Approaches problems by analogies such as human information processing model. . Modeled fractals may be sounds,[17] digital images, electrochemical patterns, circadian rhythms,[50] etc. [clarification needed]. Lateral thinking has been made popular by Edward de Bono. (or: What I Dont Think)What Is the Value of (Super) Narrow Transcription? There are several types of fractals and Mandelbrot sets are very popular. 1. Approximate fractals found in nature display self-similarity over extended, but finite, scale ranges. In case of optical computers, the photons in a light beam are used to do computation. Recognizing the chaotic, fractal nature of our world can give us new insight, power, and wisdom. [citation needed] Lateral-computing sometimes arrives at a novel solution for particular computing problem by using the model of how living beings, such as how humans, ants, and honeybees, solve a problem; how pure crystals are formed by annealing, or evolution of living beings or quantum mechanics etc. Multiple subcellular structures also are found to assemble into fractals. An instance of FPM is a tree structure of nested components; each component contains a memory, a processor, and child components. The fractal character of some quantum properties has been shown for systems described by continuous variables. They add up the transactions, do the simple math, and produce 25,000 bills. Treats the problem with rigorous mathematical analysis. A fractal dimension is a ratio for figuring out the complexity of a system given its measurement. My quick-n-dirty code is below (not guaranteed to be bug-free, but a good outline). B. Kosko (1994); Fuzzy Thinking, Flamingo Publishers. [clarification needed] These computers rely on the much faster reactions of DNA nucleotides binding with their complements, a brute force method that holds enormous potential for creating a new generation of computers that would be 100 billion times faster than today's fastest PC. The feature of "self-similarity", for instance, is easily understood by analogy to zooming in with a lens or other device that zooms in on digital images to uncover finer, previously invisible, new structure. Over a period of time, some unconventional computing techniques become integral part of mainstream computing. K. Compton and S. Hauck (2002); Reconfigurable Computing: A survey of Systems and Software, ACM Computing Surveys, Vo. In this paper, the following three were addressed: To answer these questions, the researchers started by modeling the fractal parallel machine (FPM), an abstract parallel computer modeled from FvNA. They also use fractals to create models of how earthquakes work. The samples covered embarrassingly parallel, divide-and-conquer, and dynamic programming algorithms, all of which were demonstrated as efficiently programmable. 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. A qubit can exist not only in a state corresponding to the logical state 0 or 1 as in a classical bit, but also in states corresponding to a blend or quantum superposition of these classical states. 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. A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results. Like approximation algorithms, they can be used to more quickly solve tough NP-complete problems. Ian Wong and co-workers have shown that migrating cells can form fractals by clustering and branching. This approach has become highly successful in solving some of the pattern recognition problems. In other words, a qubit can exist as a zero, a one, or simultaneously as both 0 and 1, with a numerical coefficient representing the probability for each state. For several applications such as fingerprint matching, DNA sequence comparison, etc., reconfigurable computers have been shown to perform several orders of magnitude better than conventional computers.[16]. In a concrete sense, this means fractals cannot be measured in traditional ways. [4] The computing speed is improved by using several computing elements. However, we do not guarantee individual replies due to the high volume of messages. Different researchers have postulated that without the aid of modern computer graphics, early investigators were limited to what they could depict in manual drawings, so lacked the means to visualize the beauty and appreciate some of the implications of many of the patterns they had discovered (the Julia set, for instance, could only be visualized through a few iterations as very simple drawings). Fractal Programming means a single developer builds a small system on her laptop with all the features for the eventual production system. [1] This thinking technique is applied to generate creative ideas and solve problems. Smart volume control for mobile phones: The volume control in mobile phones depend on the background noise levels, noise classes, hearing profile of the user and other parameters. The length of the fractal is infinite and size of it cannot be measured. Fractal Programming is transformative because it moves decimal points. The traditional or conventional approach to solving computing problems is to either build mathematical models or have an IF- THEN -ELSE structure. The key feature is hardware performance and software flexibility. In a quantum computer, the fundamental unit of information (called a quantum bit or qubit), is not binary but rather more quaternary in nature. ", More information: 171210. Please help update this article to reflect recent events or newly available information. Then she writes the simple code to process what the customers did make a cell call or turn on a light. Fractals have also been used for many practical purposes. Lateral computing is a lateral thinking approach to solving computing problems . Statistical Self-Similarity and Fractional Dimension, Small angle scattering theory of fractally rough systems, "Fractal properties of human heart period variability: Physiological and methodological implications", "Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging", "Automated detection of proliferative retinopathy in clinical practice", "African Fractals: Modern Computing and Indigenous Design", "Chaos, Complexity, and Entropy: A physics talk for non-physicists", "Vol Libre, an amazing CG film from 1980", "Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork", "Crystal growth, biological cell growth and geometry", "The fractal scaling relationship for river inlets to lakes", "A fractal-based approach to lake size-distributions", "Mass fractal dimension and the compactness of proteins", "Motility-limited aggregation of mammary epithelial cells into fractal-like clusters", "Neurons and fractals: how reliable and useful are calculations of fractal dimensions? Fractals are SMART: Science, Math and Art! Fractal Programming delivers major production apps into the users hands in time to impact the business. [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]. In theory, images can be calculated infinitely but in practice are approximated to a certain level of detail. Just add customer records. The result is that one must need infinite tape to perfectly cover the entire curve, i.e. Also, these may include calculation or display artifacts which are not characteristics of true fractals. It will be tough task classifying a computing technique as a conventional or lateral computing technique as shown in the figure. or, by Intelligent Computing. [25] Fractals generation involves small iterative algorithms. A straight line, for instance, is conventionally understood to be one-dimensional; if such a figure is rep-tiled into pieces each 1/3 the length of the original, then there are always three equal pieces. Lateral-computing techniques which use the human like information processing models have been classified as "Soft Computing" in literature. 34, No.2, June 2002, pp. This fractal system is hosted on a small server, think an Intel NUC costing $5,000. For more detailed info, please download our 20 page Educators Guide (7.5Mb). Hence Lateral computing includes those techniques which use semi-conventional or hybrid computing. Voter integrity teams were ferociously analyzing state voter rolls with SQL, relational, Mongo, Excel type systems the equivalent of emptying a swimming pool with a spoon. These algorithms are highly successful in solving search and optimization problems. Now, consider the Koch curve. These simulations are powerful strategic tools for "what-if" scenario analysis: as managers change agent characteristics or "rules," the impact of the change can be easily seen in the model output. If a system is "fractal," according to the researchers, it implies that the system always uses the same program regardless of the scale. "Compared with Valiant's multi-BSP, FPM minimized the parameters for simpler abstraction," the researchers said. The cost savings was 90%. Images and other outputs of modelling are normally referred to as being "fractals" even if they do not have strictly fractal characteristics, such as when it is possible to zoom into a region of the fractal image that does not exhibit any fractal properties. Fractals surround us in so many different aspects of life. Computer scientist Keenan Crane, PhD, is asked to explain fractals to 5 different people; a child, a teen, a college student, a grad student, and an expert. In essence, a Fractal is a pattern that repeats forever, and every part of the Fractal, regardless of how zoomed in, or zoomed out you are, it looks very similar to the whole image. This document is subject to copyright. [75][76][77], Recently, fractal analysis has been used to achieve a 93% success rate in distinguishing real from imitation Pollocks. One interesting swarm intelligent technique is the Ant Colony algorithm:[6]. FvNA is scale-invariant to program, thus making the development of a family of. [85] When humans view fractal patterns with D values between 1.3 and 1.5, this tends to reduce physiological stress. Karl Menger (1902-1985) was a 20th-century Austrian-American mathematician. So, start by scanning every point in that rectangular area. While random mutation provides change, the selection is through survival of the fittest. 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. [32] However, this requirement is not met by space-filling curves such as the Hilbert curve. "Fractalness" is a borrowed geometric concept that describes the self-similar patterns applied to any scale. Instead of looking at the world as hundreds of tables, crammed into a relational database, the fractal programmer gathers 100% of the customer data for 25,000 customers in one shard. There is Code Project now with C# claiming to implement Fractal Encryption. It will take 18 24 months. There are numerous advantages of using optical devices for computing such as immunity to electromagnetic interference, large bandwidth, etc. [citation needed] They provide a way of developing innovative solutions resulting in smart systems with Very High Machine IQ (VHMIQ). Ants communicate using pheromones; trails are laid that can be followed by other ants. Mandelbrot himself summarized it as "beautiful, damn hard, increasingly useful. If the equation converges for chosen Z, then Z belongs to M. It is a kind of computer art and digital art which are part of new media art. Fractal Computing are objects displaying self-similarity at different scales. Language links are at the top of the page across from the title. And the answer is that Fractal computing delivers quantum computing results right now, on current hardware, with current skills. Thank you for taking time to provide your feedback to the editors. The numbers Z which belong to M are computed by iteratively testing the Mandelbrot equation. The behaviors of these agents are programmed with rules that realistically depict how business is conducted. Fractals: Self-similarity n Level of detail remains the same as we zoom in n Example: surface roughness or profile same as we zoom in n Types: . Epstein and W.A. One of the earliest applications of fractals came about well before the term was even used. 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). Some of the techniques in lateral computing use "unexplained jumps". The following brings out some important differentiators for lateral computing. [1] The brain as center of thinking has a self-organizing information system. So DNA is part of a highly complex natural computing system. [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. In 90 days, a full production billing system was delivered with 1 million customers. [notes 1]. A fractal mindset sees the world differently. These phenomena are often described by fractal mathematics, which captures the infinite complexity of nature. They are created by repeating a simple process over and over in an ongoing feedback loop. Fractal patterns have been reconstructed in physical 3-dimensional space[24]:10 and virtually, often called "in silico" modeling. The slow and regular cooling of the metal allows the atoms to slide progressively their most stable ("minimal energy") positions. [17] The computing problem is redesigned as a simulated annealing exercise and the solutions are arrived at. Mandelbrot, B. It is also nonlinear: fluids cannot be unmixed. Such computational techniques are referred to as randomization, yielding probabilistic algorithms. In fractal software values for a set of points on the complex plane are calculated and then rendered as pixels. Optical computing is to use photons rather than conventional electrons for computing. Fractal programming is revolutionary because it moves decimal points. We loaded Wisconsin and within hours had it in . Customers perform transactions, like using a cell phone or flicking a light switch. Authors disagree on the exact definition of fractal, but most usually elaborate on the basic ideas of self-similarity and the unusual relationship fractals have with the space they are embedded in. Carnielli (1989); Computability, Computable Functions, Logic and The Foundations of Mathematics, Wadsworth & Brooks/Cole Advanced Books and Software. 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. Every transaction, going back 10 years is cross tested for accuracy. Here, a definition of quantum fractal states is given that suits the discrete systems used in quantum information processing, including quantum coding and quantum computing. The fractals are at the intersection of generative art and computer art. I.e., the Mandelbrot set is infinitely complex. What are Fractals? They are capable of describing many irregularly shaped objects or . Example applications of DNA computing are in solution for the Hamiltonian path problem which is a known NP[clarification needed] complete one. Here is a small set of applications that illustrates lateral computing: Above is a review of lateral-computing techniques. Feedback: Systems often become chaotic when there is feedback present. Images of fractals can be created by fractal generating programs. Fractal Programming means a single developer builds a small system on her laptop with all the features for the eventual production system. This is rare as most conventional computers use electrons to carry signals. Provocative use of information processing is the basic underlying principle of lateral thinking. Sierpinski gasket), but that the edited novel is "more like a lopsided Sierpinsky Gasket".[26]. Lateral computing takes the analogies from real-world examples such as: Differentiating factors of "lateral computing": It is very hard to draw a clear boundary between conventional and lateral computing. In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. The number of required lab operations using DNA grows linearly with the number of vertices of the graph. Personal computing Definition fractal By TechTarget Contributor A fractal is a non-regular geometric shape that has the same degree of non-regularity on all scales. And today, I've been asked to explain fractals at five levels of increasing complexity. 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. [35] [8]:1124 Also in the last part of that century, Felix Klein and Henri Poincar introduced a category of fractal that has come to be called "self-inverse" fractals. [82][83], Ethnomathematician Ron Eglash has discussed the planned layout of Benin city using fractals as the basis, not only in the city itself and the villages but even in the rooms of houses. Uses indirect models or looks for analogies to solve the problem. The information you enter will appear in your e-mail message and is not retained by Tech Xplore in any form. [8][9] [8]:7[9], In addition, the quotient difference becomes arbitrarily large as the summation index increases. Lateral computing is a lateral thinking approach to solving computing problems. [36], In his writings, Leibniz used the term "fractional exponents", but lamented that "Geometry" did not yet know of them. The randomized approach to this problem would be to choose a pivot at random, thus saving time at the beginning of the process. Fractal Programming did not just happen. They interface with scores of tech layers purpose-built to be anything for anyone. Lateral-computing is for building new generation artificial intelligence based on unconventional processing. M. Sima, S. Vassiliadis, S. Cotofona, J. T. J. Ozhovan M. I., Dmitriev I. E., Batyukhnova O. G. Fractal structure of pores of clay soil. The measurement on noise level and loudness level involve imprecision and subjective measures. Her app may process 25,000 customers out of the app's domain of 100 million. Ants are behaviorally unsophisticated; collectively they perform complex tasks. Fractal Programming delivers a micro app rather than a microservice. B. Mandelbrot (1997); The Fractal Geometry of Nature, Freeman Publishers, New York. Truck backup problem: This is an interesting problem of reversing a truck and parking it at a particular location. It contains computation algorithms and knowledge that have evolved over *at least* the last 4 billion years. Atomic Energy, 74, 241243 (1993). The problem may hardly have any relation to the computing technique used. [clarification needed][7] Agents are considered to be autonomous (independent, not-controllable), reactive (responding to events), pro-active (initiating actions of their own volition), and social (communicative). Then several lateral-computing techniques have been described followed by their applications. Even slight errors in measuring the state of a system will be amplified dramatically, rendering any prediction useless. Please select the most appropriate category to facilitate processing of your request. The working principle of simulated annealing is borrowed from metallurgy: a piece of metal is heated (the atoms are given thermal agitation), and then the metal is left to cool slowly. The network converges through several hundreds of iterative computations. Each agent may have its own task and/or role. 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. Driven by recursion, fractals are images of dynamic systems the pictures of Chaos. Water logic, in someways, resembles fuzzy logic. Fractal Programming recognizes the complexity of current app development is mostly from current system design constraints. He commented that "When Europeans first came to Africa, they considered the architecture very disorganised and thus primitive. FPM was built on Valiant's multi-BSP, a homogeneous multilayered parallel model, with only minor extensions. The result is a type of abstract art. The connection between fractals and leaves, for instance, is currently being used to determine how much carbon is contained in trees. 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. Lateral-computing is valuable while solving numerous computing problems whose mathematical models are unavailable. Click here to sign in with part may be reproduced without the written permission. The fuzzy sets differ from crisp sets since they allow an element to belong to a set to a degree (degree of membership). This means one formula is repeated with slightly different values over and over again, taking into account the results from the previous iteration. (Rapid cooling would have "frozen" them in whatever position they happened to be at that time.) [1] This thinking technique is applied to generate creative ideas and solve problems. Mixing is thorough because turbulence occurs at all scales. "We clarified that, although originally developed from the domain of ML, fractal parallel computing is fairly generally applicable," the researchers concluded, drawing from their preliminary results that FPM, general-purpose and cost-optimal as it is, is as powerful as many fundamental parallel computing models such as BSP and alternating Turing machine. Agents are encapsulated computer systems that are situated in some environment and are capable of flexible, autonomous action in that environment in order to meet their design objectives. Fractals are distinct from the simple figures of classical, or Euclidean, geometrythe square, the circle, the sphere, and so forth. [31] Mandelbrot based it on the Latin frctus, meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.[1][32][33]. [8] The applications of grid computing are in: The autonomic nervous system governs our heart rate and body temperature, thus freeing our conscious brain from the burden of dealing with these and many other low-level, yet vital, functions. However, in lateral computing, the problem is solved using unconventional information processing whether using a sequential or parallel computing. In 1975[32] Mandelbrot solidified hundreds of years of thought and mathematical development in coining the word "fractal" and illustrated his mathematical definition with striking computer-constructed visualizations. It will take 18 -20 highly skilled programmers, project managers. [11] There are quite a few instances of optical computers and successful use of them. The outputs of the modelling process may be highly artistic renderings, outputs for investigation, or benchmarks for fractal analysis. Koch Snowflakes Pseudocode, to draw K n: If (n equals 0) draw straight line This number is called the fractal dimension of the Koch curve; it is not the conventionally perceived dimension of a curve. A well-designed randomized algorithm will have a very high probability of returning a correct answer. A fractal that models the surface of a mountain (animation), Humans appear to be especially well-adapted to processing fractal patterns with D values between 1.3 and 1.5. Such agents invariably need to interact with one another in order to manage their inter-dependencies. Since the DNA molecule is also a code, but is instead made up of a sequence of four bases that pair up in a predictable manner, many scientists have thought about the possibility of creating a molecular computer. [6], Analytically, many fractals are nowhere differentiable. The word "fractal" often has different connotations for the lay public as opposed to mathematicians, where the public is more likely to be familiar with fractal art than the mathematical concept. Some specific applications of fractals to technology are listed elsewhere. Provided by Agent-based systems are computer programs that try to simulate various complex phenomena via virtual "agents" that represent the components of a business system. DNA computing has been heralded as the "first example of true nanotechnology",[citation needed] and even the "start of a new era",[citation needed] which forges an unprecedented link between computer science and life science. Fractals are infinitely complex patterns that are self-similar across different scales. Harry R. Lewis, Christos H. Papadimtrou (1997); Elements of Theory of Computation, 2nd edition, Prentice Hall Publishers. [9] The idea of self-similar curves was taken further by Paul Lvy, who, in his 1938 paper Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole, described a new fractal curve, the Lvy C curve. Lateral computing does a provocative use of information processing similar to lateral-thinking. But he is best known for his cube-like fractal known as a "sponge". This in turn further affects the price of the stock, causing it to rise or fall chaotically. W. H. Freeman and Company, New York (1982); p. 15. Since 1999 numerous scientific groups have performed fractal analysis on over 50 paintings created by Jackson Pollock by pouring paint directly onto horizontal canvasses. These interactions involve agents cooperating, negotiating and coordinating with one another. Sun Microsystems (2003); Introduction to Throughput Computing, Technical Report. "Story of cities #5: Benin City, the mighty medieval capital now lost without trace". 12 Answers Sorted by: 61 Programming the Mandelbrot is easy. The content is provided for information purposes only. "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. C is a constant. Mandelbrot equation: A Randomized algorithm makes arbitrary choices during its execution. The Mandelbrot set M is a collection of complex numbers. Distributed supercomputing applications use grids to aggregate substantial computational resources in order to tackle problems that cannot be solved on a single system. The Fractal Define 7 is the seventh generation of the Define R series of cases. E. Charniak and D. Mcdermott (1999); Introduction to Artificial Intelligence, Addison Wesley. The error is back propagated and the network weights are adjusted using gradient descent. [51] Phenomena known to have fractal features include: Frost crystals occurring naturally on cold glass form fractal patterns, Fractal basin boundary in a geometrical optical system[58], A fractal is formed when pulling apart two glue-covered acrylic sheets, High-voltage breakdown within a 4in (100mm) block of acrylic glass creates a fractal Lichtenberg figure, Romanesco broccoli, showing self-similar form approximating a natural fractal. R. Herken (1995); Universal Turing Machine, Springer-Verlag 2nd Edition. So there will always be an overlap between conventional and lateral computing. It teaches us to expect the unexpected. Does not directly approach the problem through mathematical means. Use this form if you have come across a typo, inaccuracy or would like to send an edit request for the content on this page. [86][87], Common techniques for generating fractals. In colloquial usage, a fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole". The patterns are formed by sublimation of frozen CO2. To mathematicians, a symmetry is an action that when applied to a shape will leave it looking (more or .
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