What is Chaos: Definition and 199 Discussions

The Symbol of Chaos originates from Michael Moorcock's Eternal Champion stories and its dichotomy of Law and Chaos. In them, the Symbol of Chaos comprises eight arrows in a radial pattern. In contrast, the symbol of Law is a single upright arrow. It is also called the Arms of Chaos, the Arrows of Chaos, the Chaos Star, the Chaos Cross, the Star of Discord, the Chaosphere (when depicted as a three-dimensional sphere), or the Symbol of Eight.
Alternative symbols of chaos (owing nothing to Moorcock) include the Sacred Chao and the Five Fingered Hand of Eris of Discordianism.

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  1. Justice Hunter

    Writing a Script - Chaos Theory

    Hey everyone, So I'm writing the script for a Youtube show I'm making, and it's pretty heavy on the science/physics side in terms of exposition. So before i jump into what i want to ask let me just briefly explain the story. A Time traveler and his time traveling machine go back 30 years in...
  2. Auto-Didact

    Defining chaos: expansion entropy

    Hunt & Ott 2015, Defining Chaos NB: For a more introductory version, phys.org ran a piece on this article two summers ago This paper was published as a review of the concept of chaos in the journal Chaos for the 25th anniversary of that journal. The abstract is extended with a clearer...
  3. Auto-Didact

    A Correspondence between entanglement and chaos?

    Neill et al. 2016, Ergodic dynamics and thermalization in an isolated quantum system NB: For a more introductory version, phys.org ran a piece on this article last summer From my understanding entanglement is generally seen as purely a quantum phenomenon, while on the other hand chaos is...
  4. nomadreid

    I Classical Chaos: Can a Particle Move Chaotically and Be Subject to Force?

    Suppose we are talking about a purely classical phenomena (OK, nothing is purely classical, but suppose we consider quantum effects as insignificant, that is, we ignore them). In this context, I came across someone talking about "a particle in chaotic continuous motion as the particle is...
  5. haushofer

    Liouville, the second law and chaos

    Dear all, I've never really understood how exactly Liouville's theorem about time-conservation of phase space volume can be reconciled with the second law of thermodynamics. Recently I came across this popular article, http://www.necsi.edu/projects/baranger/cce.pdf "Chaos, Complexity, and...
  6. L

    A Explaining Chaos in Constant Accelerating Systems

    Chaos could appear in the system if there is some nonlinearity. My question is how to explain that there is no chaos in constant acceletating system s(t)=v_0t+\frac{at^2}{2} when equation is nonlinear? Why is important only that difference and differential equation be nonlinear. It confusing me.
  7. C

    A Exploring Quantum Chaos: Is it Truly Random or Deterministic?

    Hi, I was curious to know what the perception of quantum chaos is. It seems a bit on the fringe, but at the same time it seems interesting. An adviser I'm considering working for works on both solid state physics applications and does some theoretical work in quantum chaos, so I'm wondering if...
  8. Passionate Eng

    A Exploring Randomness vs Chaos: Decoding the Nature of the Universe

    The universe is random or chaotic?
  9. dreens

    I Variational Equations, Chaos Indicators

    I work with an electromagnetic molecule trap, and I'd like to determine which orbits are chaotic. To this end, I intend to study the evolution of a perturbation on a trajectory with time. I'd like to compute something called the fast lyapunov indicator for various trajectories y(t), where I...
  10. H

    Chaos & Scales in Turbulent Flows

    Suppose you want to solve the Navier-Stokes equation for an incompressible turbulent flow. This is, in principle, possible. However, for higher Reynolds number, this isn't really feasible since the smallest eddy sizes are really small. First question 1) Why would this prevent you from...
  11. A

    Classical Duffing Oscillator: Get Resources to Study it

    Can someone please suggest me a good reference for studying the duffing oscillator?
  12. Michele Zappano

    Fractal Symmetry & Noether's Theorem: Chaos & Conservation

    I was reading a Steven Strogatz book and he said that the self similarity of fractals is a symmetry. Has any conservation law been linked to this type of symmetry using Noether's Theorem?
  13. A

    Lyapunov exponents of a damped, driven harmonic oscillator

    Homework Statement I am supposed to calculate Lyapunov exponent of a damped, driven harmonic oscillator given by ## \ddot{x} + 2\beta \dot{x} + \omega_0^2 x = fcos(\omega t)## Lyapunov exponent is ## \lambda ## in the equation ## \delta x(t) = \delta x_0 e^{\lambda t} ## The attempt at a...
  14. G

    I Harmonic oscillator: Why not chaotic?

    Hi. As far as I know, the movement of a harmonic oscillator normally is not considered to be chaotic. Why not? Since the angular frequency can never be known to absolute precision, an error in the phase builds up. I can see that this build-up is only linear in time (if we assume the angular...
  15. F

    Applied Nonlinear Dynamics & Chaos: Is It Possible to Jump In Mid-Book?

    Here is the table of contents of Nonlinear Dynamics and Chaos (by Strogatz) Overview Flows on the Line Bifurcations Flows on the Circle Linear Systems Phase Plane Limit Cycles Bifurcations Revisited Lorenz Equations One-Dimensional Maps Fractals Strange Attractors Last quarter, there was a...
  16. C

    What are current research directions in Quantum Chaos?

    What are the topics which are been perceived by researchers around the World on the topic of Quantum Chaos? I know my questions is not specific, but I do not have any idea to ask about anything specific.
  17. F

    Chaos and the Lorenz Equations

    Take the Lorenz equations x'=σ(y-x) y'=rx-y-xz z'=xy-bz with σ=10, b=8/3 and r=28 as a typical example of chaos (I am using primes to indicate total time derivatives in this post). A basic property of a chaotic system (where the flow in phase space is a strange attractor) is that if you pick...
  18. G

    Throw of a die: Dependance on initial conditions and chaos

    Hi, We normally use a simple symmetry argument to show that the probability of each outcome of a throw of a fair, cube-shaped die is 1/6. However, is it possible to actually model the physics of the throw and show that the probabilities are 1/6? Since this is classical physics, the outcome can...
  19. H

    Chaos (Non-Linear Dynamics) Driven Damped Pendulum

    I want to investigate the phenomenon of Chaos in the form of how its driving amplitude affects _____, in a driven, damped pendulum, using a computer simulation given. Initially I was looking at 'degree of chaos' for the dependent variable - to measure this I wanted to use the Lyapunov...
  20. U

    Lorentz Chaos - The 'Butterfly Effect'

    Homework Statement Given the lorentz system for ##\sigma=10, b = \frac{8}{3}, r = 28##, and ##x(t)## from the first lorentz system, show that we can solve for y(t) and z(t) for the modified lorentz system by finding ##\dot E##.[/B] Homework EquationsThe Attempt at a Solution I have found...
  21. B

    Chaos Theory and the Prolate Spheroid

    Rugby balls and American footballs are prolate spheroids. As such, their bounce patterns seem sporadic - they tend to bounce to different heights and in different directions even when they appear to hit the ground with a constant angle, speed, and spin. Does this behaviour relate to chaos...
  22. laramman2

    Applied What Are the Best Textbooks for Self-Studying Nonlinear Dynamics?

    What textbooks would you recommend for self studying Nonlinear Dynamics? I am a undergraduate junior who will be doing research on nonlinearity of spiking neurons. I have taken courses on ODE, vector calculus, probability, statistics, and linear algebra.
  23. I

    Can't tell if I made a chaotic circuit or if I broke the sim

    So, I was playing around with a couple of voltage multiplier circuits a few months ago, and while optimizing one design, I came up with a pretty neat (not to brag) way of converting a sine wave to a square wave by using transformers in a completely different way than normally. A little while...
  24. Y

    Nonlinear transform can separate function composition?

    I am solving a nonlinear ODE in the form of Newton's Second Law. In the equation, there is a Heaviside Theta Function of the function which I am solving (##\theta (x(t)##). Since it is quite troublesome to have both the left side of the ODE and the imput of the ODE to contain function of unknown...
  25. U

    Pendulum - Stability and fixed points

    Homework Statement (a): Show the lagrangian derivative in phase space (b)i: Show how the phase space evolves over time and how they converge (b)ii: Find the fixed points and stability and sketch phase diagram (c)i: Find fixed points and stability (c)ii: Show stable limit cycles exist for T>ga...
  26. Xiaomin Chu

    How to tell the difference between randomness and chaos?

    Found this question while think of determine&random. If a system if very complex, it may looks like random. Even GUT is found, it is still impossible to tell what a determined system will be after a long period because of Heisenberg's uncertainty principle. An error in initial conditions, even...
  27. S

    Quantum Chaos, Level spacing distr. in integrable system

    Hello all, For an undergraduate essay, I am studying the development of quantum chaos in a 1D spin 1/2 chain (my main source paper can be found here:http://scitation.aip.org/content/aapt/journal/ajp/80/3/10.1119/1.3671068). One of the main tools used to distinguish chaotic from non chaotic...
  28. U

    Lorentz Equations - Chaos and Stability

    Homework Statement The figure below shows the path of a particle governed by the Lorenz equations with r = 28, σ = 10, b = 8/3. The x'es and boxes show points where the path crosses the plane z = r − 2σ > 0. (a) Which indicator shows a decreasing z and which shows an increasing z? (b) Show...
  29. LokiReise

    The Illusion of Free Will: Is Determinism Really the Same Thing?

    So I get the gist of Chaos Theory, and I read through another thread on this forum stating that Chaos does exist, which quotes Chaos Theory. Does this not seem to be a tad counter intuitive ? Chaos theory simply states not knowing the starting attributes of a mathematical system that you can't...
  30. X

    Help with research in Chaos theory

    Hello I'm an undergraduate who is currently doing research in Chaos theroy. So far I've built a double pendulum and simulated it on my computer using mathematica. I'm going to use a tracker software to track the empirical motion of the pendulum and try to match it with the my theoretical...
  31. J

    Chaos vs pseudo-random process

    Numbers generated by a pseudo-random process will eventually repeat, which is how PR processes can be differentiated from a truly "random" process. Some chaotic processes follow closed trajectories in state space; i.e., their attractors are periodic, so number sequences generated by those...
  32. J

    Why are fractals and chaos theory synonymous?

    I'm doing a presentation in a few weeks on fractals and chaos theory. To me, their link is more intuitive than mathematically/physically sound, and I'm really struggling to put the link into words. I've tried googling it, but no where seems to give a satisfactory explanation of the link...
  33. S

    Chaos Attractor: +inf as Attractor?

    Can we consider +inf as an attractor for a map for which trajectories emanating from any point in the state space tends to +inf.
  34. T

    Unraveling the #1 Mystery in Physics: Is There Order in Chaos? | LiveScience"

    I was reading this post on livescience web site It's saying that the #1 unsolved mystery in physics is that we are not sure if there is order in chaos I was confused since I thought that chaos only exist due to the lake of infinitely precise calculations, but if there is an all seeing eye...
  35. L

    What Causes Chaos? Can We Predict Its Patterns?

    Well here's my question: what does really "create" chaos?jump between attractions?Can one sit and produce a function which will determine the chaos? P.S my question migh seem a little stupid just because I'm still trying to get a general sense of everything. Thanks.
  36. M

    Can you help me interpret the patterns in these chaos numbers?

    I have a list of chaos numbers Average each 10 results as display below Sum each 10 results as display below Average the 30 results as displayed below here’s my question: I believe that I can see as the average goes up we have larger sums So I think I can predict something from the last...
  37. marellasunny

    Testing for chaos in data(method by Doyne Farmer for 3D discrete data)

    Testing for chaos in data I have data for 3 variables ,each with respect to the discrete time values. How do I check for the existence of chaos for this discrete 3D system?(I don't have the analytic eqs.,just the data.) MY IDEAS ON CHECKING FOR CHAOS FROM DATA:(which of these are feasible...
  38. A

    Exploring Chaos Theory & Statistics: How Do They Intersect?

    Good afternoon, I've come here to hopefully resolve an issue that cropped up in a debate with a friend. We were discussing weather patterns and chaos theory was brought up. My understanding of chaos theory is that it is a way of explaining behavior of certain deterministic systems aka...
  39. T

    Applying Chaos Theory to history

    Let's say you wanted to determine what day in a certain amount of time had been the most influential in our lives today. I theorized that whatever the time period, the first day in that time period would automatically be the most influential day. I though this because as you go farther back in...
  40. N

    Archived Nonlinear Dynamics and Chaos, Strogatz: 2.1.5

    Homework Statement a) Find a mechanical system that is approximately governed by \dot{x}=sin(x) b) Using your physical intuition, explain why it now becomes obvious that x*=0 is an unstable fixed point and x*=\pi is stable. Homework Equations \dot{x}=sin(x) (?) The Attempt at a Solution...
  41. N

    Where do I fit? Nonlinear Dynamics and Chaos, and High Energy Physics

    Hello all, My question is really simple. I really like working on problems that involve Nonlinear Dynamics and Chaos, and I also really enjoy fields of Theoretical Physics that probe the nature of reality (quantum mechanics, high energy & elementary particle physics, string theory, etc.) I...
  42. P

    What the best beginner textbook for chaos, fractal, & random analysis?

    Hi all, I'm trying to self-learn about chaos, fractal, or anything that correspondence to random analysis (maybe with some material from statistical physics). Anyone know what the best textbook for these fields?
  43. M

    Can an Ellipsoidal Region Contain All Trajectories of the Lorenz Equations?

    Homework Statement Show that there is a certain ellipsoidal region E of the form rx2 + σy2 + σ(z-2r)2 ≤ C such that all trajectories of the Lorenz equations eventually enter E and stay in there forever. Homework Equations Lorenz Equations: \dot{x} = \sigma (y - x) \dot{y} = rx -...
  44. R

    How important are these courses for chaos theory/dynamical systems?

    I'm currently a physics major with a year left, and deciding whether to switch into mathematical physics, mathematics or applied mathematics. I'm definitely switching into one of them, as I can meet the requirements for either in my last year and all of them align better with my interests...
  45. R

    Chaos Theory and Schrodinger's Cat: A Quirky Connection

    Can we categorize the Schrodinger's cat as the chaotic system?:cool:
  46. marcus

    Dynamical Chaos and the Volume Gap (Haggard's ILQGS talk)

    Hal Haggard's ILQGS talk should be quite interesting. The plan is to have the slides PDF uploaded sometime Monday at http://bohr.physics.berkeley.edu/hal/pubs/Talks/ILQGS2013/haggard021213.pdf It's potentially helpful to let people look at the slides a day in advance of the Tuesday 12 February...
  47. M

    Bohm Mechanics and Quantum Chaos

    Hello everyone, I would like to know if Bohm Mechanics (and weak measurement) could be useful in understanding Quantum Chaos theories? I'm currently in search of a PhD in Foundation of QM and I would like to know if doing a project that combine the trajectories coming from Bohm Mechanics with...
  48. marellasunny

    Chaos theory vs catastrophe theory

    I am taking a course in non-linear dynamics and I read that Lorenz systems exhibit 'chaotic behaviour' and the spruce-budworm non-linear D.E follows the criteria of 'catastrophe theory'.Is there a difference between these 2 theories?If yes,does this mean that small changes in the spruce-budworm...
  49. G

    MATLAB Is fortran 90 or matlab better for simulating non-linear dynamics (Chaos)?

    I am going to be simulating damped driven oscillators for my project and I was wondering if someone could give me a definitive answer on the matter. I know MATLAB is more of a 'tool' than a language so I'm thinking the maths behind damped driven oscillators might be easier to implement into...
  50. R

    Schools Studying Chaos Theory & Dynamic Systems: A Guide for Postgraduates

    Hi everyone, it's been a while since I visited here. However, I now find myself in need of help as to how to best go about studying something related to chaos theory and dynamic systems in postgraduate school. I'm currently in my third year of physics and my first question would be what...
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