Chaos is the science of surprises, of the nonlinear and the unpredictable. Fascinating rhythm: a primer on chaos theory and its application to cardiology. This study provides an overview encompassing multi-chaos, fractal, fractional and Artificial Intelligence (AI) way of. Fractal Geometry. Crossref Medline Google ScholarJulien Clinton Sprott. The values for ho, sigma and eta were 45. Show more. There is a relationship between chaos and fractals—the strange attractors in chaotic systems have a fractal dimension. Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and meteorology. 2. Designed by Jonas T. New concepts like “strange attractors” and “fractals” resulted in the view that turbulence may be regarded as a manifestation of “deterministic chaos”. 2017 - Entdecke die Pinnwand „Mandelbrot“ von David Voge. Fractals. X Tattoo. [1] Chaos theory states that within the. Her current research interests are control theory of chaos, fractal in social, financial and economic systems and its applications. Also, such objects are self-similar in nature; thus, their shape is independent of the scale and remains the same under dilatation or contraction. Contributed by: Rob Morris and Rickey Bowers Jr. Pinterest. 1990; 120:1419–1440. Atoms are composites of elementary particles and follow the same equations and behavior. 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. The mathematical beauty of fractals lies at. Abstract. Dates: 5/21/79, 11/12/86, 8/27/10. And fear is rampant, anger and. (Brigs 65). Abstract. Wikimedia Foundation. Menger sponge. Jun 25, 2019 - Explore nezar BİLEN's board "Chaos theory" on Pinterest. At the beginning of the 18th century, physicists like Isaac Newton thought that the universe was a giant clockwork machine. chaos theory, in mechanics and mathematics, the study of apparently random or unpredictable behaviour in systems governed by deterministic laws. The use of fractal mathematics and chaos theory presents significant difficulties both at the level of the theory and at the level of application. A. As a mathematics field, it has focused on the dynamical systems’ behavior with extreme sensitivity to primary conditions. Kotel’nikov IREE RAS for exactly 35 years. 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. These sensitive nonlinear dynamical systems have now been explained using chaos theory and fractal geometry. The Mandelbrot set is an example of a fractal in mathematics. the theory of chaos for financial markets is a set of rules for the behavior of markets in general, and some parts and. Lancet 1996; 347 :1312-1314. In the momentum regime, returns are positively correlated. See more ideas about tattoos, tattoo designs, tribal lion. The use of fractal mathematics and chaos theory presents significant difficulties both at the level of the theory and at the level of application. The 20 best chaos theory books recommended by Peter Jukes, Charlie Munger and Nic 'It's Over' Carter, such as Chaos and Math Geek. Thanks to LastPass for sponsoring this video. Linear and Nonlinear Dynamics and Vibrations Laboratory at the University of Illinois Diarsipkan 2005-12-15 di Wayback Machine8. Chaos theory provides a radically different framework for studying complex dynamics. Dates: 5/21/79, 11/12/86, 8/27/10. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and. It explains the duality behavior of financial markets modeled by these two theories, and more importantly, on how they are related to quantum finance for financial engineering in contemporary financial institutions. In the equation y kx(1 x), take k 3 and a starting value of x 0. It teaches us to expect the unexpected. Analysis of HR dynamics by methods based on nonlinear systems theory has opened a novel approach forstudying the abnormalities in. Touch device users, explore by touch or with swipe gestures. JAMA. vn compilation. Watch. Results were obtained in two urban dwellings for family use and for two different. The Lancet Essay Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside A. Have you ever thought about your life as a fractal? Have you embraced the infinite? PhD student Robin Andrews explains the chaotic theory you will find everywhere. It enables the description of a series of phenomena from the field of dynamics, ie, that field of physics concerning the effect of forces on the motion of objects. Discover Pinterest’s 10 best ideas and inspiration for Fractal tattoo. Wall Stickers Murals. 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). A system is simply a set of interacting components that form a larger whole. Circuit Board Tattoo. Probably not, but maybe I could at least show them a photo… My appointment was with the same tattoo artist that Goth Girl used. Google Scholar. K. Lancet. II. Conventionally, HR variability has been analyzed with time and frequency domainmethods. Interdisciplinary Research on Chaos Theory 5. There are also images related to simple fractal tattoo, sacred geometry fractalModern portfolio theory: Fractal portfolio theory: Connections: The EMH is a special case of FMH, while the FMH expands the meaning of the EMH; the EMH and the FMH have inherent Uniformity. 00. Apr 27, 2022 - Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations. 5. Chaos theory and fractal geometry have begun to appear as an important issue in secondary school mathematics. 4. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers, etc. Presently, there are several journals dedicated solely to the study of chaos. A list of mathematical and physical topics relating chaos theory applied to atmosphere sciences is given in Sec. (bitRAKE) (March 2011)The fractal mathematics Mandelbrot pioneered, together with the related field of chaos theory, lifts the veil on the hidden beauty of the world. • Chaos Theory represents a big jump from the way we have thought in the past – a paradigm shift. The word usually carries a negative connotation involving undesirable disorganization or confusion. 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. Description. This comes from the discrete-time dynamical system. Chaos Theory and Applications (June 2020-Volume 2-Issue 1) Authors: Murat Erhan Çimen. Fullscreen. This fractal tattoo creates balance between chaos and order because it was spawned by the coupling of a Julia set and a Sierpinski carpet. The relationship between the mathematics of chaos and probabilistic notions, including ergodic theory and uncertainty modeling, are emphasized. Chaos theory is usually defined as, “ The branch of mathematics focusing on the behaviour of dynamical systems that are highly sensitive to initial conditions. Studies by many economists and physicists have shown that the financial system is an open, complex. Big data tec hnologies make it possible to approximate the. 9. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. 00001. See more ideas about fractals, sacred geometry, fractal art. Interdisciplinary Research on Chaos Theory 5. 1 Theory of Chaos Analysis. Deterministic chaos paints a mathematically different. [Google Scholar] Woo MA, Stevenson WG, Moser DK, Middlekauff HR. 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. The exact details can be viewed in its open source code. See more ideas about chaos theory, chaos, fractals. In this paper, the author explores a need for a greater understanding of the true nature of human–system interactions from the perspective of the theory of complex adaptive systems, including the essence of complexity, emergent properties of system behavior, nonlinear systems dynamics, and deterministic chaos. This means that a part of the fractal is identical to the entire fractal itself except smaller. When autocomplete results are available use up and down arrows to review and enter to select. In this figure, we show how a single sub-triangle at prefix (x) is transformed to the sub-triangle at prefix (a cdot x) where (a) is the vertex chosen by. Wells’s The Island of Dr. Get inspired and try out new things. Lancet. 3. 4. 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. Fractal tattoo with repeating geometric patterns in colour. Chapters. 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. ”. It was Gleick who, in his epoch-making 1980 book Chaos: The Making of a New Science (public library), did for the notion of fractals what Rachel Carson did for the notion of ecology, embedding it in the popular imagination both as a scientific concept and as a sensemaking mechanism for reality, lush with material for metaphors that now live in. chaos of paint. Universe Tattoo. Extant theories of careers had largely ignored these. Potential applications of fractals and chaos theory to senescence. are illustrated above, where the letters to stand for coefficients of the quadratic from to 1. There are also images related to14. Pick apart any number of equations in geometry, physics, probability and statistics, even geomorphology and. On the surface, chaos theory sounds like something completely unpredictable, but fractal geometry is about finding the order in what initially appears to be chaotic. 347:1312–14,1996. It teaches us to expect the unexpected. 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. Background: Dynamic analysis techniques may quantify abnormalities in heart rate variability (HRV) based on nonlinear and fractal analysis (chaos theory). Chaos is the science of surprises, of the nonlinear and the unpredictable. The beginning of its application coincided with the transition of finance to the use of big data. Update images of fractal art tattoo by website es. What appears to be the broadest framework for the exactly computable moment theory of p-balanced measures — that of linear i. Chaos Theory. Crossref Medline Google ScholarThe drawing corner includes four pages covered in blue-ink sketches by Otto Rössler, a German biochemist who works on chaos theory. 144 (4), 2005)The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. It is a mathematical branch with applications in physics, economics, engineering. the overarching patterns-of-patterns within which human cultures. The first step is the same as in the. Using these approaches to characterize physiological signals (a subfield commonly referred to as “fractal physiology” [ 1 ]) has shown promising results in the. Goldberger AL. Causes: low moral in a country. 269. Fractal Tattoo. 1. Choose any arbitrary point (x,y) ( x, y) anywhere on the plane either inside or outside the triangle. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. xn+1 = rxn(1−xn), x n + 1 = r x n ( 1 − x n), where r r is a parameter you can vary. For a while, in the 1980s and early 1990s, chaos was touted as the next big revolution in science, on par with quantum mechanics. A work of popular science in the tradition of Stephen Hawking and Carl Sagan, this 20th-anniversary edition of James Gleick’s groundbreaking. It’s not just that different iterated maps give qualitatively similar results; when one measures the convergence rate this turns out be exactly and quantitatively the same—always δ ≃. However, the. One great example is the pendulum. They cannot be truly predicted. 2 2. Moreover, fractal geometry is applied in many radiographic analyses. Prior to joining First Quadrant he spent 23 years with PanAgora Asset Management where he was over time an equity. 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 . Manus J. This chapter introduces two vital contemporary finance engineering theories: chaos and fractals. When autocomplete results are available use up and down arrows to review and enter to select. This is definitely a tattoo idea for. You can produce an infinite variety of fractals just by changing a few of the initial conditions of an equation; this is where chaos theory comes in. Objects having a fractional dimension are termed as a fractal. Complexity - Chaos, Fractals, Science: One of the most pernicious misconceptions about complex systems is that complexity and chaotic behaviour are synonymous. 1. There are also images related to simple tattoo, tattoo for girls, fibonacci fractal tattoo, chaos theory fractal tattoo, negative space fractal tattoo, simple fractal tattoo, minimalist fractal tattoo, sacred geometry fractal tattoo, geometric fractal tattoo, small. 3. Reading material and additional slides. Fractal Art. === Musashi-Fractal-Dimension === This tool is part of my research on the fractal nature of the markets and understanding the relation between fractal dimension and chaos theory. However, chaos is not a random motion. In the equation y kx(1 x), take k 3 and a starting value of x 0. their structures. 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). Fractal Design. A canonical 3-dimensional Mandelbrot set does not exist, since. von Schilling, in International Encyclopedia of Human Geography, 2009 Chaos Theory. 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. Abstract. Donahue's Chaos Theory & Fractal Geometry Project Diarsipkan 2005-03-12 di Wayback Machine. Benoit B. Patterns of Chaos. " (F. . As computers and knowledge became more powerful chaos theory could become a larger part of evaluating and predicting in financial markets. There is a relationship between chaos and fractals—the strange attractors in chaotic systems have a fractal dimension. A plot of Lorenz's strange attractor for values ρ=28, σ = 10, β = 8/3. Parametric Design. 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. Having said that, here are some more ideas for both men and women to get a fractal tattoo: Psychedelic fractal tattoo. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. 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. Expand. In the 1970s the turbulence problem became associated with the theory of nonlinear dynamical systems, in the popular parlance often labelled as “chaos theory”. 4 Proposed Method 3. 13. Chaos theory is a part of mathematics. Lancet (1996) B. Books Categories Experts Reading List. The chaos theory is a revolutionary approach to understanding and forecasting the behavior of financial markets. Indeed, the world of mathematics and science has, untilChaos is the science of surprises, of the nonlinear and the unpredictable. Fractal geometry and chaos theory are closely related to each other by the concepts ofscaling, and iteration (recursive composition). Lancet. The main MATLAB function that we use for this process is Boxcount. A. Linear and Nonlinear Dynamics and Vibrations Laboratory at the University of Illinois Diarsipkan 2005-12-15 di Wayback Machine On the basis of nonlinear theory, chaos theory is “a kind of science concerning process and evolution, rather than state and existence (p. " on Pinterest. Chaos Theory, a combination of conceptual, mathematical and geometric methods, deals with nonlinear, complex and dynamic systems characterized by its fractal structure (Gokmen, 2009; Tuna-Orhan, 2013). This work is an extension of his earlier research on fractals, chaos theory and behavioral finance. For example, L-systems form convincing models of different patterns of tree growth. Earnshaw H. At the University of Oregon, he is a professor of physics, psychology and art, and the director. . If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age. This is why even large computers cannot tell the weather for more than a few days. Chapters. Fractals are introduced as self-similar geometric objects and analysed with the self-similarity and box-counting. Julie Belaval. See more ideas about fractals, fractal art, sacred geometry. Touch device users, explore by touch or with swipe gestures. Kulkarni. Chaos theory “attempts to systemize that which appears to function outside of any system. See more ideas about chaos theory, chaos, fractals. ANNOUNCEMENT (March 13): Due to new directives from the university, we have to suspend in-person classes. After discussing the central premises of the theory itself, it applies chaos theory to issues management, the evolution of interest groups, crises, and rumors. This chapter provides an introduction to chaos theory and fractal geometry to aid the reader in following the arguments presented in the next chapters. The edging of the set shows a self-similarity, which is perfect, but because of the minute detail, it looks like it evens out. L. See more ideas about geometry, fractal geometry, fractals. Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Keywords: Chaos theory, Fractals, Sensitive dependence on initial conditions (SDIC) Introduction The word Chaos comes from the Greek word “Khaos”, meaning “gaping void”. Deterministic chaos, fractals and quantumlike mechanics in atmospheric flows, Can. Chaos Theory is a delicious contradiction - a science of predicting the. First, there are reasons that have nothing to do. 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. About this book. Apr 27, 2022 - Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations. Topics Applications of Nonlinear Dynamics and Chaos Theory, Vibration, Dynamical Systems, Control, Complex Systems, History. 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. ”. Vintage Poster Art. In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Analysis of HR dynamics by methods based on chaos theory and nonlinear system theory has. This special issue of the European Physical Journal Special Topics titled “Frontiers of Fractals for Complex Systems: Recent Advances and Future Challenges” is a collection of cutting-edge research proposing the application of fractal features to the dynamics of highly nonlinear complex systems. Multiscroll attractor. In this paper, a novel metaheuristic algorithm called Chaos Game Optimization (CGO) is developed for solving optimization problems. Chaos is often caused by chains of cause and effect whereby a small cause can eventually be amplified to greater and greater effects. 1996; 347:1312–1314. Chaos theory means deterministic systems can be unpredictable. Get inspired and try out new things. Tangle Doodle. 2. It is also called the. Of course, the application of chaos theory cannot solve all problems, but such an interdisciplinary approach may increase the understanding of. See more ideas about fractals, fractal art, fibonacci. The Buddhabrot is the probability distribution over the trajectories of points that escape the Mandelbrot fractal. Dec 2, 2016 - The Lorenz Attractor, named after Edward Norton Lorenz, The Father of Chaos Theory, is a fractal structure corresponding to the long-term behavior of the Lorenz Oscillator. 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. To take full advantage of this indicator, you need to incorporate some principles and concepts: - Traditional Technical Analysis is linear and Euclidean, which. 56). 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. Causes: bad night's sleep. in pathology, neuropsychiatry, cardiology. •. 4. Chaos theory is a mathematical theory, and it is still in development. As you have seen, the motion can be descr. However, these tools are embedded in the. There is a fundamental connection between chaos theory and fractal geometry. Although the "paradox of length" was previously noted by Hugo Steinhaus, the first systematic study of. Chaos theory in the social science of education was adapted from chaos theory in physics and mathematics (Harshbarger, 2007). The Julia sets, for example, are complex fractals that are formed from the sets of repelling periodic points of the mapping 𝑐( )= 2+ أخبار عاجلة. Fractal patterns are everywhere: in mathematics 1, industry 2, the stock market 3, climate science 4, galaxies 5, trees 6, and even in the films we watch and games we play 7,8 (). Chaos theory is the qualitative study of unstable periods in deterministic nonlinear. See more ideas about photo manipulation, surreal photo manipulation, surreal photos. Raei R. I decided a cool thing to get would be a bifurcation diagram showing the period doubling route to chaos. Chaos theory is the extensive study of evidently random or uncertain behaviour in bodies or events controlled by deterministic laws. JAMA. Thus, a fractal is infinitely complicated. See more ideas about fractal geometry, fractal art, sacred geometry. Share images of fractal tattoo by website tnbvietnam. Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. There is a fundamental connection between chaos theory and fractal geometry. Find and save ideas about chaos theory on Pinterest. It describes a world in which there is chaos in order, but also order in chaos. They are created by repeating a simple process over and over in an ongoing. Fractal Chaos. This system demonstrates chaos theory and how small variations lead to large changes. S. Figure 3 empirically confirms a fact known from chaos theory that whenever a fractal represents full chaos, the ruler dimension may be greater than 2 (Peitgen et al. For example: Initial Condition: uncomfortable pillow. In the second equation, a transitio between two different types of horseshoe chaos (spiral chaos and screw chaos) is possible. Star Trek Tattoo. Grenfell Chance and chaos in measles dynamics. 1994). The very name "chaos theory" seems to contradict reason, in fact it seems somewhat of an oxymoron. Hexagonal fractal tattoo designs on sleeve. This set, {z} {z}, is what became known as the Cantor set. e. It describes the theory of fractals, focusing on the importance of scaling and ordinary differential equations. Thus the relationship of quantum mechanics with deterministic chaos ( which is the chaos used in physics) is similar to the relationship a Picasso picture has to the atoms and molecules composing it. The concept is extended to the time series analysis, and the time series in. Discover Pinterest’s 10 best ideas and inspiration for Chaos theory. Visualizza altre idee su frattali, arte frattale, immagini. Chaos and tur- bulence are two of the three phases of the standard dy- namics [1,2]; some cases of turbulence are fractal. For small values of r r, there’s a single, stable equilibrium at the origin. Jul 16, 2017 - Explore Ibrahim Ajeez's board "chaos theory" on Pinterest. vn September 16, 2023. For example, unlike the behavior of a pendulum, which adheres to a predictable pattern a. " Chaos, Solitons & Fractals 19. In 1883 Georg Cantor, who attended lectures by Weierstrass during his time as a student at the University of Berlin [9] and who is to set theory what Mandelbrot is to fractal geometry, [3] introduced a new function, ψ , for which ψ' = 0 except on the set of points, {z} {z}. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. That is the chaos theory. Start counting. Abstract Tattoo Designs. The Chaos Theory of Careers (CTC) was developed at the turn of the Millenium to address complexity, change and chance in career development. 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. It concerns a cyclic attractor. Fractals – Often refers to the geometry of the objects. Nearly all nontrivial real-world systems are nonlinear dynamical systems. 3 Fractal Dimension Computation of an MRI Volume of the Brain White Matter with a Boxcount-Based MATLAB Script. 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. Top 130+ fractal art tattoo latest. Option 1: Draw a fractal triangle. Apr 14, 2018 - Explore Amy Stephens Wulfekuhl's board "chaos tattoo" on Pinterest. The debate can hardly be settled if one does not go beyond the standard theories of chaos and random fractals, since the. Dynamical systems theory applied to management accounting: chaos in cost behaviour in a standard costing system setting. edu. In recent decades, nonlinear dynamics ("chaos theory") and fractal geometry have provided powerful new tools to analyze physiological systems. Chaos Theory: A mathematical concept that explains that it is possible to get random results from normal equations. Mid-sized branches of a tree are remarkably similar in shape. ISBN: 978-981-12-7326-1 (ebook) USD 30. Architecture Tattoo. Continuing the Post-Modern perceptions of cosmos, chaos theory, fractals… have arrived on the scene. Instructor: Matilde Marcolli. Jun 17, 2013 - Explore Rhiannon Noon's board "Time Ideas" on Pinterest. In mathematics, iterated function systems ( IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. Additionally, the “process” and “evolution” are two of the most important characteristics of Chinese traditional music, embodied in the music texts as well as its inheritance. Introduction. Initially, it explains complexity economics, as the economic discourse of Chaos Theory. Goldberger. It teaches us to expect the unexpected. edu. Tree. PDF | On Nov 1, 2012, Eulanda Sanders published Fractal. 1 Recommendation. Source: UnsplashChaos Theory. Initially, Williams' ideas aroused much controversy because of their revolutionary nature. In the last example, we show how to calculate the FD of a 3D volume representing the brain white matter. Traditionally, this discrete chaos is controlled. even within yourself. 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. Chaos also refers to the question of whether or not it isThis paper presents a thorough review of chaos theory and its application in image encryption schemes. Discover Pinterest’s 10 best ideas and inspiration for Chaos theory. Chaos theory explains why some phenomena are unpredictable even though the phenomena are described by mathematical equations that are known perfectly well. How a double pendulum.