Reverse Butterfly Effect: Saving Alternate Histories of Virtual Worlds

2016 ◽  
Author(s):  
Zi Ye
Keyword(s):  
Popular Culture ◽  
Virtual Worlds ◽  
Chaos Theory ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Storage Model ◽  
Simulation Gaming ◽  
Non Linear Systems ◽  
Butterfly Effect ◽  
Random Nature

Chaos theory is a recent field of study which has become extremely influential in science and in popular culture. Chaos theory deals with complex, non‐linear systems which are extremely sensitive to their initial conditions (commonly known as the butterfly effect), and whose behaviour quickly become unpredictable over short periods of time. Despite their seemingly random nature, chaotic systems are fully deterministic. This means that the same initial conditions will always yield the same future states. When I looked at the butterfly effect backwards, and applied it to computer simulations, the result was a way to store many alternate histories of virtual worlds in a very small amount of data. This time storage model may have applications in scientific simulation, gaming, and cryptography, and provides a different look at chaos theory.

Visualising the invisible: performing chaos theory

Leonardo ◽  
2020 ◽  
pp. 1-8
Author(s):  
Emma Weitkamp
Keyword(s):  
Complex Systems ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Starting Point ◽  
Weather And Climate ◽  
Butterfly Effect ◽  
Long Term Behavior ◽  
The Invisible

Edward Lorenz, the pioneering figure in the field of chaos theory coined the phrase “butterfly effect” and posed the famous question “Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?” In posing the question, Lorenz sought to highlight the intrinsic difficulty of predicting the long term behavior of complex systems that are sensitive to initial conditions, like, for example, the weather and climate; these systems are often referred to as chaotic. Taking Lorenz' butterfly as a starting point, Chaos Cabaret sought to explore the nuances of chaos theory through performance and music.

scholarly journals Sources of uncertainty in deterministic dynamics: an informal overview

2011 ◽  
Vol 369 (1956) ◽  
pp. 4705-4729 ◽  
Author(s):  
Ian Stewart
Keyword(s):  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Sources Of Uncertainty ◽  
Deterministic Systems ◽  
Coin Tossing ◽  
Random Switching ◽  
Butterfly Effect ◽  
Basin Boundaries ◽  
Sensitivity To Initial Conditions

The discovery of chaotic dynamics implies that deterministic systems may not be predictable in any meaningful sense. The best-known source of unpredictability is sensitivity to initial conditions (popularly known as the butterfly effect), in which small errors or disturbances grow exponentially. However, there are many other sources of uncertainty in nonlinear dynamics. We provide an informal overview of some of these, with an emphasis on the underlying geometry in phase space. The main topics are the butterfly effect, uncertainty in initial conditions in non-chaotic systems, such as coin tossing, heteroclinic connections leading to apparently random switching between states, topological complexity of basin boundaries, bifurcations (popularly known as tipping points) and collisions of chaotic attractors. We briefly discuss possible ways to detect, exploit or mitigate these effects. The paper is intended for non-specialists.

scholarly journals Chaotic Systems and Their Recent Implementations on Improving Intelligent Systems

Economics ◽  
2015 ◽  
pp. 1167-1200
Author(s):  
Utku Köse ◽  
Ahmet Arslan
Keyword(s):  
Artificial Intelligence ◽  
Chaos Theory ◽  
Intelligent Systems ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Research Effort ◽  
Nonlinear Dynamical ◽  
Main Research ◽  
Reference Guide

Chaos Theory is a kind of a scientific approach/research effort which is based on examining behaviors of nonlinear dynamical systems which are highly sensitive to their initial conditions. Currently, there are many different scientific studies based on the Chaos Theory and the related solution approaches, methods, or techniques for problems of this theory. Additionally, the theory is used for improving the introduced studies of different fields in order to get more effective, efficient, and accurate results. At this point, this chapter aims to provide a review-based study introducing recent implementations of the Chaos Theory on improving intelligent systems, which can be examined in the context of the Artificial Intelligence field. In this sense, the main research way is directed into the works performed or introduced mostly in years between 2008 and 2013. By providing a review-based study, the readers are enabled to have ideas on Chaos Theory, Artificial Intelligence, and the related works that can be examined within intersection of both fields. At this point, the chapter aims to discuss not only recent works, but also express ideas regarding future directions within the related implementations of chaotic systems to improve intelligent systems. The chapter is generally organized as a reference guide for academics, researchers, and scientists tracking the literature of the related fields: Artificial Intelligence and the Chaos Theory.

Chaotic Systems and Their Recent Implementations on Improving Intelligent Systems

2014 ◽  
pp. 69-101 ◽  
Author(s):  
Utku Köse ◽  
Ahmet Arslan
Keyword(s):  
Artificial Intelligence ◽  
Chaos Theory ◽  
Intelligent Systems ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Research Effort ◽  
Nonlinear Dynamical ◽  
Main Research ◽  
Reference Guide

Chaos Theory is a kind of a scientific approach/research effort which is based on examining behaviors of nonlinear dynamical systems which are highly sensitive to their initial conditions. Currently, there are many different scientific studies based on the Chaos Theory and the related solution approaches, methods, or techniques for problems of this theory. Additionally, the theory is used for improving the introduced studies of different fields in order to get more effective, efficient, and accurate results. At this point, this chapter aims to provide a review-based study introducing recent implementations of the Chaos Theory on improving intelligent systems, which can be examined in the context of the Artificial Intelligence field. In this sense, the main research way is directed into the works performed or introduced mostly in years between 2008 and 2013. By providing a review-based study, the readers are enabled to have ideas on Chaos Theory, Artificial Intelligence, and the related works that can be examined within intersection of both fields. At this point, the chapter aims to discuss not only recent works, but also express ideas regarding future directions within the related implementations of chaotic systems to improve intelligent systems. The chapter is generally organized as a reference guide for academics, researchers, and scientists tracking the literature of the related fields: Artificial Intelligence and the Chaos Theory.

A New Image Encryption Scheme Using Dual Chaotic Map Synchronization

2020 ◽  
Vol 18 (1) ◽  
Keyword(s):  
Image Encryption ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Chaotic Map ◽  
Security Applications ◽  
The Common ◽  
And Diffusion ◽  
Confusion And Diffusion ◽  
Sensitivity To Initial Conditions ◽  
Diffusion Properties

Chaotic systems behavior attracts many researchers in the field of image encryption. The major advantage of using chaos as the basis for developing a crypto-system is due to its sensitivity to initial conditions and parameter tunning as well as the random-like behavior which resembles the main ingredients of a good cipher namely the confusion and diffusion properties. In this article, we present a new scheme based on the synchronization of dual chaotic systems namely Lorenz and Chen chaotic systems and prove that those chaotic maps can be completely synchronized with other under suitable conditions and specific parameters that make a new addition to the chaotic based encryption systems. This addition provides a master-slave configuration that is utilized to construct the proposed dual synchronized chaos-based cipher scheme. The common security analyses are performed to validate the effectiveness of the proposed scheme. Based on all experiments and analyses, we can conclude that this scheme is secure, efficient, robust, reliable, and can be directly applied successfully for many practical security applications in insecure network channels such as the Internet

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

Deep Learning Based Classification of Time Series of Chaotic Systems over Graphic Images

2021 ◽  
Author(s):  
Süleyman UZUN ◽  
Sezgin KAÇAR ◽  
Burak ARICIOĞLU
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Transfer Learning ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Step Size ◽  
Learning Methods ◽  
Data Set ◽  
Graphic Images ◽  
Different Chaotic Systems

Abstract In this study, for the first time in the literature, identification of different chaotic systems by classifying graphic images of their time series with deep learning methods is aimed. For this purpose, a data set is generated that consists of the graphic images of time series of the most known three chaotic systems: Lorenz, Chen, and Rossler systems. The time series are obtained for different parameter values, initial conditions, step size and time lengths. After generating the data set, a high-accuracy classification is performed by using transfer learning method. In the study, the most accepted deep learning models of the transfer learning methods are employed. These models are SqueezeNet, VGG-19, AlexNet, ResNet50, ResNet101, DenseNet201, ShuffleNet and GoogLeNet. As a result of the study, classification accuracy is found between 96% and 97% depending on the problem. Thus, this study makes association of real time random signals with a mathematical system possible.

scholarly journals The State-space Model of Micro-chaos

2021 ◽  
Vol 15 ◽  
pp. 184-189
Author(s):  
Gabor Csernak ◽  
Gabor Stepan
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
State Space Model ◽  
Unstable State ◽  
Considerable Influence ◽  
Chaotic Oscillations ◽  
Controlled System ◽  
Space Model ◽  
Digitally Controlled

Micro-chaos is the phenomenon when the sampling, the delay and the round-off lead to small amplitude chaotic oscillations in a digitally controlled system. It has been proved mathematically during the last few years in a couple of simple cases that the evolving vibrations are indeed chaotic. In this study, we partially generalize these results to the case when an originally unstable state of a system is stabilized by digital feedback control. It is pointed out that this type of systems are sensitive to initial conditions and there exists a finite attracting domain in their phase-space. We also show that the oscillations, related to micro-chaos may have a considerable influence on the accuracy and settling time of the control system. The application of numerical techniques is unavoidable in the case of chaotic systems. Several possibilities are highlighted in the paper for the numerical determination of important characteristics of microchaotic oscillations.

Nonlinear Techniques for Signals Characterization

2011 ◽  
pp. 1266-1272
Author(s):  
Jesús Bernardino Alonso Hernández ◽  
Patricia Henríquez Rodríguez
Keyword(s):  
Time Series ◽  
Signal Processing ◽  
Order Statistics ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Digital Signal ◽  
Higher Order ◽  
Higher Order Statistics ◽  
Three Body ◽  
Nonlinear Signal

The field of nonlinear signal characterization and nonlinear signal processing has attracted a growing number of researchers in the past three decades. This comes from the fact that linear techniques have some limitations in certain areas of signal processing. Numerous nonlinear techniques have been introduced to complement the classical linear methods and as an alternative when the assumption of linearity is inappropriate. Two of these techniques are higher order statistics (HOS) and nonlinear dynamics theory (chaos). They have been widely applied to time series characterization and analysis in several fields, especially in biomedical signals. Both HOS and chaos techniques have had a similar evolution. They were first studied around 1900: the method of moments (related to HOS) was developed by Pearson and in 1890 Henri Poincaré found sensitive dependence on initial conditions (a symptom of chaos) in a particular case of the three-body problem. Both approaches were replaced by linear techniques until around 1960, when Lorenz rediscovered by coincidence a chaotic system while he was studying the behaviour of air masses. Meanwhile, a group of statisticians at the University of California began to explore the use of HOS techniques again. However, these techniques were ignored until 1980 when Mendel (Mendel, 1991) developed system identification techniques based on HOS and Ruelle (Ruelle, 1979), Packard (Packard, 1980), Takens (Takens, 1981) and Casdagli (Casdagli, 1989) set the methods to model nonlinear time series through chaos theory. But it is only recently that the application of HOS and chaos in time series has been feasible thanks to higher computation capacity of computers and Digital Signal Processing (DSP) technology. The present article presents the state of the art of two nonlinear techniques applied to time series analysis: higher order statistics and chaos theory. Some measurements based on HOS and chaos techniques will be described and the way in which these measurements characterize different behaviours of a signal will be analized. The application of nonlinear measurements permits more realistic characterization of signals and therefore it is an advance in automatic systems development.

Managing Chaos

2016 ◽  
Vol 49 (2) ◽  
pp. 296-315 ◽  
Author(s):  
Harri Raisio ◽  
Niklas Lundström
Keyword(s):  
Public Administration ◽  
Chaos Theory ◽  
Real World ◽  
Public Officials ◽  
The Real ◽  
Butterfly Effect

Could public administration research gain something by analyzing issues, practices, and events in ways “beyond the usual”? Could we learn something by analyzing movies? As public administration researchers, we are curious to see what lessons can be drawn from movies based on chaos theory. In this article, three movies, Chaos Theory, The Butterfly Effect, and Mr. Nobody, are analyzed. Analyzing these movies provides two advantages. First, it illustrates the content of chaos theory in an easy-to-understand format. Second, it links the actions in the movies with those of public officials in the real world, providing ideal models of “chaos management.”

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