Fractal Architecture Research Articles

Study on Sensing Urine Concentrations in Water Using a Microwave Sensor Based on Hilbert Structure.

In this study, a two-port network-based microwave sensor for liquid characterization is presented. The suggested sensor is built as a miniature microwave resonator using the third iteration of Hilbert's fractal architecture. The suggested structure is used with the T-resonator to raise the sensor quality factor. The suggested sensor is printed on a FR4 substrate and has a footprint of 40×60×1.6mm3. Analytically, a theoretical investigation is made to clarify how the suggested sensor might function. The suggested sensor is created and put to the test in an experiment. Later, two pans to contain the urine Sample Under Test (SUT) are printed on the sensor. Before loading the SUT, it is discovered that the suggested structure's frequency resonance is 0.46 GHz. An 18 MHz frequency shift is added to the initial resonance after the pans are printed. They monitor the S-parameters in terms of S12 regarding the change in water content in the urine samples, allowing for the sensing component to be completed. As a result, 10 different samples with varying urine percentages are added to the suggested sensor to evaluate its ability to detect the presence of urine. Finally, it is discovered that the suggested process' measurements and corresponding simulated outcomes agreed quite well.

Fractal penis and golden penis. The hidden dimensions of penile tissue

The penis is an organ with a unique and complex structure. It is formed by a fractal architecture, meaning its design is based on highly complex repetitive patterns. In addition, its dimensions follow what are known as "golden proportions", also known as "the divine proportion". These proportions are a mathematical relationship that is found in many natural structures and, in the case of the penis, provide stability and improve its performance. This design is not the result of chance, but rather the result of an underlying mathematical message. Fractal geometry, based on complex numbers, is a key tool in understanding the internal structure of the penis, which cannot be described using traditional Euclidean geometry. In addition to fractal geometry, the presence of golden proportions in the penis suggests that its design is influenced by mathematics. To fully understand this relationship, additional studies are required and the creation of innovative mathematical models that include tools such as artificial intelligence. In conclusion, the penis is an example of how mathematics and nature are closely related and how mathematical complexity can improve the functioning of natural structures.

Fractal Electronics for Stimulating and Sensing Neural Networks: Enhanced Electrical, Optical, and Cell Interaction Properties.

Imagine a world in which damaged parts of the body - an arm, an eye, and ultimately a region of the brain - can be replaced by artificial implants capable of restoring or even enhancing human performance. The associated improvements in the quality of human life would revolutionize the medical world and produce sweeping changes across society. In this chapter, we discuss several approaches to the fabrication of fractal electronics designed to interface with neural networks. We consider two fundamental functions - stimulating electrical signals in the neural networks and sensing the location of the signals as they pass through the network. Using experiments and simulations, we discuss the favorable electrical performances that arise from adopting fractal rather than traditional Euclidean architectures. We also demonstrate how the fractal architecture induces favorable physical interactions with the cells they interact with, including the ability to direct the growth of neurons and glia to specific regions of the neural-electronic interface.

Fractal Architecture of the Universe Based on Primary-Centric World-View - A Post Copernican Conjecture

This paper investigates the fractal architecture of our Universe based on Primary-Centric Theoretical Formulation. Through theoretical analysis of Earth-Moon System, I arrived at the planetary satellite dynamics which was found to apply equally well to Solar and Exo-solar systems. This gave the theoretical foundation of the New Perspective of the birth and evolution of Exo-solar Systems. This was further extended to the theoretical analysis of star pairs and Neutron-Star pairs. This laid down the Primarycentric World View which I postulate as the physical process which has been shaping the evolution of the Universe and the hot-spots of the Cosmic Microwave Background Radiation right from 380,000 yrs after the Big Bang to date in top-down model resulting into Super-clusters, Clusters, Galaxies and Solar Systems. Primary-centric analysis corresponds to keplerian Analysis for negligibly small mass ratio less than 0.001. In the Copernican Framework, Kepler’s Third Law places no restriction on the orbit of the secondary component in a celestial pair. In Primary Centric Framework there is a very definite constraint on the permitted stable orbit, introduced due to periodic tidal deformations . There are two Clarke’s Orbits which are fully circularized and synchronized and hence nondissipative and equilibrium orbits called inner and outer Clarke's orbits equivalent to two geosynchronous orbits in Earth-Moon scenario. Outer Clarke’s Orbit is permissible as a stable orbit if the mass ratio of secondary to primary is greater than 0.2, Inner Clarke’s Orbit is permissible if mass ratio is less than 10-4 . If the mass ratio is between 10-4 to 0.2 then secondary spirals-out from inner Clarke’s Orbit to outer Clarke’s Orbit if it tumbles into super-synchronous orbit and spirals-in if it tumbles into sub-synchronous orbit destined to be destroyed by the primary. My conjecture states that every cosmological sub-system has a Monarch (or dominant) Primary (M_primary) Component anchoring the given sub-system and this Primary decides the stable equilibrium orbits of the secondary/secondaries. Planet-Satellite has a Planet as the M_primary, Solar System and exo-Solar Systems have a planet hosting star (PHS) as the M_primary, Galaxy has a Super-Massive Black Hole(SMBH) as the M_primary, Cluster has a cD galaxy (central dominant Galaxy) which is also known as Brightest Cluster Galaxy(BCG) as the M_primary, Super-Cluster has a massive Cluster hosting a QUASER/Blazer as the M_primary. This goes adinfinitum until a Cosmic Web is woven with Cosmic filaments. This conjecture gains a definite credence after the recent discoveries of the over-massive Black Holes in M_Galaxies namely Messier 87 in Virgo Cluster, NGC 3842 in Leo Cluster, NGC 4889 in Coma Cluster[68] and NGC 1277 in Perseus Cluster[66] which had been proposed as M_Galaxies on general considerations even before the confirmation of over-massive black holes. In 2011, a group of floating planets have been discovered. This is a transitory event and is an exception to this conjecture.

Acoustic transmission loss in Hilbert fractal metamaterials

Acoustic metamaterials are increasingly being considered as a viable technology for sound insulation. Fractal patterns constitute a potentially groundbreaking architecture for acoustic metamaterials. We describe in this work the behaviour of the transmission loss of Hilbert fractal metamaterials used for sound control purposes. The transmission loss of 3D printed metamaterials with Hilbert fractal patterns related to configurations from the zeroth to the fourth order is investigated here using impedance tube tests and Finite Element models. We evaluate, in particular, the impact of the equivalent porosity and the relative size of the cavity of the fractal pattern versus the overall dimensions of the metamaterial unit. We also provide an analytical formulation that relates the acoustic cavity resonances in the fractal patterns and the frequencies associated with the maxima of the transmission losses, providing opportunities to tune the sound insulation properties through control of the fractal architecture.

Experimental and Numerical Studies on the Hilbert Fractal Architecture as an Acoustic Metamaterial

Experiments and numerical methods were used to investigate the key parameters which affect the transmission loss behaviour of Hilbert fractal acoustic metamaterials. The tests were conducted using a four-microphone impedance tube, and the numerical simulation was performed using COMSOL Multiphysics software. Fractal order and cavity slot widths on Hilbert fractal metamaterials were investigated. 3D printing manufacturing techniques were used to make polylactic acid specimens. The COMSOL model developed utilised thermo-viscous and lossless domains with boundary layer mesh in the fractal cavities. The tests and simulations' frequency range were 0.2 kHz to 3.0 kHz, with parametric gap widths ranging from 0.5 mm to 3.0 mm. There is a reasonable agreement between the numerical models and the experimental results; the second-order Hilbert fractal had the most significant effect on transmission loss, with an experimental peak of nearly 50 dB around 1600 Hz. Moreover, multiple transmission loss peaks were observed as a function of the gap width in the five Hilbert fractal orders studied. The gap width is one of the critical parameters for optimising the performance of the Hilbert fractal as an acoustic metamaterial.

A self-similar sine-cosine fractal architecture for multiport interferometers.

Multiport interferometers based on integrated beamsplitter meshes have recently captured interest as a platform for many emerging technologies. In this paper, we present a novel architecture for multiport interferometers based on the sine-cosine fractal decomposition of a unitary matrix. Our architecture is unique in that it is self-similar, enabling the construction of modular multi-chiplet devices. Due to this modularity, our design enjoys improved resilience to hardware imperfections as compared to conventional multiport interferometers. Additionally, the structure of our circuit enables systematic truncation, which is key in reducing the hardware footprint of the chip as well as compute time in training optical neural networks, while maintaining full connectivity. Numerical simulations show that truncation of these meshes gives robust performance even under large fabrication errors. This design is a step forward in the construction of large-scale programmable photonics, removing a major hurdle in scaling up to practical machine learning and quantum computing applications.

Ractal structures in architectural design

The high rate of urbanization in the modern world requires a conscious approach to architectural design. A person needs an environment that fills him with new strength and does not drown out his creative potential with monotonous routine. Due to its natural feature, fractal architecture meets these requirements. The article examines the signs of fractal systems in relation to architecture, highlights the concept - "the principle of fragmentation of a fractal", the term "self-similarity" is broader. In addition, the existing experience of fractal architecture has been analyzed, and the relationship between fractality and the success of the project has been revealed using the example of existing objects. The materials of this article can serve for the further development of the theory of creating fractal architecture.

Decorated fractal Ni-Cu foam with Pd nanoparticles as a high-performance electrocatalyst toward hydrogen evolution reaction

• The Ni-Cu foam was decorated with Pd nanoparticles by galvanic replacement method. • The Tafel slope of Ni-Cu/Pd is 72 mV dec −1 which is 94 mV dec −1 less than substrate. • The fractal architecture of Ni-Cu/Pd provided a high surface area (112.5 cm 2 ). • Ni-Cu/Pd requires 134 mV overpotential at the current density of 10 mA cm −2 . Fractal Ni-Cu foam with palladium nanoparticles on (Ni-Cu foam / Pd) was prepared by electrodeposition and galvanic replacement method. The results showed that after the fabrication of Pd particles on Ni-Cu foam, the hydrogen evolution reaction (HER) activity of the electrode improved dramatically. The morphology and phase structure of deposited layers were studied by field emission scanning electron microscopy, and X-ray diffraction methods, respectively. In order to investigate the morphology of the coatings in more details, transmission electron microscope was used, which its figures authenticated the presence of Pd nanoparticles on the fractal structures of Ni-Cu. Based on the electrochemical tests in KOH (1.0 M), the Ni-Cu foam / Pd electrode has good electrocatalytic properties, with a low overpotential of 134 mV at 10 mA cm −2 and Tafel slope of 72 mV dec −1 . Cyclic voltammetry measurements showed that the Ni-Cu foam/Pd possesses a high electrochemical surface area of 112.5 cm 2 that was attributed to the presence of both fractal Ni-Cu foam and Pd nanoparticles. Overall, this study proposes a feasible approach for the fabrication of a highly-porous, super hydrophilic, and scalable electrode with a great performance toward HER.

Halogen Bonded Chiral Emitters: Generation of Chiral Fractal Architecture with Amplified Circularly Polarized Luminescence

AbstractSelf‐assembled chiroptical materials have attracted considerable attention due to their great applications in wide fields. During the chiral self‐assembly, it remains unknown how achiral molecules can affect the assembly process and their final chiroptical performance. Herein, we report an achiral molecule directed chiral self‐assembly via halogen bonds, exhibiting not only an unprecedented chiral fractal architecture but also significantly amplified circularly polarized luminescence (CPL). Two axially chiral emitters with halogen bond sites co‐assemble with an achiral 1,4‐diiodotetrafluorobenzene (F4DIB) and well‐ordered chiral fractal structures with asymmetry amplification are obtained. The enhancement of the dissymmetry factors of the assemblies was up to 0.051 and 0.011, which was approximately 100 folds than those of the corresponding molecules. It was found that both the design of the chiral emitter and the highly directional halogen bond played an important role in hierarchically chirality transfer from chiral emitters to the micrometer scale chiral fractal morphology and amplified dissymmetry factors. We hope that this strategy can give a further insight into the fabrication of structurally unique featured highly efficient chiroptical materials.

Halogen Bonded Chiral Emitters: Generation of Chiral Fractal Architecture with Amplified Circularly Polarized Luminescence.

Self-assembled chiroptical materials have attracted considerable attention due to their great applications in wide fields. During the chiral self-assembly, it remains unknown how achiral molecules can affect the assembly process and their final chiroptical performance. Herein, we report an achiral molecule directed chiral self-assembly via halogen bonds, exhibiting not only an unprecedented chiral fractal architecture but also significantly amplified circularly polarized luminescence (CPL). Two axially chiral emitters with halogen bond sites co-assemble with an achiral 1,4-diiodotetrafluorobenzene (F4 DIB) and well-ordered chiral fractal structures with asymmetry amplification are obtained. The enhancement of the dissymmetry factors of the assemblies was up to 0.051 and 0.011, which was approximately 100 folds than those of the corresponding molecules. It was found that both the design of the chiral emitter and the highly directional halogen bond played an important role in hierarchically chirality transfer from chiral emitters to the micrometer scale chiral fractal morphology and amplified dissymmetry factors. We hope that this strategy can give a further insight into the fabrication of structurally unique featured highly efficient chiroptical materials.

Cell Mechanics and Signalization: SARS-CoV-2 Hijacks Membrane Liquid Crystals and Cytoskeletal Fractal Topology

We highlight changes to cell signaling under virus invasion (with the example of SARS-CoV-2), involving disturbance of membranes (plasma, mitochondrial, endothelial-alveolar) and of nanodomains, modulated by the cytoskeleton. Virus alters the mechanical properties of the membranes, impairing mesophase structures mediated by the fractal architecture initiated by actomyosin. It changes the topology of the membrane and its lipid composition distribution. Mechano-transduction, self-organization and topology far from equilibrium are omnipresent. We propose that the actomyosin contractility generates the cytoskeletons fractal organization. We focus on three membranar processus: The transition from lamellar configuration in cell and viral membranes to a bi-continuous organization in the presence of ethanolamine (the energy for this transition is provided by change of the folding of the viral fusion protein from metastable to stable state). The action of mitochondrial antiviral signaling protein on the external mitochondrial envelope in contact with mitochondrial-associated membranes, modified by viral endoribonuclease, distorting innate immune response. The increased permeability of the epithelial-alveolar-pulmonary barrier involves the cytoskeleton membranes. The pulmonary surfactant is also perturbed in its liquid crystal state. Viral subversion disorganizes membrane structure and functions and thus the metabolism of the cell. We advocate systematic multidisciplinary exploration of membrane mesophases and their links with fractal dynamics, to enable novel therapies for SARS-CoV-2 infection.

A quint mode fractal architecture based resonator and its efficacy in the design of multiband bandpass filters

This paper presents a new approach to design multiband bandpass filters (BPF) using multimode resonator topology inspired from Bamileke fractal architecture in the form of fractal shaped resonator. The proposed resonator architecture exhibits quint mode resonance behavior where resonance frequencies are determined using ABCD matrix. It offers flexibility in terms of choosing passband center frequencies precisely. Initially a second order dual band BPF is presented by suppressing higher order modes using asymmetric feed line. The same structure is used further to implement a triband and a quad band BPF where the input/output coupling circuit is modified to extract the higher order modes. Two stub loaded resonators are also embedded to improve the passband selectivity and to improve upper stopband characteristics. The design guidelines are demonstrated through the external quality factor (Qe) and coupling coefficient (k) synthesis approach. The developed filters are fabricated and measured to verify the predicted and simulated results. A close agreement is observed between them. The fabricated multiband BPFs has a very compact size, less insertion loss and good return loss profile.

Spatial architecture of biliary tree in mammals: Fractal and Euclidean geometric features.

The study of the fractal architecture of various organs and structures expanded the possibilities for determining the ranges of their functioning and structural arrangement, which, as a result, was reflected in the development of new approaches to diagnostics and therapeutic impacts. The architecture of the excretory duct systems, similar to the hemo- and lymph- circulatory beds and the bronchial tree, is considered fractal. At the same time, information about hitherto unknown structures of the biliary tree continues to appear in the literature. We aimed to study the features of the spatial geometry of the biliary tree and assess the significance of both its fractal and Euclidean characteristics for the development of approaches that facilitate comprehensive description of intrahepatic biliary tract architecture. We investigated the architecture of the biliary trees of six men, seven male canines, and seven male Wistar rats using the corrosion casting method. Corrosion casts were prepared by injecting solidifying latexes into the bile ducts. The preparations were studied using a light stereomicroscope and a scanning electron microscope. Biliary tree branching is of various types. In addition, the correlation between variations in the caliber and length of the bile ducts and their order is not significant. Therefore, the biliary tree should not be considered as a classical fractal and it consists of the main modules, represented by the network of the bile canaliculi (first nonfractal module) and a biliary tree with a fractal branching (second module) that drains the bile canaliculi mesh and the additional modules represented by the mucosal biliary glands (in mammals with the gallbladder) or the periportal biliary plexus (in mammals without a gallbladder) and the aberrant biliary ducts. Such a configuration of the biliary bed should optimally ensure the smooth implementation of the physiological function of the liver, as well as its adaptation to different pathologies accompanied by biliary hypertension. It also might be considered in the diagnosis and assessment of ductular reaction, biliary regeneration, and/or carcinogenesis.

Investigation of the volumetric fractal structure shaping

On the basis of a specially developed algorithm, shaping of the fractal structures, the formation of which is regulated by the power index of the fractal, has been carried out. A sphere and an ellipsoid were used as the basic shapes. The formation analysis has made it possible to determine the characteristic principles of the fractal structure growth. The performed numerical experiment with respect to volumetric fractal structures of power 8 made it possible to determine the spectrum of frequencies and forms of natural oscillations. The offered objects of fractal architecture are analogs of unique high-rise and large-span buildings and structures. The application of the fractal shaping paradigm in combination with digital technologies and innovative materials will make it possible to create completely new objects of architecture.

Фрактальная архитектура: прошлое, настоящее и будущее

Architects of the past widely used the principle of fractal structure. Building designs are separate elements that are self-similar objects. The article presents examples of various unique structures of the past and present. The modern approach to the development of fractal architecture allows architects to create wonderful structures, search for the most unusual forms and harmony of orderly structures and dynamics of chaos.

Visual and Structural Analysis of Fractal Geometry in the Sheikh Lotfollah Mosque Ornaments (Isfahan-Iran)

The Islamic era is the period of new s‌tyles and beyond its own time. Shamsa, Muqarnas, S‌tar, geometric motifs, and decorative elements have fractal nature, which was used as a tool to express the architect’s idea by repeating the same components in a spatial dimension. We will reach the effect of Islamic impacts on fractal architecture and semantic cognition, and by finding the roots of theories about fractal with an analytical-descriptive approach, we will unders‌tand the relationship between fractals and how they are used by architects. Our focus is on comprehensive s‌tudy and calculation, not only in ornaments but also in s‌tructure, to find patterns of fractal form, to represent coordination between components. Firs‌t, we proved and extracted the fractal properties and patterns between the cons‌tituent elements, including self-similarity, repeatability, small-scale, and non-integer dimension, using visual analysis, and then we set up the Box-counting analysis technique with two purposes of calculating fractal dimension and finding their relationship. Aware of the mathematical proportions and relationships between the components of nature, the architect of the Sheikh Lotfollah Mosque has displayed the geometric sequence limit with an ascending equation in the interior ornaments of the dome. His goal is both to create the world of spirituality on a micro-scale and make it unders‌tandable for an observer. Thus, in this way, he has sometimes expressed his concept through mathematics, proportions, and sometimes by showing beliefs in concepts such as unity in diversity, all of which in their essence have concepts consis‌tent with fractal forms.

Photonic Fractal Metamaterials: A Metal–Semiconductor Platform with Enhanced Volatile‐Compound Sensing Performance

Advance of photonics media is restrained by the lack of structuring techniques for the 3D fabrication of active materials with long-range periodicity. A methodology is reported for the engineering of tunable resonant photonic media with thickness exceeding the plasmonic near-field enhancement region by more than two orders of magnitude. The media architecture consists of a stochastically ordered distribution of plasmonic nanocrystals in a fractal scaffold of high-index semiconductors. This plasmonic-semiconductor fractal media supports the propagation of surface plasmons with drastically enhanced intensity over multiple length scales, overcoming the 2D limitations of established metasurface technologies. The fractal media are used for the fabrication of plasmonic optical gas sensors, achieving a limit of detection of 0.01 vol% at room temperature and sensitivity up to 1.9nm vol%-1 , demonstrating almost a fivefold increase with respect to an optimized planar geometry. Beneficially to their implementation, the self-assembly mechanism of this fractal architecture allows fabrication of micrometer-thick media over surfaces of several square centimeters in a few seconds. The designable optical features and intrinsic scalability of these photonic fractal metamaterials provide ample opportunities for applications, bridging across transformation optics, sensing, and light harvesting.

Complex model of fractal architecture building

The fractal structures paradigm is applicable for creating the complex architectural objects. Using special programs, it is possible to implement a comprehensive model of the fractal architecture building as a structure consisting of an endostructure and an exostructure. During the study, the first two iterations of the endostructure on the possibility of using such structures’ element as a supporting skeleton of a fractal architecture building were considered. The endostructure elements of the first iteration strengthen the exobase and the lower surface of the f-quarks of the exostructure. The endostructure of the second iteration is much more complex and voluminous than the structure of the first iteration and strengthens the upper part of the exostructure. To ensure the stability of the fractal architecture building, the framework is formed by connecting the elements of the endostructures of the first and second iteration. Based on the fractal structures’ formation analysis results, the unique building stiffness cores formed from the f-quarks exobase have been developed. The strength and rigidity of the building is ensured by the combined action of the endostructure’s elements, the exostructure’s elements and the developed stiffness cores. Comprehensive building model was implemented in ANSYS PC. According to the numerical experiments’ results, the maximum displacements, shapes and frequencies of the fractal architecture object’s natural vibrations are determined. The proposed design solutions for a complex model of a building based on a fractal structure are unique and require the use of innovative technologies and materials.

A Self-Operating Time Crystal Model of the Human Brain: Can We Replace Entire Brain Hardware with a 3D Fractal Architecture of Clocks Alone?

Time crystal was conceived in the 1970s as an autonomous engine made of only clocks to explain the life-like features of a virus. Later, time crystal was extended to living cells like neurons. The brain controls most biological clocks that regenerate the living cells continuously. Most cognitive tasks and learning in the brain run by periodic clock-like oscillations. Can we integrate all cognitive tasks in terms of running clocks of the hardware? Since the existing concept of time crystal has only one clock with a singularity point, we generalize the basic idea of time crystal so that we could bond many clocks in a 3D architecture. Harvesting inside phase singularity is the key. Since clocks reset continuously in the brain–body system, during reset, other clocks take over. So, we insert clock architecture inside singularity resembling brain components bottom-up and top-down. Instead of one clock, the time crystal turns to a composite, so it is poly-time crystal. We used century-old research on brain rhythms to compile the first hardware-free pure clock reconstruction of the human brain. Similar to the global effort on connectome, a spatial reconstruction of the brain, we advocate a global effort for more intricate mapping of all brain clocks, to fill missing links with respect to the brain’s temporal map. Once made, reverse engineering the brain would remain a mere engineering challenge.