffles and the levels of mixing were observed at 60, 120, 180 and 240 seconds after the beginning of introduction of methanol in the stirred tank. An effectiveness of the fractal baffles will be evaluated by determining the Coefficient of Variation (COV). The simulation results also were compared in term of homogeneity level of palm oil-methanol mixing to the normal baffles in order to determine the significant effect of the fractal baffles. Based on the simulation results, the value of COV for the mixing process in the stirred tank equipped with fractal baffles at the selected time interval are 0.066, 0.0436, 0.0326 and 0.0226 respectively. Since the values of COV between 0.01 and 0.05 are a reasonable target for many industry applications, the results for new approach of stirred tank with fractal baffles represent completely homogeneous mixing for the palm oil-methanol simulated in this study. Definitely this new approach of fractal baffles gave better results because of lower number of COV compared to the stirred tank with normal baffles.