Fractal Design Research Articles

HYBRID ALGORITHM FOR THE CLASSIFICATION OF FRACTAL DESIGNS AND IMAGES

The fractal patterns are recursive patterns and are self-similar in nature. The fractal geometry provides better understanding of natural patterns as compared to the Euclidean geometry. The fractal designs have been used extensively in the fields of applied sciences due to the systematic methods used for their generation. These methods provide benchmarks to analyze the roughness, narrow/broad vision of the objects. In the fields of architecture and design, computational methods for fractal generation can prove to be more reliable tools. The fractal patterns can be simulated and the architecture can be modeled, with several options, before implementing it practically. During this research, this strategy is opted to design novel fractal tile designs. Several designs are selected from a series of simulations, based on the final visionary evaluation, according to the requirement of the walls of different zones in modern buildings. Four fractal patterns are simulated with several orientations and final designs are documented with corresponding geometrical evaluation.

Collecting the space-distributed Maxwell's displacement current for ultrahigh electrical density of TENG through a 3D fractal structure design

A three-dimensional fractal structured nanogenerator (FSNG), which can efficiently collect the space-distributed Maxwell's displacement current and significantly improve the electrical energy density of TENG, has been developed.

Retracted: Fractal Visual Art Graphic Design Based on Computer‐Aided Algorithms

Retracted: Fractal Visual Art Graphic Design Based on Computer‐Aided Algorithms

Manipulation of Fractal Nano‐Kirigami by Capillary and Electrostatic Forces

AbstractFractals are beautiful forms of geometric patterns, usually having high degrees of freedom of shape change. Recently, fractal and fractal‐like designs have aroused great interest in scientific research. Here, fractal‐like nano‐kirigami structures with rotational symmetries are proposed and demonstrated, in which topological morphologies can be transformed by growing fans and coiling units. Experimentally, the nano‐kirigami structures with different fractals are manipulated by using the capillary force‐induced 3D deformation process. Benefited from the fractal‐like designs, the structral deformations exhibit strong fractal dependence, with which the stress threshold and reflection spectrum can be tailored by changing the number of fans and coiling units. The modulation of fractal nano‐kirigami is further demonstrated by using the electrostatic forces when external voltage is applied. The fractal nano‐kirigami structures are also envisioned with capability of conveniently generating fractal‐dependent optical vortices. The special fractal design strategy in this work can bring new opportunities to functional 3D micro/nano structures with improved optical tunability and customization.

Fractal interwoven resonator based penta-band metamaterial absorbers for THz sensing and imaging

This paper presents a unique penta-band metamaterial absorber platform for terahertz imaging systems.The proposed fractal metamaterial absorber (FMMA) consists of fractal triangle section metasurfaces. By combining fractal resonators posing different operation skills in the same unit cell, the absorber shows multiband spectral response. The proposed unit cell structure operates at five near perfect absorption modes corresponding to the frequency bands of 1.1 THz, 3.4 THz, 4.9 THz, 5.9 THz, and 7.8 THz, respectively. Based on the fractal metamaterial absorber array, we also propose a sensing pixel design for bimaterial cantilever array sensing systems. The single pixel assembles 4x6 fractal resonator array and SiO_2-Al bimaterial microcantilevers. The sensing region of the FMMA pixel can bend the bimaterial cantilevers effectively at multiple modes, enhancing the imaging capacity. The effective medium theory is executed to visualize the constitute parameters during the absorption and reveal the origin of the rising modes. The absorption mechanism is also discussed based on the surface current distributions and electric field profiles. The numerical outcomes prove that the proposed fractal metamaterial unit cell is a promising candidate as an absorbing platform for THz band sensing and imaging applications. The derived iterative formula used in the fractal design procedure is explained for further investigations of microelectromechanical systems (MEMS) compatible compact absorber arrays.

Multiple Slot Fractal Structured Antenna for Wi-Fi and Radio Altimeter for uncertain Applications

A multiple slot fractal antenna design has been determined communication efficiency and its multi-function activities. High-speed small communication devices have been required for future smart chip applications, so that researchers have been employed new and creative antenna design. Antennas are key part in communication systems, those are used to improve communication parameters like gain, efficiency, and bandwidth. Consistently, modern antennas design with high bandwidth and gain balancing is very difficult, therefore an adaptive antenna array chip design is required. In this research work a coaxial fed antenna with fractal geometry design has been implemented for Wi-Fi and Radio altimeter application. The fractal geometry has been taken with multiple numbers of slots in the radiating structure for uncertain applications. The coaxial feeding location has been selected based on the good impedance matching condition (50 Ohms). The overall dimension mentioned for antenna are approximately 50X50X1.6 mm on FR4 substrate and performance characteristic analysis is performed with change in substrate material presented in this work. Dual-band resonant frequency is being emitted by the antenna with resonance at 3.1 and 4.3 GHz for FR4 substrate material and change in the resonant bands is obtained with change in substrate. The proposed Antenna is prototyped on Anritsu VNA tool and presented the comparative analysis like VSWR 12%, reflection coefficient 9.4%,3D-Gain 6.2% and surface current 9.3% had been improved.

The Promotion Effect of Computer-Aided Technology Combined with RBF Neural Network Algorithm on Art Design

In order to improve the effect of fractal art pattern design, this study combines RBF neural network algorithm to design and evaluate CAD fractal art pattern to improve the effect of fractal art pattern design. Moreover, this study proposes a dynamic weight-based NSC method. Because noise is ubiquitous in reality, the evolution of system dynamics often cannot be carried out strictly according to the iterative rules. In addition, this study shows the changing rules of the competition relationship and the distribution of competitors under the interference of noise. Finally, this study controls the style of the art pattern design in the spatial domain and uses the mask image pattern to disguise the art style. The experimental study shows that the CAD fractal art pattern design system based on the RBF neural network algorithm proposed in this study has a good effect on fractal art pattern design.

Direct electrohydrodynamic printing of aqueous silver nanowires ink on hydrophobic substrates for flexible and stretchable electronics

Stretchable conductors based on metal nanowires, such as silver nanowires (AgNWs), are essential for the fabrication of stretchable electronics. Electrohydrodynamic (EHD) printing has been developed as a promising technique for patterning various conductive nanomaterials on stretchable substrates. However, the printing performance is adversely affected by poor wettability of the ink on the surface of the stretchable substrates, which are mostly low-surface-energy elastomeric polymers, like polydimethylsiloxane (PDMS). The surface treatments of the substrate surface could improve the printability of the ink on these substrates, but also impose many limitations, as the surface treatment could unfavorably affect the mechanical properties of the polymer and may cause damage to the underlying layer or other existing features on the substrate. The paper investigates EHD direct printing of aqueous AgNWs ink on untreated PDMS using surfactant (i.e., Capstone FS30) modified ink for the fabrication of stretchable electronics. The static contact angles at the different FS30 ratios were measured to analyze their effect on regulating the ink wettability. A set of printing experiments were performance to select the right ink composition to tailor and optimize the ink printability and printing performance. The morphology and electrical properties of printed AgNWs-based conductors can be controlled by selecting different the EHD printing speed. Furthermore, to illustrate the potential for reliable EHD direct printing of AgNWs for stretchable electronics, a wearable electronic patch with a fractal design of the AgNWs pattern was printed on an untreated PDMS substrate using the surfactant modified AgNWs ink, which provides stable electronic response under the bending, tension and compression.

Cognitive Computing for Multimodal Sentiment Sensing and Emotion Recognition Fusion Based on Machine Learning Techniques Implemented by Computer Interface System

A multiple slot fractal antenna design has been determined communication efficiency and its multi-function activities. High-speed small communication devices have been required for future smart chip applications, so that researchers have been employed new and creative antenna design. Antennas are key part in communication systems, those are used to improve communication parameters like gain, efficiency, and bandwidth. Consistently, modern antennas design with high bandwidth and gain balancing is very difficult, therefore an adaptive antenna array chip design is required. In this research work a coaxial fed antenna with fractal geometry design has been implemented for Wi-Fi and Radio altimeter application. The fractal geometry has been taken with multiple numbers of slots in the radiating structure for uncertain applications. The coaxial feeding location has been selected based on the good impedance matching condition (50 Ohms). The overall dimension mentioned for antenna are approximately 50X50X1.6 mm on FR4 substrate and performance characteristic analysis is performed with change in substrate material presented in this work. Dual-band resonant frequency is being emitted by the antenna with resonance at 3.1 and 4.3 GHz for FR4 substrate material and change in the resonant bands is obtained with change in substrate. The proposed Antenna is prototyped on Anritsu VNA tool and presented the comparative analysis like VSWR 12%, reflection coefficient 9.4%,3D-Gain 6.2% and surface current 9.3% had been improved.

A Double Random Matrix Design Model for Fractal Art Patterns Based on Visual Characteristics

This paper adopts the method of visual characteristics of the double random matrix to conduct in-depth research and analysis on the design of fractal art patterns. For the practical application needs in fractal graphic design, a method is proposed to automatically extract the core base pattern based on fractal graphic content and generate a four-sided continuous pattern. The method first uses the Canny operator for edge detection to analyze the area of the main pattern. Then, it uses a grayscale cogeneration matrix to extract and analyze the graphic texture features, based on which the best splicing method is selected to splice the extracted pattern, and then, it achieves two splicing methods of flat row and staggered four-sided continuous pattern. The method has good practicality with low complexity and high versatility under the premise of ensuring the beauty of the generated four-sided continuous pattern. It can assist designers to design patterns, improve efficiency, and save design costs. In this paper, we improve the existing image segmentation methods, adopt two segmentation methods, namely quadratic tree segmentation and HV segmentation, propose a new local codebook selection strategy, and study the degree of self-adaptation of different methods to images in terms of segmentation methods and local codebook selection strategies. It makes the network unable to train efficiently on long text prediction problems. Finally, the improved algorithm of this paper is tested on the standard and living image libraries, and the experimental results show that the use of local codebooks makes the image coding speed significantly improved compared with the fixed fractal. In the face of the image to be retrieved, it is only necessary to perform the coding operation to obtain the fractal code to perform similarity matching, which can meet the requirement of real-time retrieval. Applying the improved distance formula, the search accuracy obtained on the test gallery is significantly better than that of the grayscale histogram algorithm.

Fractals and resistors run in parallel in the classroom

Using fractal design to learn about both resistor networks and fractional dimensions

2.5 GHz to 3.5 GHz fractal metasurface microstrip antenna design for high bandwidth wireless applications

In this paper, the microstrip slot antenna is designed for a wireless application with fractal structure having 2.5 - 3.5 GHz coverage and 30% bandwidth. The circular slot antenna with seven triangular slots is considered and six single rings are added to the antenna. As a last step, the enhancement of the matching is produced by a disk located the central part of the slot. The fractal model improves the bandwidth, modifies the antenna matching and controls the current distribution in such a way that it is used in the S (short) band in our case for WiMAX technology, which allows wireless transmission of voice, data and video in areas of up to 48 km radius. It was projected as a wireless alternative to ADSL and cable broadband access, and a way to connect Wi-Fi nodes in a metropolitan area network. The antenna gain is about 19.37 dB with a compact size of 60 × 60 mm2. The metasurface structure helps us to improve the bandwidth. The antenna was simulated with Ansoft Designer V.3.5. The antenna is designed in FR4 as the most suitable material as well as being low cost and accessible. It is proved that the fractal shape is used to improve the bandwidth. The result of combining the metasurface with the antenna can be considered to improve the bandwidth

A numerical comprehensive evaluation of a micro-type plate autothermal methanol steam reformer with different channel configurations

Hydrogen production from methanol steam reforming (MSR) is one of the solutions of mobile hydrogen source for fuel cell. In this paper, a three-dimensional numerical model of a micro-type plate autothermal methanol steam reformer with different channel configurations is established. The effects of the Point-Grow-Naturally (PGN), Point-To-Line (PTL) and Point-To-Circle (PTC) fractal channel designs and operation conditions on the heat and mass transport between the combustion chamber and catalytic chamber are investigated and compared with parallel channels. The results show that the existence of branches enhance the mixing effect of reactants, but increases the pressure drop at the same time. When the branch ratio and the branch number satisfy the mathematical relationship nβ>1, the fractal channel can be equivalent to a gradually expanding channel, which is conducive to MSR in the direction of volume increase. In all configurations, PTC has more uniform temperature distribution, better heat transfer performance, low pump power consumption and higher methanol conversion.

Fractal Art Pattern Information System Based on Genetic Algorithm

In order to solve the problem of fractal art pattern innovative design in specific fields, this paper proposes a new method of fractal technology and visualization technology based on genetic algorithm to support art pattern innovative design. In these models, the function of the fractal structure is represented by the binary structure, while the main function represented by the wooden structure is the function of creating new offspring. Provide high-quality services to meet customer needs faster and better. The experimental results show that after 14 generations, the force curve appears to be more stable, the weight scale is studied, and a new model is developed. At the same time, the pattern elements of interest to users are retained for genetic algorithm. Conclusion. This method can help designers quickly design fractal art patterns appreciated by users.

Crossover behavior for a periodic chaotic model in its fractal and mirror symmetrical design

Dynamical systems related to damped and driven oscillators and those with both periodic and chaotic oscillations have proven to be fascinating for many researchers around the world who are dealing with non-linear oscillatory models. Adding to theses processes, a mirror symmetrical structure can only be more captivating since their applications in sciences and engineering are widely increasing. That is why in this paper, we combine two dynamical structures, namely the mirror symmetrical structure and the fractal effect. The mirror symmetrical aspect is analyzed by inserting into the system an additional term, a quadratic function involving a duality-symmetric multi-segment. Secondly, the fractal effect is analyzed by inserting into the system the fractal–fractional operator with the power law kernel. The final model reveals the existence of the so-called fixed-point chaotic attractor involved in a self-duplication process via the mirror-fractal process. The final model is also able to generate a new type of mirror fractal dynamical process with y-oriented crossover structure and both chaotic periodic and chaotic oscillations. As we gradually change some of the model’s parameters , the lower and higher parts of the attractors are shown to be moving away from the crossover junction line due to the fractal effect. The results show another way of considering some dynamical models related to damped and driven oscillators.

Ethnomathematics and creativity study in the construction of batik based on fractal geometry aided by GeoGebra

This study aims to describe geometric objects that used by students on constructing fractal batik using Geogebra, procedure that used to construct fractal batik design, and students creativity on the process of constructing fractal batik. The qualitative descriptive research was applies including data collection, data separation, data analysis and conclusions. The research data were obtained from 97 students of tadris mathematics IAIN Kediri. The research results showed that fractal batik was constructed from a single geometric shape and combination of 2, 3, and 4 single geometric shapes through steps (a) made basic patterns using geometric shapes in Geogebra, (b) Made New Tools to perform repetitions (iteration), (c) Determined the type of transformation that used to repeat the basic patterns, and (d) Constructed geometric fractal batik. Based on the creativity indicators fluency, 3 types of geometric fractals can be obtained, namely (a) Fractals with Repetition and Enlargement (FPB), (b) Fractals with Repetition and Change Position (FPS), and (c) Fractals with Mix Repetition (FPC). Based on the flexibility indicator, there are 32 basic geometric shapes that develop basic patterns by applying 15 types of transformation consist of Single Transformation, Double Transformation, Triple Transformation and Quadruple Transformation. Meanwhile, on the originality indicator, P3 is the basic shape that has been mostly developed into geometric fractal batik which is a combination of equilateral triangles and squares.

Linear and rotational fractal design for multiwing hyperchaotic systems with triangle and square shapes

Since the German biochemist Otto Rössler proposed the first hyperchaotic model in the years 1970s and showed to the scientific community how important hyperchaos can be in describing real life phenomena, it has become necessary to develop and propose various techniques capable of generating hyperchaotic attractors with more complex dynamics applicable in both theory and practice. We propose in this paper, an innovative method with analytical and numerical aspects able to generate a class of hyperchaotic attractors with many wings and different shapes. We use a fractal operator to obtain an expression of the modified fractal-fractional Lü system, which is therefore solved numerically. After showing that the initial model is hyperchaotic, we perform some numerical simulations that prove that the hyperchaotic status of the system remain unchanged. The results show that the modified system can generate hyperchaotic attractors of types n-wings, n × m-wings, n × m × p-wings and n × m × p × r-wings (m, n, p, r ∈ ℕ), using both linear and rotational variations. It appears that the system is involved in fractal designs comprising a linear or rotational self-duplication process happening in different scales across the system and ending up with the triangular or square shape.

Damage delocalisation in skeletal muscle-inspired hierarchical armoured structures for impact protection

We propose a skeletal muscle-inspired hierarchical structure for the alumina ceramic layer in ceramic composite armour structures to achieve greater energy dissipation under impact. We mimic the nano-architecture of skeletal muscle tissues by introducing hierarchy both with self-similarity using a fractal design, and without self-similarity in the hierarchical levels to explore the function of hierarchy in improving the protective capability of the armour structure. The numerical simulations showed that increasing the structural hierarchy can boost stress reduction by up to 30% for the third order hierarchical structure without self-similarity compared to the first order hierarchical structure with the same weight. The underlying mechanism that increases the impact resistance in the higher order hierarchical structures is the delocalisation of the damage over multiple crack paths in the different hierarchical levels. This bio-inspired concept can be used to generalise the design of future impact-resilient structures which optimise the suppression of stresses and reduce the associated weight penalty for use in protective gear and armoured structures.

Fabrication and performances of silver grid transparent conducting films and heaters on glass and PET substrates based on fractal periodic grid pattern design

A metal grid transparent conducting film (TCF) requires an excellent trade-off between optical transparency and electrical conductivity, both of which are affected by grid patterns and parameters. In this work, the fractal geometry was introduced to design fractal periodic grid patterns, which were employed to fabricate fractal periodic Ag grid TCFs with different grid periods, pitches and thicknesses on glass substrates by magnetron sputtering Ag films and laser localized removal. By comparing with the corresponding conventional periodic Ag grid, the fractal periodic Ag grid was confirmed to enable a significant improvement in trade-off between optical transparency and electrical conductivity, and thus excellently improving the comprehensive properties of the TCFs. The optimal fractal periodic Ag grid TCF achieved a figure of merit of 15.04 × 10–2 Ω–1, which was higher than that of the optimal conventional periodic Ag grid TCF (11.38 × 10–2 Ω–1). In addition, transparent heaters were prepared by using the optimal fractal periodic Ag grid TCFs on glass and flexible PET substrates, and showed excellent heating performances, good performance stability and deicing availability. This work provides a simple and extendable method for tailoring optical transmittance and electrical conductivity to fabricate high-performance TCFs.

Fractal Visual Art Graphic Design Based on Computer-Aided Algorithms

Embedded machine vision algorithm development platform is of great significance. Based on the elaboration of visual communication design, this paper further details the design of fractal visual art graphics based on computer-aided algorithms to design edge detection schemes, where edges represent sudden changes in the signal and are able to characterize the rich information of an image. In response to the problems of poor robustness and difficult parameter selection of the currently widely used edge detection algorithms, the platform encapsulates joint edge detection graphic components in a higher-order processing library to achieve the requirements of high-precision detection and to realise enhanced edge detection effects. Finally, the experimental analysis shows that the proposed algorithm has a more accurate detection effect and can meet the user's high-precision detection requirements.