chaos theory equation tattoo. Schuldberg, in Encyclopedia of Creativity (Second Edition), 2011 Introduction. chaos theory equation tattoo

 
 Schuldberg, in Encyclopedia of Creativity (Second Edition), 2011 Introductionchaos theory equation tattoo  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"

As can be seen from the graph, even the slightest. 1990; 120:1419–1440. Different types of chaotic flow are possible in the 3-dimensional state spaces of two simple non- linear differential equations. The word usually carries a negative connotation involving undesirable disorganization or confusion. More aptly, for example, is there any known way in which the Navier-Stokes equation can "emerge" from the equations of Schrödinger, Pauli or Dirac (or even the equations of. Dans le document Chaos Theory Tamed (Page 173-178) This chapter looks at various nonlinear equations that can give rise to chaos. It describes the models and implementation ideas. Jun 28, 2019 - Explore Tom Robinson's board "Chaos theory" on Pinterest. The photo is accompanied by a section of prose: “She asked him, ‘Tell me something nice!’. Answer. While so far there have been no. Catastrophe Theory. In everyday language "chaos" implies the existence of unpredictable or random behavior. Half a century ago, the pioneers of chaos theory discovered that the “butterfly effect” makes long-term. xm×n } are produced by two one-dimensional logistic maps. The so-called butterfly effect has become one of the most popular images of chaos. His companions have walked ahead toward the. Edward Lorenz coined the term after he hypothesized that a distant butterfly’s flapping wings could set off a complex series of events, leading to a tornado somewhere else. d x d t = r x ( 1 − x K), i. 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. It looks at certain systems that are very sensitive. The use of ⋄ means that the stochastic integral of Itô (Skorohod) type is considered. One is of a dead cat, and one if of a cat that is very much alive and active. . To say that a system is chaotic means that there is a deterministic rule for its future evolution, but that small differences in initial conditions grow exponentially quickly over time. 0001 and 1. It is one of the Chaos theory's most iconic images and illustrates the phenomenon now known as the Butterfly effect or (more technically) sensitive dependence on initial conditions. A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 / 3. The modern understanding of Newton's first law is that no inertial observer is privileged over any other. It enables the description of a series of phenomena from the field of dynamics, ie, that field. One of the rst and most famous equations regarding these two topics, the Lorenz Equation, will be discussed. Drake Equation Of Physics Tattoo On Forearm. and anything technical. Roopnarine, in Encyclopedia of Ecology, 2008 Catastrophe theory is a mathematical framework that deals with discontinuous transitions between the states of a system, given smooth variation of the underlying parameters. 4 Proposed Method 3. Lorenzian chaos, "sandwich" chaos, and "horseshoe chaos. The Origins of Chaos Theory . 98. The Einstein Portrait Tattoo is a tribute to one of the most iconic scientists in history. Chaos Theory is a delicious contradiction - a science of predicting the. So if you're gonna get a math tattoo, ideally get something that's aesthetically pleasing* independent of the mathematical significance. By trends. Geniale Tattoos. The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus or "broken"/"fraction". Sorted by: 1. Causes: low moral in a country. It is clear the subject continues to attract a great deal of attention among scientists in the scientific community. A side note — map is just another way of saying function. By Phil Dooley. y = ax-ax². 495 BC) explained patterns in nature like the harmonies of music as arising from number, which he took to be the basic constituent of existence. Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. vn compilation. 1. Forearms Physics Friendship Tattoos. X is the population, while T and R are the rate of growth. Nonlinear Dynamics and Chaos in Agricultural Systems. Chaos theory, more technically nonlinear dynamical systems (NLDS) theory, is an exciting, rapidly developing area of mathematics with increasing application in the physical, biological, and social sciences. About a decade later, chaos theory started to catch on in scientific circles. 892, 0. Chaos theory is a part of mathematics. However, for very large value of r such as r = 400, all solutions become periodical again (see Figure 08). 1 Chaos theory is potentially one of the most controversial fields in mathematics. The infinitely intricate computer-generated image of the set serves as an icon for the burgeoning field of chaos theory and has attracted enormous public attention. of ordinary differential equations in which it is possible to exhibit chaotic behavior. This syllabus section provides the course description, an outline of course topics, and. After learning her mother was diagnosed with breast cancer on Valentine’s Day, Josephine got a tattoo of one of the formulas for a heart curve, a fitting symbol of support and a. See Lorenz (1993), p. Pick some area of your body that is. 1 Dynamical Systems and Determinism. To use the equation, you start with a fixed value of r and an initial value of x. This equation is May’s logistic map. The double pendulum phase space plot from the section on the double pendulum shows extremely chaotic behavior. Thus chaos theory is, very generally, the study of forever changing complex systems based on mathematical concepts of. 1016/0167-2789(92)90001. The left hand side of this equation describes the helical trajectory F 2 (t) = {x 2 (t) + y 2 (t) + [z (t) - r - ] 2 } / 2. . One can define a dynamical system fromList of chaotic maps. It was written by Paul Cull, Mary Flahive, and Robby Robson, and published by Springer. Traditional nonlinear dynamics with relation to physical applications (mainly electronics and radio) was developed by Mandelshtam, Andronov, etc. Chaos is devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines. Chaos theory, Bush says, is "really simply a statement of lack of precision on the initial conditions of a system. Chemistry: Chaos TheoryIntroductionChaos theory is the study of mathematical systems that exhibit certain characteristic properties, one of which is extraordinarily erratic behavior. Fascinating rhythm: a primer on chaos theory and its application to cardiology. vn compilation. Chaotic Equations. Edward Lorenz defined chaos as “when the present determines the future, but the approximate present does not approximately determine the future. Entropy as a word disappearing tattoo design. A side note — map is just another way of saying function. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers, etc. [3]May 8, 2021 - Explore Michael Conroy's board "Physics tattoos" on Pinterest. Causes: a soccer team loses the world cup. The Sciences. What you’re about to see is an impressive feat of complexity arise from something that may appear very simple — maybe even mundane. FEČKAN: Homoclinic orbits of slowly periodically forced and weakly damped beams resting on weakly elastic bearings, Adv. 1509 Words4 Pages. effect that. . 1. The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. Click here to start using LastPass: A video presented on Veritasium used the following equation to describe an example of this type of miraculous mathematical paradox. . You could make equations about it, and figure out the answer pretty easily. 2. This is the onset of chaos! Bifurcation Diagram — Chaos starts at x = 3. Wang LaGuardia Community College of the City University of New York The general public has been made aware of the research field of Chaos by the book of that title by James Gleick. The latest version of the meme includes a photo of a tattoo representing the Dirac equation, which is a equation discovered by British physicist Paul Dirac and published in 1928. And the butterfly effect, also known as. The purpose of1. The butterfly effect is an underlying aspect of chaos. The Pythagorean Theorem. 2 Defining Chaos 1. 1). It describes a process evolving through time — x t + 1, the level of some quantity x in the next time period — is given by the formula on the right, and it depends on x t, the level of x right now. The term catastrophe, derived from the French in this usage, refers to the abrupt nature of the. Fascinating rhythm: a primer on chaos theory and its application to cardiology. Discover (and save!) your own Pins on PinterestFormally, chaos theory is defined as the study of complex nonlinear dynamic systems. We. It is often described by fractal mathematics, which captures the infinite complexity of nature. Published by Brooks/Cole, Cengage Learning, 2011. J. Much of mathematics invented up until now has been "linear", or related to a line. it is a mathematically generated pattern that can be reproducible at any magnification or reduction. Section 4 is the heart of the paper, presenting a linear wave equation with gain and showing it satisfies the conditions required by the definition of chaos. For low values of r , xn (as n goes to infinity) eventually. The mathematical treatment is friendly and informal, but still careful. Chaos Theory. Causes: a soccer player performs poorly. The Lorenz Attractor is a strange attractor, which means the equation is non-periodic, as thus never repeats itself. In the social sciences, chaos theory is the study of complex non-linear systems of social complexity. Casino legal online gambling, casino online ireland; Tatuaje casino, tatuaj cazinou; Casino constanta vector, csgo casino minesweeper min There is a basic equation that is used to produce a logistics map whenever chaos theory and the butterfly effect are being examined. Read the 20th-anniversary edition of this best-selling now-classic work (published in every major language). 1. A particularly simple example of this is the polynomial f(z)=z2+cf(z) = z^2 + cf(z)=z2+c for some constant ccc. A tattoo of equations and stuff like that just makes it look like you're trying too hard to look smart. Apr 27, 2022 - Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations. Chaos is an exception in the world of nonlinear dynamics. This was discovered by the North American theoretical meteorologist, Edward Norton Lorenz (1938-2008). davidope for Quanta Magazine. This code was developed for this YouTube video from Veritasium. This theorem is foundational to our understanding of geometry. I even have a tattoo they represents the symbol on my left shoulder. In the following communication, we wish to add to Gelfand and Engelhart (2012), some emphasis on the dynamical systems theory (DST) applications in practical and theoretical psychology, and. The photo is accompanied by a section of prose: “She asked him, ‘Tell me something nice!’. If you're thinking of chaos as in a big change with slightly different. A dynamical system may be defined to be a. The drawing corner includes four pages covered in blue-ink sketches by Otto Rössler, a German biochemist who works on chaos theory. 31. F. They just replaced x with − x, and similarly for y. The Chaos Theory Of Heart Attacks. Chaos is the disorder of a dynamical system but it is not completely unpredictable. The initial conditions for x and z were kept the same but those for y were changed between 1. The Pythagorean Theorem. Although many complex systems appear to behave in a random manner, chaos theory shows that, in reality, there is an underlying order that is difficult to see. Lorenz equations used to generate plots for the y variable. One then runs the equation recursively, obtaining x1, x2 , . Difference Equations: From Rabbits to Chaos is an undergraduate-level textbook on difference equations, a type of recurrence relation in which the values of a sequence are determined by equations involving differences of successive terms of the sequence. Strange attractors are also coupled with the notion of chaos and sensitive independance on initial conditions, in that one cannot predict where on the attractor the system will be in the future. Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation. Chaos theory helps climate scientists model the changing climate over multiple iterations and multiple models. The best part of her job is her growing friendship/flirtation with the strangely trend-resistant Bennett O'Reilly, a chaos theory researcher who seems to float through life unaffected by herd instincts of any kind. Jan 4, 2023 - The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. edu. The infinitely intricate computer-generated image of the set serves as an icon for the burgeoning field of chaos theory and has attracted enormous public attention. These complex systems may be weather patterns, ecosystems, water flows,. Two researchers have created a strikingly simple model of chaotic behavior, in which variations in initial conditions become so tangled and. Author links open overlay panel Jiu Li, Hongyan Zang, Xinyuan Wei. Weather's just one example. P. ) Jump to:Details images of schrodinger equation tattoo by website vova. This equa- tion has the form P,+1 = P, * R * (1 - P,)Since chaos was first discovered by American meteorologist Lorenz in the 1960s, it becomes a hot topic of research around the world all the time. I decided a cool thing to get would be a bifurcation diagram showing the period doubling route to chaos. So why not embrace it? after all, Chaos is the mother of all creation. The aim of this second structure is to analyse and compare the dynamical behaviours. For example: Initial Condition: uncomfortable pillow. The Lorenz Attractor: A Portrait of Chaos. 8333333,. Crossref Medline Google Scholar; 14 Goldberger AL. But the MIT scientist needed something even simpler if he hoped to get a better look at the tantalizing effects he glimpsed in his simulated weather. It produces at least three types of chaos: Lorenzian chaos, "sandwich" chaos. Lorenz's computer model distilled the complex behavior of Earth's atmosphere into 12 equations -- an oversimplification if there ever was one. The latest version of the meme includes a photo of a tattoo representing the Dirac equation, which is a equation discovered by British physicist Paul Dirac and published in 1928. Mitchell Jay Feigenbaum proposed the scenario called period doubling to describe the transition between a regular dynamics and chaos. Nonlinearity and chaos is a broad and active field and thus this chapter will focus only on a few examples that illustrate the general features of non-linear systems. May 2018. in around 1930 and it was based on so-called "qualitative theory of differential equations. 1990; 120:1419–1440. ends with a. D. ∂ t a = σ a + ξ 2 ∂ x x a − w ∂ x a − Λ − 1 ∫ 0 x a ( x ′, t) d x ′ − g a 3. A double pendulum is a system so simple that a fifth-grader could make it. Not because of the choice of axioms or some of the results, but due to the fact that no-one can agree what chaos actually means. 2. From $20. In physics, and especially quantum chaos, a wavefunction scar is an enhancement (i. Chaos theory is not about randomly looking for similarity patterns. The equation's history, properties, and graphical interpretations will be examined. The entire financial market is a chaotic unpredictable complex system that is inherently chaotic and constantly on the move from order to disorder and back. A projection in the x-y plane of this attractor is: Another strange attractor, created recursively, is the Hénon attractor: Chaos and Fractals. 185. The scientific meaning of chaos can be summed up in the following. Suppose you want to calculate the square root of 2 with only a simple calculator. How a double pendulum. For chaos theory is the study of orderly patterns in turbulent, erratic, or dynamical systems. It is this: xt+1 = rxt (1-xt). This strange branch of. Chaos Theory. 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. To set this template's initial visibility, the |state= parameter may be used: |state=collapsed: { {Chaos theory|state=collapsed}} to show the template collapsed, i. Else the grade is F. Chaos, from the Greek khaos, “abyss, that which gapes wide open, that which is vast and empty”, is a relatively young scientific discipline, which however has old and important roots, dating back (at least) to James Clerk Maxwell in 1860 and Henry Poincaré in 1890. His simple model exhibits the phenomenon known as "sensitive dependence on initial conditions. Two. Basic Theory of Stochastic Resonance. Black Math Formula Equation Tattoos On Fingers. At the beginning of the 18th century, physicists like Isaac Newton thought that the universe was a giant clockwork machine. The equation looked like this: X n+1 = rx n (1 - x n) where r equals the driving parameter, the factor that causes the population to change, and x n represents the population of the species. In 1961, Lorenz wanted to recreate a. 2001, World Scientific Series on Nonlinear Science Series A. They want to know if the chaos that Lorenz (definition 2) found in his early toy weather model, which led to the accepted concept that “weather is chaotic” meant that weather (as we experience it in the real world day-to-day, week-to-week and month. This quadratic map is capable of very complicated behavior. 75 1/ 1/ € s t E Since, s=t E sin sin q 1/ 1/ 100. For a while, in the 1980s and early 1990s, chaos was touted as the next big revolution in science, on par with quantum mechanics. Deterministic chaos has been rigorously and extensively studied by mathematicians and other scientists. (I) Topics to be covered: basic existence and uniqueness theory, systems of equations, stability, differential inequalities, Poincare-Bendixon theory, linearization. Comments. 95[x(n)][1-x(n)] is chaotic because it is deterministic, as can be seen by the multiplication of the previous term in the equation. For only nonlinear equations can model such systems, and "the struc-tures that provide the key to nonlinear dynamics proved to be fractal" {Chaos, 114). . where r is the so-called driving parameter. The figure shows the main ideas running in each direction. . Then you run the equation iteratively to obtain values of x 1, x 2, x 3. 892, 0. , fully visible. Next, take a die and color two of the faces red, two blue, and two green. The purpose of the present chapter is once again to show on concrete new examples that chaos in one-dimensional unimodal mappings, dynamical chaos in systems of ordinary differential equations, diffusion chaos in systems of the equations with partial derivatives and chaos in Hamiltonian and conservative systems are generated by. Xn+1 = rXn(1-Xn) In this logistic model that describes how the. Apr 14, 2018 - Explore Amy Stephens Wulfekuhl's board "chaos tattoo" on Pinterest. The values for ho, sigma and eta were 45. The sockeye salmon that spawn in British Columbia’s Fraser River offer a prime example. Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive constant sometimes known as the "biotic potential" gives the so-called logistic map. A limit cycle is a periodic orbit of a continuous dynamical system that is isolated. They were discovered and explained in 1984 by E. Image of a strange attractor. Chaos theory is a scientific principle describing the unpredictability of systems. So it's kinda like. Chaos Theory is a mathematical sub-discipline that studies complex systems. computational knowledge engine. He answered her, ‘ (∂ + m) ps = 0’ This is the equation of Dirac. Homework Helper. 494–c. 984T Put, t 4 Fair Coin Equation t t E²11 Pioneer Women in Chaos Theory Frank Y. However, in the scientific realm this unpredictable behavior is not necessarily undesirable. So nerdy I became professor and combined my love of maths. A process called Newton’s method says you should start with any guess — let’s say 3 — and plug it into the function f ( x) = x 2 + 1 x . Not an equation, but I actually got the dynkin diagram for E8 IRL! I imagine there's someone who really hates their Maxwell's equation tattoo since someone told them that dF=0 and d*F=j. Topics: Security. The concept of Chaos Theory dates back to ancient Greek and Chinese civilizations. Visually the graph splits into two as there are two stable populations. The logistic difference equation is given by. starkid. It is well adapted to the modelling and study of unstable dynamical behaviours: it enables to detect and extract the. Lorenz equations used to generate plots for the y variable. chaos theory: A field of research in math and physics that studies the patterns of dynamic — or chaotic — systems to better understand and predict their behavior. 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 ). She might start with chapter 21 Trace formulas and/or online course part 2, and work her way back or forth, as needed. He first observed the phenomenon as early as 1961 and, as a matter of irony, he discovered by chance what would be called later the chaos theory, in 1963, while making calculations with uncontrolled approximations aiming at predicting the weather. This latter formulation was also applied to the cumulative number of deaths D Σ with its. The fern is one of the basic examples of self-similar sets, i. The course grade will be based on the cumulative quiz-grade, and a binary-grade term paper. You can see instances of the butterfly effect every day. Figure 1: a) Pattern formed by the vibration of sand on a metal plate; b) Vibration of a thin film of glycerine. This section includes the full set of lecture notes for all 26 lectures. Well, it’s choas, and messy is what chaos does. This is not a library, but rather a collection of standalone scripts!On May 23, 1917, American mathematician, meteorologist, and a pioneer of chaos theory Edward Norton Lorenz was born. 1 Theory of Chaos Analysis. 0. Chaos theory, or the butterfly effect, is the idea that small changes have the potential to cause major changes across chaotic systems. focused on one solution at a time. In the second equation, a transitio between two different types of horseshoe chaos (spiral chaos and screw chaos) is possible. Oct 30, 2021 - This Pin was discovered by Lauren Hesemeyer. Chaos theory equation pdf Complex quadratic polynomials A complex quadratic polynomial is a standard quadratic equation where the variable involved can be a complex number. Schuldberg, in Encyclopedia of Creativity (Second Edition), 2011 Introduction. It is notable for having chaotic solutions for certain parameter values and. For the first time in the history of physics we therefore have a framework with the capacity to explain every fundamental feature upon which the universe is constructed. I was the nerdiest person in my high school, publicly teased for my love of maths and Doctor Who. Examples of these complex systems that Chaos Theory helped fathom are earth's weather system, the behavior of water boiling on a. Armband Math Maxwell Equation Tattoo. See moreI decided a cool thing to get would be a bifurcation diagram showing the period doubling route to chaos. Crossref Medline Google Scholar; 14 Goldberger AL. One area where the pi symbol can be found is in physics. We’ve all seen this simple quadratic equation: y = ax-ax². Improve this answer. The article . 1. Pantano/E. What you’re about to see is an impressive feat of complexity arise from something that may appear very simple — maybe even mundane. Details images of schrodinger equation tattoo by website tnbvietnam. Answer. The output, f (3) = 1. com FREE DELIVERY and Returns possible on eligible purchases Amazon. The diagram displays period-doubling as r increases, eventually producing chaos. . Then you run the equation iteratively to obtain values of x 1, x 2, x 3. This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. 4. It is the study of the behaviour of dynamic systems. (a) ˙x versus x; (b) bifurcation diagram. Chaos: An Interdisciplinary Journal of Nonlinear Science. "Chaos theory" is the popular term used to describe a novel, quite revolutionary approach to a wide range of mathematical, pure science, and applied science fields. This course provides an introduction to nonlinear dynamics and chaos in dissipative systems. 894. The use of the pi symbol in this context is derived from its use in. linear equations for this purpose. A classic example of this is. Chaotic systems can be stabilized (or chaotified) with small perturbations, yet. Let’s begin with some most important MCs of Chaos Geometry. Understand the historic context for the emergence of the concept of chaos. Chemistry is one of the ancient branches of science that evolved from alchemy. These heart diseases. The values for. " They gave full and complete analyses of two-dimensional systems and showed that the only attractors in 2D. Chaos is a product of uncertainty and unexpectedness and at the same time engine of them. . Fourier Physics Wristband Tattoo. In this context, chaos already arises in certain nonlinear functions of a Chaos theory is a mathematical theory, and it is still in development. Based on the above assumptions, a weakly nonlinear modulation equation for a ( x, t) was derived in Ref. Summary: Chaos theory is a mathematical theory that can be used to explain complex systems such as weather, astronomy, politics, and economics. ” In his 1963 paper in the Journal of Atmospheric. One can define a dynamical system from this map via the recursion \ (z_ {n+1} = f (z_n)\). Chaos theory is a complex mathematical theory that attempts to explain. Update images of chaos theory equation tattoo by website in. The basic concepts of the mathematical theory of chaos are presented through a brief analysis of some interesting dynamical systems in one-, two- and three-dimensional space. Causes: bad night's sleep. (2. Deterministic chaos refers to a class of deterministic systems in which seemingly random behavior is the result of dynamics described by nonlinear differential or recurrence equations (e. Iterating this equation produces regions of distinct values, involving period doubling, as well as regions of chaos. 893, and 0. Bubble Chamber Physics Tattoo On Girl Hand. 5 Elements. The drawing corner includes four pages covered in blue-ink sketches by Otto Rössler, a German biochemist who works on chaos theory. Jul 20, 2011 at 7:38. edu. Chaos was – most Greek cosmologies tell us – the very first of all, the origin of everything, the empty, unfathomable space at the beginning of time. Chaos Theory. Early Greek philosophers attempted to explain order in nature, anticipating modern concepts. Examples of such systems include population growth, turbulent fluids, and the motion of the planet's. Geometry. Ian Malcolm explains Chaos Theory and claims that prediction of chaotic systems through computers is impossible, while talking about how the desire to predict. Barnsley's 1988 book. - Merriam-Webster Dictionary. Dec 3, 2021 - Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations. Discover (and save!) your own Pins on PinterestJanuary 7, 2020. While John von Neumann had suggested. Here, two series of x and y values diverge markedly over time from a tiny initial difference. Art Prints. Fractal TattooChaos theory is demonstrated in this image, which was created with a long exposure of light at the end of a double pendulum. Chaos theory deals with models that are entirely impossible to predict or. Maps may be parameterized by a discrete-time or a continuous-time parameter. On the one hand, I would like to give a very elementary presentation of chaos theory, as a mathematical theory, and to give some general overviewThe procedure of the encrypted algorithm will be as follows: Step NO. Including tattoos. Learn Chaos theory facts for kids. Birkhoff, A. Feature image from Pinterest. The Lorenz attractor arises in the study of the Lorenz oscillator, a dynamical system. Chaotic maps often occur in the study of dynamical systems . Snapshot 2: convergence on a 2-cycle. Discrete maps usually take the form of iterated functions. In Gleick’s book Chaos, the author interviewed a whole bunch of chaos scientists (chaosists?) and not one of them could agree on a. In physics, the pi symbol is often used to represent momentum, which is defined as mass times velocity.