To associate your repository with the lorenz-attractor topic, visit your repo's landing page and select "manage topics. Another approach is developed for generating two-wing hyperchaotic attractor, four-wing chaotic attractor, and high periodic orbits such as period-14 from a sinusoidally driven based canonical Lorenz system. β is set to 8/3. z (i+1)=z (i)+h* (1/6)* (m1+2*m2+2*m3+m4); end. DOI: 10. You can see the definition of an attractor here: wikipedia. 勞侖次吸引子 （Lorenz attractor）是 勞侖次振子 （Lorenz oscillator）的長期行為對應的 碎形 結構，以 愛德華·諾頓·勞侖次 （Edward Norton Lorenz）的姓氏命名。. Ghys. Plotted this image of the Lorenz attractor in college, thought it would make a nice shirt for anyone into maths/physics. Animating the Lorenz Attractor with Python. English: An icon of chaos theory - the Lorenz attractor. Lorenz attractor is a set of differential equations that describe a simplified atmospheric convection model. We study a class of geometric Lorenz flows, introduced independently by Afraimovič, Bykov & Sil′nikov and by Guckenheimer & Williams, and give a verifiable condition for such flows to be mixing. Red Ink Tattoos. Quotes To Live By. It was proven in [8] that the. Lorenz system being real, but the rigorous techniques of dynamical mathematics were unable to prove it. 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. Even more, Lorenz links are fibered: any finite collection of periodic orbits defines a fibered link. Tatoos. The resulting model prediction in Fig. Lorenz Attractor. Chaos Tattoo. Sci. 0:00 Introducing today's topic 0:55 Differential Equations 2:30 Lorenz systems 3:36 Non-linear, chaotic systems 4:30 Start Coding! 6:07 Every cycle through draw is 1 unit of time 6:30 Add formulas to code 8:19 Change of time per frame 10:10 Modify the inputs 12:48 Plot the system 14:08 Scale the scene 14:42 Add an array list to store the data. 74 30. Hi everyone! i want to simulate Lorenz Attractor using the script I found in Matlab File Exchange by Moiseev Igor. Description. It also arises naturally in models of. For example, a limit cycle is a loop-shaped attractor (1D). Geometry. It also arises naturally in models of lasers and dynamos. Lorenz Attractor Made by Samuel Volin for Fall 2015 CSCI-4229. Highlighting chaotic nature of Lorenz system. 18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015View the complete course: mill is also very sensible to initial conditions, and a 3D graph of the three parameters has the shape of a butterfly, just like the Lorenz attractor. A tiny cause can generate big consequences!The topological structure of the Lorenz attractor is preserved by the reconstruction. However, the the trajectory is much smoother throughout the training. [2] Chaos theory and the sensitive dependence on initial conditions were described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890, who later proposed that such phenomena could be common, for. But, it hasn't been easy to find pre-existing work that I like. tomrocksmaths. The Lorenz System designed in Simulink. Math tattoos - Lorenz attractor? Since I learned about the Lorenz attractor a couple of years ago, it has come to mean a lot to me personally. 48 followers. Plotted this image of the Lorenz attractor in college, thought it would make a nice shirt. The Lorenz Attractor is a system of differential equations first studied by Ed N, Lorenz, the equations of which were derived from simple models of weather phenomena. For the Lorenz attractor, it was reported that the fractal dimension slightly larger than two, for example, in [2], d ≈ 2. Pinterest. Feb 3, 2019 - This Pin was discovered by Mario Andrés. 3. Acad. 로렌즈 끌개는 3차원 속의 곡면 속에 존재하며, 프랙털 모양을 하고 있다. Download files and build them with your 3D printer, laser cutter, or CNC. Maze Runner. Meterologist, Edward Lorenz discovered it by chance in 1961 while running computer simulations to study atmospheric convection and weather patterns. Updated 24 Mar 2019. It turns out that. Since convection is a huge factor driving weather, the equations are useful in weather prediction models. Have you ever thought about getting inked with a geisha tattoo? Find out more about the history and meaning of this tattoo. There are also conservative chaotic system but not attractors. Search. motion induced by heat). The Lorenz Attractor. Chaotic systems are the category of these systems, which are characterized by the high sensitivity to initial conditions. The Lorenz attractor first appeared in numerical experiments of E. Edward Lorenz and his wife, Jane, on Cape Cod. pyplot as plt # This import registers the 3D projection, but is otherwise unused. This notebook contains a full TDA pipeline to analyse the transitions of the Lorenz system to a chaotic regime from the stable one and viceversa. com ) In popular media the ‘BUTTERFLY EFFECT’ stems. . vector fields, every Lorenz attractor supports a unique equilibrium state. I searched for the solutions in different sites but i didn't find many using rk4. Presumably the "2D disks" you've seen are just projections of the real object. Strange attractors are produced by a stretching and folding. The results are compared with statistics for a couple of other. 01 m thick layer of water at 20°C using the Rayleigh constant, the Prandl number and a critical number, Rc, (eqs. Plot in SVG vector format, Projection of trajectory of Lorenz system in phase space with "canonical" values of parameters r=28, σ = 10, b = 8/3. It begins with symmetry (part I) and Cayley tables (part II), before introducing Lagrange's Theorem (part III) and semi-direct products (part IV) to form a list of all groups up to order 16. Abstract. The animation we gone develop here depicts this system’s behavior over time in Python, using scipy to integrate the differential equations, matplotlib to draw the 3D plots, and pillow to create the animated GIF. Lorenz Attractor. This was discovered by the North American theoretical meteorologist, Edward Norton Lorenz (1938-2008). 3 MB. C’est la vie. It is intended to promote the industry and create positive exposure for talented artists, as well as provide resources for tattoo. Premium Powerups Explore Gaming. Theorem 1. Change of time per frame. MIT RES. F. Imagine a rectangular slice of air heated from below and cooled from. plot3 (x,y,z) But the solutions are not right. Bit of an update. Simply type in your desired image and OpenArt will use artificial intelligence to generate it for you. Tucker, C. A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 3. Pi Shirt. That’s why it’s so often tied to butterflies screwing with the. On 13 the stable periodic orbits St,2 coalesce in pairs with the saddle orbits Ct,z and disappear. hw2: Lorenz Attractor. Chaotic attractors in the classical Lorenz system have long been known as self-excited attractors. To study the possibly complicated behavior of three-dimensional systems, there is no better place to begin than with the famous model proposed by Lorenz in 1963. Publications Mathématiques de l'Institut des Hautes Études Scientifiques 50 , 73–99 ( 1979) Cite this article. Strange attractors are also coupled with the notion ofow is called the geometric Lorenz attractor. It always stayed within certain bounds, but at the same time, it never repeated itself. • 28 days ago. The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. The three holes exclude the three critical sets. Fractal[ edit] > The Lorenz attractor, named for Edward N. js. com. When autocomplete results are available use up and down arrows to review and enter to select. This paper, for the first time, reveals a novel hidden chaotic attractor in the. The first four are absorbing volumes while the interior of the cone is expelling. 2. At the same time, they are con ned to a bounded set of zero volume, yet manage to move in this set A Lorenz-like attractor can also be created from the z-axis torsion coming from the Gross-Pitaevskii (GP) equation 24,33,34, leading to an aesthetic attracting set shown in Fig. 06 24. CHAOS Strange Attractors and Lorenz Equations Definitions Chaos – study of dynamical systems (non-periodic systems in motion) usually over time Attractor – a set of points in phase space toward which neighboring points asymptotically approach within a basin of attraction - an attractor can be a point, curve, manifold or a complicated set of fractals. Lorenz: time series | power spectrum | mutual information | attractor | attractor 3D | autocorrelation | poincare | 1-D maps This was created by Runge-Kutta integration of the Lorenz equations. - The graph consists of two parts: Simulating the movement of particles and drawing the curve of the attractor. A rigorous proof of the existence of a strange attractor for the Lorenz attractor was given by Warwick Tucker. IntroductionThe systematic study of the differential equations: x ̇ =σ(−x+y), y ̇ =−xz+rx−y, z ̇ =xy−bz, with σ=10, r=28, and b=8/3, by Lorenz [10] led to the discovery of the butterfly-like Lorenz attractor, an image that has become commonplace in textbooks on chaos theory. The Chen system, a modified version of the Lorenz system [46] [47] [48], seems more representative since the fractional order has to be superior to 0. Explore math with our beautiful, free online graphing calculator. It is a nonlinear system of three differential equations. Lorenz system being real, but the rigorous techniques of dynamical mathematics were unable to prove it. It is fairly easy to call such movie from the Powerdot slides (written in PSTricks) but I wonder if I could create animation natively which will not require to. This review paper would like to sketch some of the main steps in the historical development of the concept of chaos in dynamical systems, from the mathematical point of view, and present the present status of the Lorenz attractor in the panorama of the theory. dx / dt = a (y - x) The picture in Figure 3 does not yet create the strange attractor, as most orbits are attracted to either C_1 and C_2. up / down arrow keys to rotate the view and the y axis. Wisdom Quotes. Lorenz Attractor from Gauss-Legendre. To this end, the main local and global bifurcations leading to the appearance and destruction of the attractors are studied in two-parameter families of such models of certain types. mentioned above is mixing. Layout Design. Find out more about the history and meaning of this tattoo. 6. It consists of multiple ordinary differential equations, which were first studied by Edward Lorenz [23]. A rigorous numerical algorithm, formally verified with Isabelle/HOL, is used to certify the computations that Tucker used to prove chaos for the Lorenz attractor. Simply type in your desired image and OpenArt will use artificial intelligence to generate it for you. The Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight. Of note, Lorenz found that the system exhibited chaotic behavior when sigma=10, rho=28, and. My goal is to solve lorenz equations and plot them as it shows in the figure. GNU Octave code that draws the Lorenz attractor. Lorenz attraktor med skalor. The "wings" don't lie in a plane; the predominantly blue portion on the right of your image seems to indicate that clearly. m and h_f_RungeKutta. e. Haut Tattoo. Anishchenko et al. lorenz attractor tattoo, highly detailed, complicated Generate unique and creative images from text with OpenArt, the powerful AI image creation tool. 10: NODE predictions for the Lorenz system. Observe that a homoclinic class although transitive (by the Birkhoff. Download beautiful free and premium royalty-free halftone vectors as well as stock photo, PSD, mockups, and illustrations at rawpixel. The attractor is a set of points in R3 R 3. Thing details. Today. Hr Giger Art. Lorenz attractor. gitignore. Pinterest. The most famous strange attractor is undoubtedly the Lorenz attractor — a three dimensional object whose body plan resembles a butterfly or a mask. In MATLAB is for example trivial to generate movie which shows creation of the Lorenz attractor. The Lorenz attractor was first studied by Ed N. Thing details. dt. 1c A dynamical system x˙=v x is said to be equivariant under a linear transformation M if Mx˙=v Mx. Williams [30,66] gave well descriptions of the structure of geometric Lorenz attractors which led more studies, for instance [3,19,42,62,63] and references therein. Self-similarity is the underlying concept in fractals. "This paper presents a rigorous proof that confirms the existence of the Lorenz attractor, an example of deterministic chaos that could only be generated by numerical approximations on a computer. Chaos Theory. The Lorenz attractor is defined by the system of equations,,, where denotes the derivative of with respect to the parameter of the curve, is the Prandtl number, and is the Rayleigh number. The Lorenz Attractor Explained. svg. 85 and B = 0. Ensembles of the Lorenz attractor r=28 2 fixed points 2 fixed points + strange attractor intermittenc - I I I I I I I I r 0 1. Welcome to the r/Tattoos subreddit community The form of the Lorentz Attractor. The “Lorenz attractor” is the paradigm for chaos, like the French verb “aimer” is the paradigm for the verbs of the 1st type. Physics. In collaboration with GMK Chaos Theory are two metal artisans: our first collaboration with HIBI, depicting the Lorenz attractor butterfly with a brass base,. 21, 22(2)). svg 2,495 × 2,880; 4. The Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight. Rajouté le mercredi 9 mars 2022. Simply type in your desired. This is produced by three deceptively simple equations: dx / dt = a (y - x) dy / dt = x (b - z) - y dz / dt = xy - c z From here emerged the idea of chaos and randomness. I have two different initial conditions [x0, 1, 0] and x0= 0 then x0 =1* 10^-5 the two values of rho are ρ= 14 and ρ=28. The Lorenz Attractor, a thing of beauty. HTML Preprocessor About HTML Preprocessors. x * (l. it possesses a transverse fractal structure expressed much stronger than that for the Lorenz type attractor, where it is visually indistinguishable. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. (SVG file, nominally 750 × 750 pixels, file size: 1. Visualize the Lorenz Attractor. Published 2002. HTML preprocessors can make writing HTML more powerful or convenient. my parameters are sigma=. Math Art. A Speech masking technique based on Lorenz System is presented in [1, 2] which uses Lorenz equation to generate Chaotic Signals, these signals are used as a base carrier signal on which the. are called the Lorenz system. Layout Design. Alexis McBeain CSCI 4229/5229 Fall 2020. Download premium vector of Geometric halftone background vector by Wan about zigzag line, zigzag, circle halftone, abstract backgrounds, and backdrop 591636. I used the subroutine rkdumb() taken from Numerical Recipes, with a step size of 0. Good Music. Tucker. HTML Preprocessor About HTML Preprocessors. A striking finding is that a fractional Lorenz system with smaller Σ , which is a sum of the orders of all involved equal derivatives, has smaller attractor radius and shorter predictability limits. In conclusion, the Lorenz Attractor is a fascinating mathematical model that captures the essence of chaos theory. →∞. Discover (and save!) your own Pins on Pinterest. More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. Tucker’s work is hugely significant, not just because it provides the Lorenz attractorDownload this Lorenz Attractor photo now. Aug 10, 2021 - Buy "Butterfly Effect / Lorenz Attractor " by FireWoman98 as a Sticker. x2 +y2 + (z − P − r)2 = 2 x 2 + y 2 + ( z − P − r) 2 = 2. Media in category "Lorenz attractors". Works of J. 1995 K. Code capable of rendering this is available. Date: 4 January 2006 (original upload date) Source: Own work: Author: DschwenThe Lorenz attractor is an example of a singular hyp erb olic a ttr actor [18 ] (uniformly. wolfram. The Lorenz chaotic attractor was discovered by Edward Lorenz in 1963 when he was investigating a simplified model of atmospheric convection. Sci. Embedded in this attractor are unstable periodic orbits described by Viswanath and this model computes a number of these orbits. Jan 4, 2023 - The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. LORENZ AND INDUCED LORENZ SYSTEMS The Lorenz dynamical system L is a three dimensional flow defined by the equations x˙ = y −x 1a y˙ =Rx− y −xz 1b z˙=−bz+xy. Hi everyone! i want to simulate Lorenz Attractor using the script I found in Matlab File Exchange by Moiseev Igor. [*] Extra terms of degree 3 were needed, [*] Arbitrarily small unfoldings, [*] Lorenz equation notin the families. ) Chaotic attractors Math model:The Strange Attractor of the Lorenz System. A Lorenz Attractor Simulator created using Three. Visit. You just have to keep iterating it out. Many chaotic attractors, such as the Lorenz Attractor, are defined as a set of differential equations. If all goes well, you should perceive the Lorenz attractor in 3D: Part of it will appear close to you, actually out in from of the screen --- try to "touch" it (locate its position) with you finger. The phenomenon you observe is a natural outcome of applying approximate solution methods to a system like the Lorenz attractor that exhibits sensitive dependence on initial conditions. It is a nonlinear system of three differential equations. Constructed explicitfamilies of ODEs with geometric Lorenz attractors. Teoria do caos – Wikipédia, a enciclopédia livre. Since its introduction to meteorology by Edward Lorenz (Lorenz 1956), empirical orthogonal function (EOF) analysis—also known as principal. " He hypothesized that the graph he created to model the motion would either reach equilibrium and stop, or create a loop that would eventually be reformed and retraced, indicating a repeating pattern. History. Previously, the Lorenz attractor could only be generated by numerical approximations. Thus, no trajectory ever coincides with any other. The attractor is a set of points in R3 R 3. the Lorenz attractor. In the first model, the refine factor has been changed to 4 for a smoother simulation and the states are saved in the workspace. It has also been referred to as ``Lorenz's Butterfly'' in honor of the butterfly effect. Lorenz’s strange vortex plotted for constants of ( ho =28), (sigma =10), and (eta =frac{8}{3}). Lorenz Attractor – Particle System | Processing. A quick summary is: For the parameter values you've given, solutions are attracted to the set -- if you imagine time going to infinity, then the solutions get closer and closer to the attractor. 2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back. A small perturbation in the initial setup of a chaotic system may lead to drastically different behavior, a concept popularly. Code of this script is written in the Vnano. Makes. " rule. – Wrzlprmft. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight. The Lorenz Attractor is Mixing. 0014 was used. We show that adding noise in the last component causes a transition from a unique to exactly two ergodic invariant measures. The Lorenz Attractor Exists – An Auto-Validated Proof. To the point @grevel, first off, the Lorentz attractor exists in a 3D phase space. More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. Aug 18. 3 The Lorenz Attractor As shown above, when 24. Math. This is an example of plotting Edward Lorenz's 1963 "Deterministic Nonperiodic Flow" in a 3-dimensional space using mplot3d. The Lorenz attractor near an intermittent cycle: much of the time the trajectory is close to a nearly periodic orbit, but diverges and returns. The what now? Ok, pick a starting state…you won’t be able to predict where any of it will go. The graph was plotted with gnuplot from the Lorenz attractor equations. Lorenz Attractor is 100% multi-threaded capable of using an unlimited number of cores for ultimate speed. The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. my parameters are sigma=. Nov 7, 2021 - Welcome to the r/Tattoos subreddit community. Have you ever thought about getting inked with a geisha tattoo? Find out more about the history and meaning of this tattoo. michelle. 4. The solutions will tend to an attractor in space, the so-called Lorenz attractor. grad)A and use familiar vector identities to obtain dv/dt = E - v x B, E = -gradV. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. To associate your repository with the lorenz topic, visit your repo's landing page and select "manage topics. The Lorenz attractor shows how a very simple set of equations can produce astonishingly different results when given minutely different starting conditions. The Lorenz attractor shows how a very simple set of equations can produce astonishingly different results when given minutely different starting conditions. 1. be isolated. Simplifications of the Lorenz Attractor J. Python scripts for some 3rd-order chaotic systems (Lorenz attractor, Nose-Hoover oscillator, Rossler attractor, Riktake model, Duffing map etc. In 1963 Lorenz published his seminal paper Deterministic Non-‐‑ periodic flow in the Journal of Atmospheric Sciences. 2. A. Aug 10, 2021 - Buy "Butterfly Effect / Lorenz Attractor " by FireWoman98 as a Sticker. In a way, one could think of the attractor as an “infinite link with infinitely many components. Previously, the Lorenz attractor could only be generated by numerical approximations on a computer. Lorenz first discovered chaos by accident while developing a simple mathematical model of atmospheric convection. A quick summary is: For the parameter values you've given, solutions are attracted to the set -- if you imagine time going to infinity, then the solutions get closer and closer to the attractor. The following 90 files are in this category, out of 90 total. Made with Chaoscope. " GitHub is where people build software. The following program plots the Lorenz attractor (the values of x, y and z as a parametric function of time) on a Matplotlib 3D projection. A quite incredible description of the fundamentals of group theory from one of my undergraduate students. The Lorenz attractor. On the contrary, for the Lorenz system. It is very unusual for a mathematical or physical idea to disseminate into the society at large. 0 coins. To address that problem some authors introduced. Pendulum. Dark Fantasy Art. x) dy = l. Wikimol, Dschwen via Wikipedia. Artistic Installation. N. Remixes. Find GIFs with the latest and newest hashtags! Search, discover and share your favorite Lorenz-attractor GIFs. g. Absolutely continuous invariant measures for one-parameter families of one-dimensional maps. Download files and build them with your 3D printer, laser cutter, or CNC. Graphic Poster Art. , 81:39–88, 1981. Watch. 0 13. A version was designed for excitable media , where information may be transmitted by spiking events, extending usage to possible. The equations are ordinary differential equations, called Lorenz equations. 6. . it’s pretty quiet here for the first time in a long while so i’m finally sitting down to write. gitignore","path":". Lorenz's Attractor. Note that there can be periodic orbits (see e. It is a nonlinear system of three differential equations. The Lorenz attractor ¶. ”. Parameters: sigma =10,beta =8/3 and rho =28. Consciousness Art. It is known as the Lorenz strange attractor, and no equilibrium (dynamic or static) is ever reached – it does not form limit cycles or achieve a steady state. Save. In 2001 mathematician Warwick Tucker proved that the paper model accurately describes the motion on the Lorenz attractor. Image by author. A Trajectory. Se trata de un sistema dinámico determinista tridimensional no lineal derivado de las ecuaciones simplificadas de rollos de convección que se producen en las ecuaciones dinámicas de la atmósfera terrestre . The system is most commonly expressed as 3 coupled non-linear differential equations. The Lorenz system consists of three differential equations: dx/dt = sigma (y-x), dy/dt = x (rho-z)-y, dz/dt = xy - beta*z. Dark Fantasy Art. A Lorenz attractor can be described by a system of ordinary differential equations: the Lorenz system. The Lorenz attractor, named for its discoverer Edward N. A Lorenz system. Today. Lorenz Attractor / Chaos Theory tattoo done by Indy @ Mission Ink & Piercing, San Francisco: tattoos | Science tattoos, Science tattoo, Chaos tattoo. The corresponding bifurcation. 1016/S0764-4442(99)80439-X;Animation:I used python and matplotlib to create an animated simulation of the Lorenz Attractor#chaostheory #butterflyeffect #matplotlib #python Sound trac. The full equations are partial/ (partialt) (del ^2phi. This behavior of this system is analogous to that of a Lorenz attractor. The Lorenz system includes three ordinary differential equations: dx/dt = sigma ( y - x ) dy/dt = x ( rho - z ) - y dz/dt = xy - beta z. The Lorenz system is related to the Rössler attractor, but is more complex, having two. This program implements the Lorenz Attractor in python 3. Re: Lorenz Attractor (Horowitz design) - problems on pcb. Chungnam National University. Created by User:Dschwen. R. Simplest flow has a strange attractor that's a Mobius strip. Understanding Chaos: The Lorenz Attractor. First of all, the periodic attractor is analyzed for the almost periodic Lorenz-84 system with almost periodically forcing, including the existence and the boundedness of those almost periodic solutions, and the bifurcation phenomenon in the. So of course, chaos theory started a race among scientists to understand what happens when a system moves from a point of stability. Edward Lorenz, the father of chaos theory, once described chaos as “when the present determines the future, but the approximate present does not approximately determine the future. A strange occurrence swirling in the sky. He simplified them and got as a result the following three-dimensional system:Atractor de Lorenz. {"payload":{"allShortcutsEnabled":false,"fileTree":{"":{"items":[{"name":"README. We call this. That mostly means no side effects and functions that perform 1 small task. is mixing for a flow. If you are looking at a static version of this notebook and would like to run its contents, head over to GitHub and download the source. motion induced by heat). To set the initial position, look at around line 81. Some-In Lorenz's water wheel, equally spaced buckets hang in a circular array. At one point, Edward Lorenz was looking for a way to model the action of the chaotic behavior of the gaseous system first mentioned above. The Lorenz attractor is an example of a singular hyperbolic attractor [MorPacPuj99] (uniformly hyperbolic, except for a singularity due to the attractor containing an equilibrium). You can linearize the system at the unstable fixed points to figure out how the system behaves like a linear system near those points, though. Doubly inspired because Animation Nodes is one of my favorite tools of all time. This dependence is such that arbitrarily small initial sets will eventually spread over the whole attractor.