"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. === 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. In mathematics, the term chaos game originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it. Chaos theory considers learning holistic, constructive, and dynamic. 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. Fractal Tattoo. 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. 00. Fractals are introduced as self-similar geometric objects and analysed with the self-similarity and box-counting. Fractal Art. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. 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. The mathematical beauty of fractals lies at. edu. How a double pendulum. An "epsilon cross" is a cross-shaped orbit trap . Jun 25, 2019 - Explore nezar BİLEN's board "Chaos theory" on Pinterest. He referred to himself as a "fractalist" and is recognized. 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 teaches us to expect the unexpected. 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. Earnshaw H. Wells’s The Island of Dr. A NON-DETERMINISTIC CELL DYNAMICAL SYSTEM MODEL FOR FLUID FLOWS: A STRING THEORY FOR FRACTAL SPACETIME Based on Townsend's. Systems of. Her current research interests are control theory of chaos, fractal in social, financial and economic systems and its applications. In fact Mandelbrot eventually proved that Lorenz's attractor was a fractal, as are most strange attractors. Grenfell Chance and chaos in measles dynamics. The edging of the set shows a self-similarity, which is perfect, but because of the minute detail, it looks like it evens out. Chaos theory is the study of how systems that follow simple, straightforward, deterministic laws can exhibit very complicated and seemingly random long term behavior. It has been revealed that highly variable data from physiological, pharmacokinetic, and pharmacodynamic studies, in contrast to errors in measurement, have their origins in nonlinear dynamical systems that can be described by chaos theory. By vova. The article emphasizes clinical and prognostic significance of dynamic changes in short-time series applied on patients with coronary heart disease (CHD) during the exercise. The economic system is an extremely complex nonlinear system involving many subject factors. By gboeing. Multiscroll attractor. 1998; 48:1697–1699. 4. A. This is why even large computers cannot tell the weather for more than a few days. 9. It is often described by fractal mathematics, which captures the infinite complexity of nature. Initially, Williams' ideas aroused much controversy because of their revolutionary nature. JAMA. Math Art. Fractal geometry and chaos theory are two branches of mathematics that deal with complex and dynamic systems, such as natural phenomena, human behavior, and financial markets. Abstract. Casino legal online gambling, casino online ireland; Tatuaje casino, tatuaj cazinou; Casino constanta vector, csgo casino minesweeper minBenoit B. L. 2. 8 Chaos and Fractals C5 A Chaos In problems 1–4, follow the procedure of Example 1 to find the possible attractors. It is named after Benoît Mandelbrot, a Polish-French-American mathematician. The fern code developed by Barnsley is an example of an iterated function system (IFS) to create a fractal. Get inspired and try out new things. It also deals with systems that appear to be chaotic, but, in fact, have underlying order. 92, 16 and 4 respectively. In the equation y kx(1 x), take k 3 and a starting value of x 0. Mar 2, 2015 - Explore Shane's board "Fractal Geometry" on Pinterest. edu. This tattoo design is essentially an incredibly complex yin yang because it balances two opposing forces. A key lemma in our proof shows that each step of the chaos game moves a point on the Sierpinski triangle to another point on the triangle. Initially, it explains complexity economics, as the economic discourse of Chaos Theory. L. Furthermore, chaos theory has a dual character. ,. Heart failure and ischemic heart disease are associated with a loss of long-range fractal-like correlations in HR, and this loss of complexity is associated with. Image courtesy William Harris/HowStuffWorks. After discussing the central premises of the theory itself, it applies chaos theory to issues management, the evolution of interest groups, crises, and rumors. Chaos theory is a mathematical theory, and it is still in development. The theory of complexity loss in aging and disease, as currently formulated, has two central postulates: 1. Mathematicians tend to rank fractal dimensions on a series of scales between 0 and 3. Today. In the second equation, a transitio between two different types of horseshoe chaos (spiral chaos and screw chaos) is possible. Fractal tattoo with repeating geometric patterns in colour. 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. This work is an extension of his earlier research on fractals, chaos theory and behavioral finance. In the past few years fractal analysis techniques have gained increasing attention in signal and image processing, especially in medical sciences, e. A. According to chaos-complexity theory, this is the best scenario for an organisation or policy system because there is a higher degree of “creativity and innovativeness” hence the term “thriving on the edge of chaos” (Praught 2004). The main precept behind this theory is the underlying notion of small. カオス理論（カオスりろん、英: chaos theory 、独: Chaosforschung 、仏: théorie du chaos ）とは、力学系の一部に見られる、数的誤差により予測できないとされている複雑な様子を示す現象を扱う理論である。 カオス力学と. A limit cycle is a periodic orbit of a continuous dynamical system that is isolated. And The signal is the fractal. ” Hmm. Chaos theory was developed by inputs of various mathematicians and scientists; its applications are found in a large number of scientific fields. It describes the theory of fractals, focusing on the importance of scaling and ordinary differential equations. edu. Abstract Complexity quantification, through entropy, information theory and fractal dimension indices, is gaining a renewed traction in psychophsyiology, as new. " Chaos, Solitons & Fractals 19. Chapters. A compact. Saved from nature. Glitch eye fractal tattoos. TLDR. evolution and order. Lancet (1996) B. 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. 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. Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. They cannot be truly predicted. When autocomplete results are available use up and down arrows to review and enter to select. com. Abstract. 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. 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. [20] using fractal geometry and damage mechanics to study the event characteristics. Universe Tattoo. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. A list of mathematical and physical topics relating chaos theory applied to atmosphere sciences is given in Sec. Authors. 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. The work objective is to consider the use of the fractal theory and effects of physical scaling in development of new informational technologies using examples of solving of up-to-date basic radar problems. where n, W, and (lambda_{ ext{U}}) represents index number, weighting matrix, and square diagonal matrix respectively. A fractal is a shape that is self-similar when you look at different scales. 5 and a starting value of x 0. Linear and Nonlinear Dynamics and Vibrations Laboratory at the University of Illinois Diarsipkan 2005-12-15 di Wayback Machine8. This study evaluates the changes in heart rate variability for 13 signals ECG signals taken from the MIT-BIH arrhythmia database to detect some major heart disease (APC, PVC, RBB, LBB) with fractal dimension. 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 figure above is today's fractal. . Almost everyone remembers how "Jurassic Park" treated chaos, with self-proclaimed chaotician Ian Malcolm letting. It is a mathematical branch with applications in physics, economics, engineering. Analysis of HR dynamics by methods based on chaos theory and nonlinear. This article uses chaos theory to model public relations situations whose salient feature is the volatility of public perceptions. Fractal Art. 24/mai/2023 - Explore a pasta "geometria" de Renato Carriti, seguida por 224 pessoas no Pinterest. Causes: a soccer player performs poorly. Google Scholar. See more ideas about fractals, fractal art, fibonacci. 1996; 347:1312–1314. J. 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. Nearly all nontrivial real-world systems are nonlinear dynamical systems. Casino legal online gambling, casino online ireland; Tatuaje casino, tatuaj cazinou; Casino constanta vector, csgo casino minesweeper min Chaos Theory and Education; Chaos Theory: A Brief Introduction Diarsipkan 2013-08-05 di Wayback Machine. Chaos Theory: A mathematical concept that explains that it is possible to get random results from normal equations. Crossref Medline Google ScholarJulien Clinton Sprott. Reading material and additional slides. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other. Category II. And could this be the vector space of quantum theory?. 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. xn+1 = rxn(1−xn), x n + 1 = r x n ( 1 − x n), where r r is a parameter you can vary. Manus J. Many physiological systems appear to present data that is random or without order. Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. , the fact that a coastline typically has a fractal dimension. The fractal theory seeks. The use of fractal mathematics and chaos theory presents significant difficulties both at the level of the theory and at the level of application. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. Chaos under control: The art and science of complexity. and Neoclassical Theory are analyzed. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers, etc. MAT1845HS: Introduction to Fractal Geometry and Chaos Theory. • Chaos Theory represents a big jump from the way we have thought in the past – a paradigm shift. Visualizza altre idee su hedgewitch, stregoneria, dark fantasy art. 4. These time series consist of Radon concentration levels and meteorological variables of temperature, pressure, and relative humidity within the boundary layer and very close to the ground. In mathematics, iterated function systems ( IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. Deterministic chaos, fractals and quantumlike mechanics in atmospheric flows, Can. Chaos theory is a mathematical theory, and it is still in development. Small differences in initial conditions (such as those due to rounding errors in numerical computation or measurement uncertainty) yield widely diverging outcomes for such. 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. . The mathematical structures of their surfaces are the most popular element in chaos theory: fractals. In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. 7. The boundary of this set is called a Julia set of and its complement is called. Lorenzian chaos, "sandwich" chaos, and "horseshoe chaos. Psychedelic Pattern. Description. A classic example of this is. 9, and three-dimensional fractals (such as a mountain) between 2. Lancet. 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. The beginning of its application coincided with the transition of finance to the use of big data. This set, {z} {z}, is what became known as the Cantor set. See more ideas about fractal tattoo, chaos theory, attractors. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers, etc. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Series ISSN 1860-0832. By vova. A "tribute to mathematics" depicting 3D representations of some of the most famous strange attractors. Feb 26, 2018 - Explore Jan Wisor's board "Fractal Curves" on Pinterest. The concept of Chaos Theory dates back to ancient Greek and Chinese civilizations. Moreau. Mathematical Tattoo. I also briefly touched on how phase diagrams (or Poincaré plots) can help us visualize system attractors and differentiate chaotic behavior from true randomness. Sprott. Have you ever thought about your life as a fractal? Have you embraced the infinite? PhD student Robin Andrews explains the. Stoppard calls it “a reconciliation between the idea of things not being random on the one hand and yet unpredictable on the other hand. 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. Indeed, the world of mathematics and science has, untilChaos is the science of surprises, of the nonlinear and the unpredictable. Amazing Art. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Chaos Theory and Education; Chaos Theory: A Brief Introduction Diarsipkan 2013-08-05 di Wayback Machine. 8. in pathology, neuropsychiatry, cardiology. Examples include the swings of a pendulum clock, and the heartbeat while resting. Scientists from different fields have begun to observe the regular patterns within the irregularity of the natural world. Malcolm is a gifted mathematician who specializes in chaos theory. The archetype of all theories of dynamics is that of Newton, concerning celestial motions. See more ideas about chaos theory, fractals, fractal art. 13 Denton TA, Diamond GA, Helfant RH, Khan S, Karagueuzian H. See more ideas about chaos theory, chaos, fractals. And this property transfers. Even so, this system and its motions are complex and extremely intriguing. Saved from Uploaded by user. What appears to be the broadest framework for the exactly computable moment theory of p-balanced measures — that of linear i. Fractals: A fractal is a never-ending pattern. Published 2009. Free Plugins. 1996 May 11; 347 (9011):1312–1314. A loss of fractal organization has been shown to be a predictor of adverse outcomes in a variety of physiological systems, including cardiac interval or stride interval time series. 3 Fractal Dimension Computation of an MRI Volume of the Brain White Matter with a Boxcount-Based MATLAB Script. Fibonacci. Visualizza altre idee su frattali, arte frattale, immagini. edu. Mandelbrot Fractal. Watch. Comments. Category II. It is a branch of mathematics that deals with systems that appear to be orderly (deterministic) but, in fact, harbor chaotic behaviors. More Complex Fractals Chaos Theory and Fractal Links Works Cited Introduction to Chaos 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. 5 and a starting value of x 0. The second section studies the application of Chaos Theory in economics and finance. 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. Designed by Jonas T. 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. K. Fractal Tattoo. Very small changes in the starting position of a chaotic system make a big difference after a while. 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. The concept is extended to the time series analysis, and the time series in. & Frame, M. Fractals. 4. Mathematical models and definitions associated with chaos are reviewed. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. Chaos Theory. The 20 best chaos theory books recommended by Peter Jukes, Charlie Munger and Nic 'It's Over' Carter, such as Chaos and Math Geek. Ruin. edu. Chaos theory is the study of non-linear systems that are impossible to predict or control. The fractal tree model while somewhat a by-product of our specific program does seem to have a great utility for many education questions. Mandelbrot (20 November 1924 – 14 October 2010) 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". Fractals: A fractal is a never-ending pattern. - Merriam-Webster Dictionary. 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. the overarching patterns-of-patterns within which human cultures. Art, Computer Science. Section of the time series of the S&P 500 Index or SPY. Chaos theory is usually defined as, “ The branch of mathematics focusing on the behaviour of dynamical systems that are highly sensitive to initial conditions. This system demonstrates chaos theory and how small variations lead to large changes. 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. Lancet. 分形在. See more ideas about chaos theory, chaos, fractals. These 3 tools are: The strange […] Pinterest. 1. Fractal Tattoo. Two" figure 8-shaped chaotic regimes of the latter type are possible simultaneously running throug, h each other like 2 links of a chain. identification of fractals and self-organized criticality in meteorology and atmospheric physics is summarized in Sec. If instead of 3, you begin with 5 dots, then you. The main MATLAB function that we use for this process is Boxcount. The theoretical fractal dimension for this fractal is 5/3 ≈ 1. Chaos, Solitons & Fractals. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Explore. Keywords: Chaos theory, Fractals, Sensitive dependence on initial conditions (SDIC) Introduction The word Chaos comes from the Greek word “Khaos”, meaning “gaping void”. Storytellers embraced its principles and worked them into their novels, films and plays. See more ideas about chaos theory, chaos, fractals. 269. The idea is that the flapping of a butterfly’s wings in Argentina could cause a tornado in Texas three weeks later. Opportunities may be endless but yet to be fulfilled. 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. John Wiley & Sons Inc. from $21. Chaos theory. I decided a cool thing to get would be a bifurcation diagram showing the period doubling route to chaos. D. It is as though we are all in a nightmare together. He is best known as the founder of modern chaos theory, a branch of mathematics. Nonlinear analysis and phenomena cover very broad fields of mathematics and science which are rapidly ex- panding. Jul 16, 2017 - Explore Ibrahim Ajeez's board "chaos theory" on Pinterest. 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. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Fractal Patterns. Abstract. This website was written in conjunction with a talk given for Intermediate Physics Seminar. 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. 3. Touch device users. Hexagonal fractal tattoo designs on sleeve. The scientific meaning of chaos can be summed up in the following. Dates: 5/21/79, 11/12/86, 8/27/10. 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. Kotel’nikov IREE RAS for exactly 35 years. Apr 8, 2020 - Explore Ignota's board "chaos theory. Watch. Chaos theory is the study of a particular type of systems that evolved from some initial conditions. Architecture Tattoo. Julie Belaval. In everyday language "chaos" implies the existence of unpredictable or random behavior. 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. Fractal-like objects were discovered in mathematics more than 100 years ago, but required the computer to bring them to life. Mandelbrot set. Crossref Medline Google Scholar; 14 Goldberger AL. In the references to chaos theory and fractals to be addressed in this section, the actual mathematical content of these disciplines, i. See more ideas about chaos theory, chaos, fractal geometry. Nonlinear means that due toChaos Theory is, in effect, the science of surprises, the nonlinear, and the unpredictable. IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and. Chaos theory. What is Chaos: An introductory. Line Images. Moreover, fractal geometry is applied in many radiographic analyses. To state as a definition, Chaos theory is the study of complex, nonlinear, dynamic systems. 2015-03-25. Traditionally, this discrete chaos is controlled. His research has been primarily in the area of experimental plasma physics and controlled nuclear fusion. Second Floor - Energy Physics A century ago, a group of creative minorities launched a radical new view. Number of Illustrations 39 b/w illustrations, 54 illustrations in colour. It does this by pushing pixels apart and filling in the gaps. The Buddhabrot is the probability distribution over the trajectories of points that escape the Mandelbrot fractal. 8 Chaos and Fractals C5 A Chaos In problems 1–4, follow the procedure of Example 1 to find the possible attractors. Today, fractals form part of the visual identity of chaos. See more ideas about chaos theory, chaos, theories. What is Chaos Theory? Chaos is the science of surprises, of the nonlinear and the unpredictable. Ian Malcolm is a fictional character from the Jurassic Park franchise created by Michael Crichton and portrayed by Jeff Goldblum. Probably not, but maybe I could at least show them a photo… My appointment was with the same tattoo artist that Goth Girl used. Lorenz equations used to generate plots for the y variable. IFSs provide models for certain plants, leaves, and ferns, by virtue of. As infinitely complex objects that are self-similar across all scales, they represent dynamical systems in all their glory. So she said “As chair, I give you permission to take your shirt off in class. Lancet. Flower Tattoo. 16/jul/2018 - Explore a pasta "Fractais Física Quântica" de Bia Pereira no Pinterest. I first heard of the Lyapunov exponent in terms of chaos theory and have noticed it a few times since then in recipes for specific neural nets and discussions of entropy. Dr. Introduction Chaos theory is a branch of mathematics that deals with nonlinear dynamical systems. 669. Apr 12, 2018 - Explore DesignedByEddie's board "Cool Fractals", followed by 360 people on Pinterest. 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}. Definition: The set of points for which the set of iterates is bounded is called a filled Julia set of . 67; its empirical fractal dimension from box counting analysis is ±1% using fractal analysis software. 1. Veja mais ideias sobre fractais, proporção áurea, quantica. It highlights the limitations that are inherent in a. Dynamical systems theory applied to management accounting: chaos in cost behaviour in a standard costing system setting. . A classic example of this is the weather. This chapter provides an introduction to chaos theory and fractal geometry to aid the reader in following the arguments presented in the next chapters. Abstract and Figures. 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。. There is a relationship between chaos and fractals—the strange attractors in chaotic systems have a fractal dimension. Get inspired and try out new things. 144 (4), 2005)The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. Find and save ideas about chaos theory on Pinterest. See more ideas about chaos theory, chaos, fractals. These sensitive nonlinear dynamical systems have now been explained using chaos theory and fractal geometry. It inspired scientists in many disciplines. [PMC free article]. vn compilation. 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. Touch device users, explore by touch or with swipe gestures. Awesome. Chaos game to get specific fractal. The book is also structured in two parts entitled: Fractals and Chaos. Although the "paradox of length" was previously noted by Hugo Steinhaus, the first systematic study of. I would like to work in a couple dates, so to speak, into the formula for the fractal to commemorate some important life events. The details are different. From 2008 - 2022 he was Managing Partner and Co-Director of Global Macro at First Quadrant, LLC in Pasadena, CA. I have, for years, wanted a fractal as a tattoo (as my tattoo collection currently is a literal playground of other math ideas such as the golden mean, infinity, and various equations). Tem. Fractal market analysis: Applying chaos theory to investment and economics. Weitere Ideen zu fraktale, fraktal, fraktale geometrie. Dieser Pinnwand folgen 124 Nutzer auf Pinterest. There are also images related to minimalist fractal tattoo, simple fractal tattoo, geometric fractal tattoo, fibonacci fractal tattoo, sacred geometry fractal tattoo, small fractal tattoo, chaos theory fractal tattoo, sacred geometry fractal tattoo.