[6], Analytically, many fractals are nowhere differentiable. However, we do not guarantee individual replies due to the high volume of messages. Fractal Programming did not just happen. Therefore, FPM cannot be programmed to be scale-dependent by definition. Likewise, if the radius of a filled sphere is doubled, its volume scales by eight, which is two (the ratio of the new to the old radius) to the power of three (the conventional dimension of the filled sphere). Here is a small set of applications that illustrates lateral computing: Above is a review of lateral-computing techniques. Ozhovan M. I., Dmitriev I. E., Batyukhnova O. G. Fractal structure of pores of clay soil. Language links are at the top of the page across from the title. It creates a provisional arrangement of information. Truck backup problem: This is an interesting problem of reversing a truck and parking it at a particular location. use of probabilistic graphical model such as Bayesian network. A fractal pattern changes with the scale at which it is measured. A fractal is a never-ending pattern. Fractal Programming is transformative because it moves decimal points. DOI: 10.34133/2022/9797623. Fractals are complex patterns that are self-similar, and therefore exhibit similar patterns at every scale. [71] Nerve cells function through processes at the cell surface, with phenomena that are enhanced by largely increasing the surface to volume ratio. This is a question often asked of the Fractal team. Please select the most appropriate category to facilitate processing of your request. Then several lateral-computing techniques have been described followed by their applications. Dedicated ML computers are thus being developed at various scales, but their productivity is somewhat limited: the workload and development cost are largely concentrated in their software stacks, which need to be developed or reworked on an ad hoc basis to support every scaled model. The patterns are formed by sublimation of frozen CO2. But he is best known for his cube-like fractal known as a "sponge". But in measuring an infinitely "wiggly" fractal curve such as the Koch snowflake, one would never find a small enough straight segment to conform to the curve, because the jagged pattern would always re-appear, at arbitrarily small scales, essentially pulling a little more of the tape measure into the total length measured each time one attempted to fit it tighter and tighter to the curve. or, by Intelligent Computing. Define fractal. Fractal Technology Fractal Disrupts The Equation Of Computing For what seems eons, technologists have been trying to get complex apps built in time to impact the business. The processor is only aware of its parent component and child components, but not the global system specification." So fractals are a sort of strange kind of shape that have detail at all different levels. A simple problem of truck backup can be used for illustrating lateral-computing[clarification needed]. [85] When humans view fractal patterns with D values between 1.3 and 1.5, this tends to reduce physiological stress. [30], The term "fractal" was coined by the mathematician Benot Mandelbrot in 1975. So DNA is part of a highly complex natural computing system. By 1918, two French mathematicians, Pierre Fatou and Gaston Julia, though working independently, arrived essentially simultaneously at results describing what is now seen as fractal behaviour associated with mapping complex numbers and iterative functions and leading to further ideas about attractors and repellors (i.e., points that attract or repel other points), which have become very important in the study of fractals. Mixing: Turbulence ensures that two adjacent points in a complex system will eventually end up in very different positions after some time has elapsed. The time savings was, well, this app was finished before the contract was completed. K. Compton and S. Hauck (2002); Reconfigurable Computing: A survey of Systems and Software, ACM Computing Surveys, Vo. [1][5][2][4][42], One point agreed on is that fractal patterns are characterized by fractal dimensions, but whereas these numbers quantify complexity (i.e., changing detail with changing scale), they neither uniquely describe nor specify details of how to construct particular fractal patterns. Fractal von Neumann architecture (FvNA) is proposed to address the programming productivity issue for ML computers. From lateral-thinking to lateral-computing, Learn how and when to remove this template message, Special Issue on Industrial Innovations Using Soft Computing, Fuzzy Logic With Engineering Applications, Energy Aware Computing through Probabilistic Switching: A study of limits, Godel, Escher, Bach: An Eternal Golden Braid, Learning to Classify Text using Support Vector Machines, https://en.wikipedia.org/w/index.php?title=Lateral_computing&oldid=1145173808, Wikipedia articles in need of updating from August 2017, All Wikipedia articles in need of updating, Wikipedia articles needing clarification from July 2009, Articles with unsourced statements from July 2009, Wikipedia articles with style issues from July 2009, Articles with unsourced statements from October 2009, Creative Commons Attribution-ShareAlike License 4.0, How slow cooling of the hot gaseous state results in pure crystals (, How simple insects such as ants and honeybees solve some sophisticated problems, How living organisms defend themselves against diseases and heal their wounds. "The lower layer is fully controlled by the higher layer, thus, only the top layer is exposed to the programmer as a monolithic processor. [1]:166, One of the next milestones came in 1904, when Helge von Koch, extending ideas of Poincar and dissatisfied with Weierstrass's abstract and analytic definition, gave a more geometric definition including hand-drawn images of a similar function, which is now called the Koch snowflake. Fractal Programming recognizes the complexity of current app development is mostly from current system design constraints. Lateral computing is a fuzzy set of all computing techniques which use unconventional computing approach. [1], The history of fractals traces a path from chiefly theoretical studies to modern applications in computer graphics, with several notable people contributing canonical fractal forms along the way. C is a constant. Jyh-Shing Roger Jang, Chuen-Tsai Sun & Eiji Mizutani (1997); Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice Hall Publishers. The number of required lab operations using DNA grows linearly with the number of vertices of the graph. This idea of being detailed relates to another feature that can be understood without much mathematical background: Having a fractal dimension greater than its topological dimension, for instance, refers to how a fractal scales compared to how geometric shapes are usually perceived. Unlike the other fractals, even though the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. Dictionary Fractal Table of Contents What Does Fractal Mean? As widely varied individual agents interact in the model, the simulation shows how their collective behaviors govern the performance of the entire system - for instance, the emergence of a successful product or an optimal schedule. Like approximation algorithms, they can be used to more quickly solve tough NP-complete problems. [13][14] This qubit property arises as a direct consequence of its adherence to the laws of quantum mechanics, which differ radically from the laws of classical physics. According to Pickover, the mathematics behind fractals began to take shape in the 17th century when the mathematician and philosopher Gottfried Leibniz pondered recursive self-similarity (although he made the mistake of thinking that only the straight line was self-similar in this sense). We see that for ordinary self-similar objects, being n-dimensional means that when it is rep-tiled into pieces each scaled down by a scale-factor of 1/r, there are a total of rn pieces. This is level zero. Treats the problem with rigorous mathematical analysis. Balancing an inverted pendulum: This problem involves balancing and inverted pendulum. They also use fractals to create models of how earthquakes work. [22] The Fuzzy logic has found enormous applications and has already found a big market presence in consumer electronics such as washing machines, microwaves, mobile phones, Televisions, Camcoders etc. [18] The Soft Computing technique comprises Fuzzy logic, neuro-computing, evolutionary-computing, machine learning and probabilistic-chaotic computing. Yongwei Zhao et al, Fractal Parallel Computing, Intelligent Computing (2022). While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. Examples: Two neighboring water molecules may end up in different parts of the ocean or even in different oceans. Explore the Mandelbrot fractal yourself, with the amazing real-time fractalzoomer, XaoS: Chaos is the science of surprises, of the nonlinear and the unpredictable. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have happened. There is something a company wants to do about that customers action: produce a bill. The network converges through several hundreds of iterative computations. They rise naturally in computer graphics because we . W. H. Freeman and Company, New York (1982); p. 15. Intelligent Computing 5 Sep 2022 Vol 2022 Article ID: 9797623 DOI: 10.34133/2022/9797623 Abstract As machine learning (ML) becomes the prominent technology for many emerging problems, dedicated ML computers are being developed at a variety of scales, from clouds to edge devices. Every line item is reconciled. Each customer has attributes. The Butterfly Effect: This effect grants the power to cause a hurricane in China to a butterfly flapping its wings in New Mexico. Cyberneticist Ron Eglash has suggested that fractal geometry and mathematics are prevalent in African art, games, divination, trade, and architecture. Some works by the Dutch artist M. C. Escher, such as Circle Limit III, contain shapes repeated to infinity that become smaller and smaller as they get near to the edges, in a pattern that would always look the same if zoomed in. "Compared with Valiant's multi-BSP, FPM minimized the parameters for simpler abstraction," the researchers said. Neither your address nor the recipient's address will be used for any other purpose. It is for problems like this that lateral computing can be useful to form a better solution. However, if a fractal's one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power that is not necessarily an integer and is in general greater than its conventional dimension. Fractals are very complex pictures generated by a computer from a single formula. [23] Chaotic Computing is based on the chaos theory.[24]. part may be reproduced without the written permission. These computer programs allow you to spot a new kind of symmetry associated with fractals. Ostwald, Michael J., and Vaughan, Josephine (2016). This page was last edited on 17 March 2023, at 16:56. B. Kosko (1994); Fuzzy Thinking, Flamingo Publishers. A consequence of this structure is fractals may have, Irregularity locally and globally that cannot easily be described in the language of traditional, Brownian motion (generated by a one-dimensional, Detecting 'life as we don't know it' by fractal analysis, Creation of digital photographic enlargements, Generation of patterns for camouflage, such as. The lateral-computing successfully tackles a class of problems by exploiting tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness and low solution cost. Days later, more customers are added and this new production level system is run in parallel with the current legacy system. Self-similarity itself is not necessarily counter-intuitive (e.g., people have pondered self-similarity informally such as in the infinite regress in parallel mirrors or the homunculus, the little man inside the head of the little man inside the head ). Apart from any fair dealing for the purpose of private study or research, no Slime mold Brefeldia maxima growing fractally on wood, Psilomelane dendrites in the Solnhofen Limestone, Fractals often appear in the realm of living organisms where they arise through branching processes and other complex pattern formation. Uses indirect models or looks for analogies to solve the problem. A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results. Who knows what the long-term effects of teaching millions of kids about chaos and fractals will be? [37] Not long after that, in 1883, Georg Cantor, who attended lectures by Weierstrass,[9] published examples of subsets of the real line known as Cantor sets, which had unusual properties and are now recognized as fractals. It is also nonlinear: fluids cannot be unmixed. Fractal defrosting patterns, polar Mars. The result is that one must need infinite tape to perfectly cover the entire curve, i.e. Provocative use of information processing is the basic underlying principle of lateral thinking. The training patterns are repeatedly presented to the network. Similarly, by applying lateral-computing techniques to a problem, it can become much easier to arrive at a computationally inexpensive, easy to implement, efficient, innovative or unconventional solution. Now, consider the Koch curve. Ninety percent of corporate apps can be built with a small, but representative number of customers, vehicles, endpoints, bills, then scaled to full production in a day or two, not a year. Fractal app development is the future of programming because it has shown that about any production app can be built or rebuilt as a fractal. It needs endless system design meetings. Atomic Energy, 74, 241243 (1993). One way that fractals are different from finite geometric figures is how they scale. Those outcomes are revolutionary and partly attributed to a new programming concept fractal programming. Approximate fractals found in nature display self-similarity over extended, but finite, scale ranges. Ants communicate using pheromones; trails are laid that can be followed by other ants. Every transaction, going back 10 years is cross tested for accuracy. The length of the fractal is infinite and size of it cannot be measured. 1924) to denote the geometry of nature, which traces inherent order in chaotic shapes and processes. Therefore, ML computers built with FvNA are programmable under a scale-invariant, homogeneous, and sequential view," the researchers explained. B.: The Fractal Geometry of Nature. Parallel computing focuses on improving the performance of the computers/algorithms through the use of several computing elements (such as processing elements). John R. Koza, Martin A. Keane, Matthew J. Streeter, William Mydlowec, Jessen Yu, and Guido Lanza (2003); Genetic Programming IV: Routine Human-Competitive Machine Intelligence, Kluwer Academic. [notes 1]. The recursive nature of some patterns is obvious in certain examplesa branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. Relative Quaternary Fractal (RQF) Computation Theory (first published May 20th 2014) should provide everything you need to know to decode this 'junk' part of the DNA. Some specific applications of fractals to technology are listed elsewhere. The error is back propagated and the network weights are adjusted using gradient descent. Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still digital images, animations, and media.Fractal art developed from the mid-1980s onwards. There is Code Project now with C# claiming to implement Fractal Encryption. A straight line, for instance, is self-similar but not fractal because it lacks detail, and is easily described in Euclidean language without a need for recursion.[1][4]. A group of helium balloons that launch together will eventually land in drastically different places. If a system is "fractal," according to the researchers, it implies that the system always uses the same program regardless of the scale. [26] The two categories of randomized algorithms are: Consider an algorithm to find the kth element of an array. Geologists use fractal geometry to understand how oil flows through underground reservoirs as well as to locate oil deposits. Recognizing the chaotic, fractal nature of our world can give us new insight, power, and wisdom. Unpredictability: Because we can never know all the initial conditions of a complex system in sufficient (i.e. I'm a geometer and professor of computer science at Carnegie Mellon University. It's a form of algorithmic art created by calculating fractal objects and representing the calculation results as digital images, animations. Frame, Michael; and Mandelbrot, Benot B.; Koutonin, Mawuna (March 18, 2016). The term "Lateral Computing" was first proposed by Prof CR SUTHIKSHN Kumar and First World Congress on Lateral Computing WCLC 2004 was organized with international participants during December 2004. One of the main components of "Lateral-computing" is soft computing which approaches problems with human information processing model. Her app may process 25,000 customers out of the apps domain of 100 million. FvNA is scale-invariant to program, thus making the development of a family of. The optimal matching between architecture and algorithm improves the performance of the reconfigurable computer. It is a genre of computer art and digital art which are part of new media art.The mathematical beauty of fractals lies at the intersection of generative art and computer art. Fractal programming is revolutionary because it moves decimal points. "Fractalness" is a borrowed geometric concept that describes the self-similar patterns applied to any scale. However, in lateral computing, the problem is solved using unconventional information processing whether using a sequential or parallel computing. As known, factoring large numbers is a relevant problem in many cryptographic applications. Multiple subcellular structures also are found to assemble into fractals. The outputs of the modelling process may be highly artistic renderings, outputs for investigation, or benchmarks for fractal analysis. [4][13][24] As one illustration, trees, ferns, cells of the nervous system,[21] blood and lung vasculature,[47] and other branching patterns in nature can be modeled on a computer by using recursive algorithms and L-systems techniques.[21]. Fractal geometry is a way to describe the "texture" of a surface.9 There are four topological dimensions in traditional Euclidean geometry: 0-D for points, 1-D for straight lines, 2-D for planes, and 3-D for volumetric objects like cubes and spheres. Since 1999 numerous scientific groups have performed fractal analysis on over 50 paintings created by Jackson Pollock by pouring paint directly onto horizontal canvasses. "[84], In a 1996 interview with Michael Silverblatt, David Foster Wallace admitted that the structure of the first draft of Infinite Jest he gave to his editor Michael Pietsch was inspired by fractals, specifically the Sierpinski triangle (a.k.a. By analogy, a computational grid is a hardware and software infrastructure that provides dependable, consistent, pervasive, and inexpensive access to high-end computational capabilities. Probabilistic computing engines, e.g. The solutions are evaluated using a fitness function and a selection process determines which solutions are to be used for competition process. It sports a new, clean branding, loads of new features and plenty of enhancements over the previous version without compromising on the core functionality and design that has defined the series this last decade. It never occurred to them that the Africans might have been using a form of mathematics that they hadn't even discovered yet. Fractals are SMART: Science, Math and Art! [72] These processes are crucial in cell physiology and different pathologies.[73]. A deterministic approach would be to choose a pivot element near the median of the list and partition the list around that element. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Diego Krapf has shown that through branching processes the actin filaments in human cells assemble into fractal patterns. "Addressing the productivity issue, we proposed ML computers with fractal von Neumann architecture (FvNA)," said Yongwei Zhao, researcher from the State Key Lab of Processors, Institute of Computing Technology of CAS. The fractal character of some quantum properties has been shown for systems described by continuous variables. It will be tough task classifying a computing technique as a conventional or lateral computing technique as shown in the figure. Although FvNA has been testified as applicable to the ML domain and capable of alleviating the programming productivity issue while functioning efficiently as its ad hoc counterparts, some problems remain to be solved. Fractals have found applications in image processing, image compression music generation, computer games etc. ", 10.1002/(SICI)1096-9896(199705)182:1<1::AID-PATH808>3.0.CO;2-B, "Anomalous dynamics of the endoplasmic reticulum network", "Fractal Analysis of Pollock's Drip Paintings", "What Makes a Pollock Pollock: A Machine Vision Approach", "Perceptual and Physiological Responses to Jackson Pollock's Fractals", "Sophisticated Mathematics Behind African Village Designs / Fractal patterns use repetition on large, small scale", "Application maps out nation's batik story", "Reduction of Physiological Stress Using Fractal Art and Architecture", "Modeling Fractal Structure of City-Size Distributions Using Correlation Functions", "An Algorithmic Approach to Generate After-disaster Test Fields for Search and Rescue Agents", "description of swizzled and hybrid tiled swizzled textures", "US8773422B1 - System, method, and computer program product for grouping linearly ordered primitives", "US20110227921A1 - Processing of 3D computer graphics data on multiple shading engines", Benoit Mandelbrot: Fractals and the Art of Roughness, Technical Library on Fractals for controlling fluid, Equations of self-similar fractal measure based on the fractional-order calculus, https://en.wikipedia.org/w/index.php?title=Fractal&oldid=1157538144, Exact self-similarity: identical at all scales, such as the, Quasi self-similarity: approximates the same pattern at different scales; may contain small copies of the entire fractal in distorted and degenerate forms; e.g., the, Statistical self-similarity: repeats a pattern, Qualitative self-similarity: as in a time series, Fine or detailed structure at arbitrarily small scales. FvNA is scale-invariant to program, thus making the development of a family of. [27] There are two classes of Machine Learning (ML): One of the well known machine learning technique is Back Propagation Algorithm.
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