29 followers. In a sense, this is like applied mathematics. Keywords: visualization; nonlinear dynamics; chaos; fractal; attractor; bifurcation; dynamical systems; prediction; python; logistic map 1. New York: W. Apr 14, 2018 - Explore Amy Stephens Wulfekuhl's board "chaos tattoo" on Pinterest. The program starts with the center C of the -sided polygon (it could be any point) and draws a new point at a fraction of the distance between C and a random vertex. See more ideas about chaos theory, chaos, butterfly effect. Goldberger MD * * Correspondence to: Dr Ary L Goldberger, Cardiovascular Division (GZ-435), Beth Israel Hospital, 330 Brookline Avenue, Boston, MA 02215, USA Harvard-Thorndike Laboratory, Department of Medicine, Beth. Discover Pinterest’s 10 best ideas and inspiration for Chaos theory. e. 1992; 267:1806–1809. Dieser Pinnwand folgen 124 Nutzer auf Pinterest. The chaos theory is a revolutionary approach to understanding and forecasting the behavior of financial markets. 1 and 2. Fractals are introduced as self-similar geometric objects and analysed with the self-similarity and box-counting. Donahue's Chaos Theory & Fractal Geometry Project Diarsipkan 2005-03-12 di Wayback Machine. X Tattoo. 1996; 347:1312–1314. the overarching patterns-of-patterns within which human cultures. They are created by repeating a simple process over and over in an ongoing feedback loop. Using Python to visualize chaos, fractals, and self-similarity to better understand the limits of knowledge and prediction. The first step is the same as in the. 1990; 120:1419–1440. These sensitive nonlinear dynamical systems have now been explained using chaos theory and fractal geometry. In the field of education, chaos theory providesincluding the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. In the references to chaos theory and fractals to be addressed in this section, the actual mathematical content of these disciplines, i. Fractal Art. The concept of Chaos Theory dates back to ancient Greek and Chinese civilizations. edu. Every day at a few minutes past midnight (local Wisconsin time), a new fractal is automatically posted using a variation of the program included with the book Strange Attractors: Creating Patterns in Chaos by Julien C. Fractal Design. Systems Theory. The dictionary definition of chaos is turmoil, turbulence, primordial abyss, and undesired randomness, but scientists will tell you that chaos is something extremely sensitive to initial conditions. In this post (adapted. The initial conditions for x and z were kept the same but those for y were changed between 1. Download/cite the article here and try pynamical yourself. Reading material and additional slides. Causes: a soccer team loses the world cup. Topics Applications of Nonlinear Dynamics and Chaos Theory, Vibration, Dynamical Systems, Control, Complex Systems, History. 分形 （英語： fractal ，源自 拉丁語 ： frāctus ，有「零碎」、「破裂」之意），又稱 碎形 、 殘形 ，通常被定義為「一個粗糙或零碎的 幾何形狀 ，可以分成數個部分，且每一部分都（至少近似地）是整體縮小後的形狀」 [2] ，即具有 自相似 的性質。. When autocomplete results are available use up and down arrows to review and enter to select. We. Analysis of HR dynamics by methods based on chaos theory and nonlinear. Loss of “complexity” and aging: potential applications of fractals and chaos theory to senescence. 1996; 347:1312–1314. Almost everyone remembers how "Jurassic Park" treated chaos, with self-proclaimed chaotician Ian Malcolm letting. Heighway dragon curve. Chaos (n): the inherent unpredictability in the behaviour of a complex natural system. The emerging unifying concept which emerges is that. No comments yet! Add one to start the conversation. Goldberger A. 347:1312–14,1996. Glitch eye fractal tattoos. It teaches us to expect the unexpected. Awesome. Transactions of the Institute of Measurement and Control, Vol. Fractal Geometry. Vintage Poster Art. In the last example, we show how to calculate the FD of a 3D volume representing the brain white matter. Description. Abstract Tattoo Designs. Choose any arbitrary point (x,y) ( x, y) anywhere on the plane either inside or outside the triangle. 13 Denton TA, Diamond GA, Helfant RH, Khan S, Karagueuzian H. The million-copy New York Times bestseller and finalist for both the Pulitzer Prize and the National Book Award that reveals the science behind chaos theory. Fractal theory. Computers helped reinvigorate the field. Visualizza altre idee su hedgewitch, stregoneria, dark fantasy art. The mathematical beauty of fractals lies at. ISBN: 978-981-12-7326-1 (ebook) USD 30. A "tribute to mathematics" depicting 3D representations of some of the most famous strange attractors. the unexpected. [1] They are so named after the researcher Clifford Pickover, whose "epsilon cross" method was instrumental in their discovery. Get inspired and try out new things. It is a three-dimensional generalization of the one-dimensional Cantor set and two. Expand. Math Geometry. Complex heart rate variability and serum norepinephrine levels in patients with advanced heart failure. The beginning of its application coincided with the transition of finance to the use of big data. Am Heart J. A buy fractal is a series of five consecutive bars where the highest high is preceded by two lower highs and is followed by two lower highs. Retro Poster. At the present time, the properties of fractals are incompletely described, and further work is needed to discover new mathematical descriptors which can be applied to fractal analysis. Also, such objects are self-similar in nature; thus, their shape is independent of the scale and remains the same under dilatation or contraction. 4. In the Wikipedia page for Chaos Game, you can see this fractal, which is the result of the rule: A point inside a square repeatedly jumps half of the distance towards a randomly chosen vertex, but the currently chosen vertex cannot be 1 or 3 places, respectively away from the two previously chosen vertices. Casino legal online gambling, casino online ireland; Tatuaje casino, tatuaj cazinou; Casino constanta vector, csgo casino minesweeper minBenoit B. It is often described by fractal mathematics, which captures the infinite complexity of nature. 3 Fractal Dimension Computation of an MRI Volume of the Brain White Matter with a Boxcount-Based MATLAB Script. S. Mandelbrot was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". And this property transfers. Although chaos was often unfavorably viewed its early stages, scientists now perform active research in many areas of the field. Motions in chaotic behavor is based on nonlinearity of the mechnical systems. Chaos Theory. Just as we have seen the merging of electronics and engine networks with nonlinear dynamics in the 1950’s–1960’s, we see the merging of the nonlinear systems dynamics and fractal geometry networks beginning in the late 1970’s and becoming what would be called ‘chaos theory’. Br J Gen Pract. Results of application of theory of fractal and chaos, scaling effects and fractional operators in the fundamental issues of the radio location and radio physic are presented. Moreau. a butterfly flapping its wings in South America can affect the weather in Central Park. The Lorenz Oscillator is a 3-dimensional dynamical system that exhibits chaotic flow, noted for its lemniscate shape. Ipod Wallpaper. Jun 25, 2019 - Explore nezar BİLEN's board "Chaos theory" on Pinterest. 1 and 1. Chaos theory provides a radically different framework for studying complex dynamics. Finally we establish the idea of control of chaos. J Am Coll Cardiol. Nearly all nontrivial real-world systems are nonlinear dynamical systems. Today. Art Graphique-silverae- by silwenka on DeviantArt. Dr. In contrast, the symbol of Law is a single upright arrow. The modern theory of fractals is the outcome of explorations by mathematicians and scientists in the 1960s and 1970s, though, as we shall see, it too has an extensive prehistory. Heavily explored and recognized during the mid-to-late 1980s, its premise is that systems sometimes reside in chaos, generating energy but without any predictability or direction. Jun 7, 2019 - Explore JG's board "Chaos Theory" on Pinterest. 5. Bothand Neoclassical Theory are analyzed. Fractal tattoo with repeating geometric patterns in colour. ; many of the systems in which we live exhibit. Fractals: A fractal is a never-ending pattern. This book offers a fun and enriching introduction to chaos theory, fractals and dynamical systems, and on the applications of fractals to computer generated graphics and image compression. L. ”. See more ideas about tattoos, tattoo designs, tribal lion. Authors. Loss of “complexity” and aging: potential applications of fractals and chaos theory to senescence. Abstract and Figures. Lancet (1996) B. In a previous post, I discussed chaos theory, fractals, and strange attractors – and their implications for knowledge and prediction of systems. Discover Pinterest’s 10 best ideas and inspiration for Fractal tattoo. edu. Chaos theory and fractal geometry have begun to appear as an important issue in secondary school mathematics. The concept is extended to the time series analysis, and the time series in. On one hand it puts an end to the dream of full predictability of deterministic dynamical systems, on the otherChaos Theory The theory of Dynamical Systems (more popularly known asChaos Theory) focuses on the behavior occurring in a system underiteration. Drawing Machine. Chaos theory seeks to reveal the general structure of the system. 26, neither one dimensional nor two (Brigs 70). See more ideas about chaos theory, chaos, fractals. " on Pinterest. Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. This book provides an elementary introduction to chaos and fractals. If you rolled a 1 or 2, then draw a new point (x0,y0) ( x 0, y 0) whose distance is half way between the points (x,y) ( x, y) and (1,2) ( 1, 2). physics, information theory and electronics. Show more. Systems of. See more ideas about chaos theory, chaos, chaos tattoo. name "chaos theory" leads the reader to believe that mathematicians have discovered some new and definitive knowledge about utterly random and incomprehensible phenomena; however, this is not entirely the case. Get inspired and try out new things. Chaos Theory. inspired by the Video Game Splinter Cell: Chaos Theory. edu. 2. The so-called butterfly effect has become one of the most popular images of chaos. chaos is associated with complex, "random" behavior and forms of unpredictability. The idea is that the flapping of a butterfly’s wings in Argentina could cause a tornado in Texas three weeks later. A. First Iteration At the earliest drawing of the fractal curve, few clues to the underlying mathematical structure. Fractal dimension is one of the best known parts of fractal analysis. New concepts like “strange attractors” and “fractals” resulted in the view that turbulence may be regarded as a manifestation of “deterministic chaos”. Maths In Nature. Fractal Patterns. Designed by Jonas T. Fractals and Chaos theory is a branch of mathematics, where chaos theory is focusing on the study of chaos—states of dynamical systems whose. The modeling and evolution analysis using fractional calculus theory has attracted more and more scholars’ attention [1]. Chaos Theory. There is a fundamental connection between chaos theory and fractal geometry. See more ideas about chaos tattoo, chaos, symbolic tattoos. Unique Sierpinski Triangle Posters designed and sold by artists. Apr 27, 2022 - Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations. See more ideas about fractal curve, fractals, quilts. It does this by pushing pixels apart and filling in the gaps. Apr 8, 2020 - Explore Ignota's board "chaos theory. 1 Theory of Chaos Analysis. Scientists from different fields have begun to observe the regular patterns within the irregularity of the natural world. 2 (2004. See more ideas about chaos theory, fractals, fractal art. Series E-ISSN 1860-0840. Mar 2, 2015 - Explore Shane's board "Fractal Geometry" on Pinterest. Mathematicians tend to rank fractal dimensions on a series of scales between 0 and 3. Crossref Medline Google Scholar; 14 Goldberger AL. Despite extensive studies on HRV using chaos theory, 1–10 fractal scaling analysis, 11–15 and many other methods in the last two decades, the issue of whether HRV is chaotic or stochastic remains highly controversial. Right, a fractal process such as heart rate regulation generates fluctuations on different time scales (temporal "magnifications") that are statistically self-similar. Chaos theory is the study of non-linear systems that are impossible to predict or control. Feb 3, 2021 - Explore AYA AYITA ARƎЯA's board "CHAOS THEORY" on Pinterest. The dragon curve is probably most commonly thought of as the shape that is generated from repeatedly folding a strip of paper in half, although there are other curves. Update images of fractal art tattoo by website es. 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. By dragging the sliders and the Locator, confirm and answer the following: • the limit exists for any , , and and . [Google Scholar] 4. . Top 130+ fractal art tattoo latest. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula. evolution and order. H. Chaos also refers to the question of whether or not it is possible to make good long-term predictions about how a system will act. The theoretical fractal dimension for this fractal is 5/3 ≈ 1. chaos theory, in mechanics and mathematics, the study of apparently random or unpredictable behaviour in systems governed by deterministic laws. PDF | On Nov 1, 2012, Eulanda Sanders published Fractal. Alongside fractals, chaos theory ranks as an essentially universal influence on patterns in nature. [1] They were introduced in 1981. Crossref Medline Google Scholar; 10 Goldberger AL. Fullscreen. thdonghoadian. Almost all fractals are at least partially self-similar. As I have argued in this essay, these intentional uses of chaos and fractals in fiction fall into four broad categories. The use of fractal mathematics and chaos theory presents significant difficulties both at the level of the theory and at the level of application. Chaos theory explains that within the visible. He has authored or coauthored about 500 scientific papers in these and related fields. Mandelbrot set. From the literature survey, it has been observed that non-linear techniques remain a black box for most of the authors who preferred to use linear filtering, feature. Discover (and save!) your own Pins on PinterestThe approaches of chaos theory and fractal mathematics point to the same targets, and the synergy of these two perspectives will be explored. J R Stat Soc Ser B (Methodological) (1992). Thus, the "chaos" that Pollock denied was not only present but was apparently evidence of a underlying structure and order that Chaos Theory could. Causes: a soccer team loses the world cup. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. The study of fractal geometry and chaos theory are two examples of new fields in mathematics that have been popularized in the past 30 years, in large part due to the availability of high-speed computers. Start counting. Chaos also refers to the question of whether or not it is possible to make good long-term predictions about how a system will act. Feb 12, 2019 - Explore Jim Lonnevik's board "Chaos Theory", followed by 1,291 people on Pinterest. 1996; 347:1312–1314. . Chaos under control: The art and science of complexity. 2. See more ideas about chaos theory, chaos, fractals. In the equation y kx(1 x), take k 3 and a starting value of x 0. A classic example of this is. The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any. The archetype of all theories of dynamics is that of Newton, concerning celestial motions. Phys. Objects having a fractional dimension are termed as a fractal. Lancet. 1. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some. Fractals, Fractal art, Fractal design. Interdisciplinary Research on Chaos Theory 5. Chaos theory is the extensive study of evidently random or uncertain behaviour in bodies or events controlled by deterministic laws. Apr 27, 2022 - Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations. He has used fractals to model a diverse range of phenomena in science and technology, but most specifically plant structures. The book includes over 200 end-of-chapter exercises. The Mandelbulb is a three-dimensional fractal, constructed for the first time in 1997 by Jules Ruis and in 2009 further developed by Daniel White and Paul Nylander using spherical coordinates. So of course, chaos theory started a race among scientists to understand what happens when a system moves from a point of stability to a mess of infinite instability. They cannot be truly predicted. 8. carl jung, fibonacci spirali, kelebek etkisi hakkında daha fazla fikir görün. A fractal dimension is an index for characterizing. Individual molecules of air all conform to basic laws of physics, but global weather patterns are anything but simple. Small differences in initial conditions (such as those due to rounding errors in numerical computation or measurement uncertainty) yield widely diverging outcomes for such. This chapter provides an introduction to chaos theory and fractal geometry to aid the reader in following the arguments presented in the next chapters. In contrast, the price of a mean-reverting stock. 2). A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems. Abstract. There is a relationship between chaos and fractals—the strange attractors in chaotic systems have a fractal dimension. Mandelbrot Fractal. The main precept behind this theory is the underlying notion of small. Pick apart any number of equations in geometry, physics, probability and statistics, even geomorphology and. 1990; 120:1419–1440. Applications of it can be extensively found in variety of disciplines such as modeling [6,7], optimization [8], stock market [9], photovoltaic plant [10], fashion cycle model [11], and other [5. Chaos is the science of surprises, of the nonlinear and the unpredictable. 98 1 Used from $21. 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. Examples include the swings of a pendulum clock, and the heartbeat while resting. Chaos Theory. edu. Biological systems and processes are inherently complex, nonlinear and nonstationary, and that is why nonlinear time series analysis has emerged as a novel methodology over the past few decades. Of course, the application of chaos theory cannot solve all problems, but such an interdisciplinary approach may increase the understanding of. Trajectories within a strange attractor appear to skip around randomly. 1992; 267:1806–1809. Abstract and Figures. Pinterest. Multiscroll attractor. Atoms are composites of elementary particles and follow the same equations and behavior. A very small change may make the system behave completely differently. It teaches us to expect. A subtly different claim of precedence has been made by Hubbard, who is now considered one of the world's experts on the Mandelbrot set. In the mathematics of dynamical systems, the double-scroll attractor (sometimes known as Chua's attractor) is a strange attractor observed from a physical electronic chaotic circuit (generally, Chua's circuit) with a single nonlinear resistor (see Chua's diode ). What are chaos and fractals? When large iterations of complex computations were first enabled by computers, strange phenomena were revealed 1,2, such as contradicting results from weather models despite increased computational precision. 56). In 1989 his interests turned to nonlinear dynamics, chaos, fractals, and complexity. The character was inspired in part by American historian of science James Gleick and French mathematician Ivar Ekeland. Fractal tattoo with Persian god in fine geometry. Veja mais ideias sobre geometria, desenho geometrico, proporção áurea. Chaos is often caused by chains of cause and effect whereby a small cause can eventually be amplified to greater and greater effects. From 2008 - 2022 he was Managing Partner and Co-Director of Global Macro at First Quadrant, LLC in Pasadena, CA. Chaos theory is a mathematical theory, and it is still in development. 23-ott-2013 - Esplora la bacheca "FRACTAL" di Michela Balzarini su Pinterest. Dates: 5/21/79, 11/12/86, 8/27/10. The limit of the process produced is the fractal. For example: Initial Condition: uncomfortable pillow. Explore. She, with co-authors, has published 9 journal papers like SIAM Journal on Applied Dynamical Systems, Nonlinear Dynamics, Communications in Nonlinear Science and Numerical Simulation, Fractals, International Journal. This results from the fractal curve–like properties of coastlines; i. Even so, this system and its motions are complex and extremely intriguing. Mary Selvam J. If you look at a fractal pattern and zoom in on any segment, that segment will look like the larger section you started with. The archetype of all theories of dynamics is that of Newton, concerning celestial motions. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaos Theory can help ‘tame’ complexity, uncertainty (that we think as random) and make them more ‘modelable’ (less uncertain) Spatial patterns and Temporal patterns can be better predicted by looking at the fractal nature – rainfall is fractal is space (if clouds are), so its. Example: f(x) = x2. Nonlinear means that due toChaos Theory is, in effect, the science of surprises, the nonlinear, and the unpredictable. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot in the late 1970s, but objects now defined as fractal in form have been known to artists and mathematicians for centuries. inspired by the Video Game Splinter Cell: Chaos Theory. IFSs provide models for certain plants, leaves, and ferns, by virtue of. A basis for chaos is established in the Butterfly Effect,. Magic Hour. Some researchers suggest that applying chaos theory to the classroom enhances learning by reinforcing systemicFractal Markets Hypothesis (FMH): An alternative investment theory to the widely utilized Efficient Market Hypothesis (EMH) , Fractal Market Hypothesis (FMH) analyzes the daily randomness of the. The acceptable definition of chaos theory states, chaos theory is the qualitative study of unstable aperiodic behavior in. Patterns of chaos in nature are all around us. A more accurate term, deterministic chaos , suggests a paradox because it connects two notions that are familiar and commonly regarded as incompatible. Freeman and Company. Chaos theory considers learning holistic, constructive, and dynamic. It introduces the key phenomena of chaos — aperiodicity, sensitive dependence on initial conditions, bifurcations — via simple iterated functions. Jan 13, 2012 - This Pin was discovered by Dan Johnson. Tem. It concludes that chaos theory is most useful as an. Richard Taylor is an expert in chaos theory, fractals, and the relationship between art and science. Explore. Lancet. I would like to work in a couple dates, so to speak, into the formula for the fractal to commemorate some important life events. Alongside fractals, chaos theory ranks as an essentially universal influence on patterns in nature. Mandelbrot's definition-"a set whose Hausdorff dimension is not an integer" -is clear in. Series ISSN 1860-0832. Also available at Amazon and Kobo. In this paper, a new fractional-order seed chaotic generator is designed to solve the problem of the complex operations of single low-dimensional systems and simple high-dimensional systems. Mitchell Jay Feigenbaum / ˈfaɪɡənˌbaʊm / (December 19, 1944 – June 30, 2019) was an American mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants . It is true, the whole world IS in chaos right now. Grenfell Chance and chaos in measles dynamics. Potential applications of fractals and chaos theory to senescence. The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system’s behavior. e. 5 and a starting value of x 0. What are the fates of differentorbitsunder iteration of f? xn+1 = f(xn)Sep 8, 2015 - Explore Kimbra Masika Rose's board "Fractals/Fibbonacci sequence" on Pinterest. chaos of paint. 2. Fractal Tattoo. Its name reflects its pareidolic resemblance to. Fractals – Often refers to the geometry of the objects. In these drawings Rössler starts with a dynamic system known. 24/mai/2023 - Explore a pasta "geometria" de Renato Carriti, seguida por 224 pessoas no Pinterest. This website was written in conjunction with a talk given for Intermediate Physics Seminar. Fractal Geometry. "The book is written for everyone who wants to learn details of chaos theory and fractal geometry, also for readers who have not much knowledge of technical mathematics. Touch device users. Ruin. Chaos theory is a part of mathematics. Kulkarni. Heart rate (HR) variability has been conventionally analyzed with time and frequency domain methods, which measure the overall magnitude of R-R interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Storytellers embraced its principles and worked them into their novels, films and plays. The study of fractal geometry and chaos theory are two examples of new fields in mathematics that have been popularized in the past 30 years, in large part due to the availability of high-speed computers. An "epsilon cross" is a cross-shaped orbit trap . . edu. Lorenz equations used to generate plots for the y variable. The chaos theory is a revolutionary approach to understanding and forecasting the behavior of financial markets. Pethkar and M. The Lancet Essay Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside A. Wells’s The Island of Dr. Let be a polynomial and denote its iterate by . Chaos and randomness are no longer ideas of a hypothetical world; they are quite realistic here in the status quo. When chaos theory is combined with fractal geometry, the math further predicts the behavioral dynamics observed in our physical reality, from weather patterns to human physiology, from social patterns to market prices on the stock exchange. This system demonstrates chaos theory and how small variations lead to large changes. Apr 12, 2018 - Explore DesignedByEddie's board "Cool Fractals", followed by 360 people on Pinterest. A NON-DETERMINISTIC CELL DYNAMICAL SYSTEM MODEL FOR FLUID FLOWS: A STRING THEORY FOR FRACTAL SPACETIME Based on Townsend's. A small perturbation in the initial setup of a chaotic system may lead to drastically different behavior, a concept popularly referred to as the butterfly effect from the idea that the actions of a butterfly may dramatically alter the physical state of the rest of the world. Also, such objects are self-similar in nature; thus, their shape is independent of the scale and remains the same under dilatation or contraction. This work is an extension of his earlier research on fractals, chaos theory and behavioral finance. vn compilation. Fractal geometry and chaos theory are closely related to each other by the concepts ofscaling, and iteration (recursive composition). Conventionally, HR variability has been analyzed with time and frequency domainmethods. If you had precise information about every object right now, you could use the laws of physics to predict what would happen in the future.