In mathematics and physics, chaos theory deals with the behavior of certain nonlinear dynamic systems that under certain conditions exhibit a phenomenon known as chaos, which is characterised by a sensitivity to initial conditions (see butterfly effect). As a result of this sensitivity, the behavior of systems that exhibit chaos appears to be random, even though the model of the system is determ ...

Including:

• Chaos theory - Description of the theory
• Chaos theory - Chaotic motion
• Chaos theory - Attractors
• Chaos theory - Strange attractors
• Chaos theory - History
• Chaos theory - Mathematical theory
• Chaos theory - Minimum complexity of a chaotic system
• Chaos theory - Other examples of chaotic systems

Read more here: » Chaos theory: Encyclopedia - Chaos theory

Including:

• Chaos Theory album - Track listing

Read more here: » Chaos Theory album: Encyclopedia - Chaos Theory album

CHAOS THEORY - science that focuses on sudden and fundamental change. (NAD)

(See also: CHAOS THEORY, Wiccan Pagan, Paganism, Pagan Dictionary)

Twenty NLP practitioners met in Vail, Colorado with the intention of exploring the psycho-spiritual motifs that exist in the consciousness of people and the systems in which they live. Using ideas inspired by family systems innovators Bert Hellinger and Virginia Satir, Chaos Theory, Systemic Thinking and Morphogenetic Fields; the group worked with patterns resident in family and organizational systems.

Read more here: » NLP - Neuro Linguistic Programming: Exploring the Psycho-Spiritual Motifs of the Family Mind

The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. The idea is that small variations in the initial conditions of a dynamical system produce large variations in the long term behavior of the system. Sensitive dependence is also found in non-dynamical systems: for example, a ball placed at the crest of a hill might roll into any of several valle ...

Including:

• Butterfly effect - Popular media

Read more here: » Butterfly effect: Encyclopedia - Butterfly effect

Complexity is the opposite of simplicity. Complexity in systems or behaviour is often described as what is "on the edge of chaos" - between order and randomness. Complexity - Study of complexity. Complexity has always been a part of our environment, and therefore many scientific fields have dealt with complex systems and phenomena. Indeed, some would say that only what is somehow complex - what displays variation without being purely random - is worthy of interest. While this has led some fiel ...

Including:

• Complexity - Study of complexity
• Complexity - Complex systems
• Complexity - Complexity in data
• Complexity - Complexity of problems
• Complexity - Specific meanings
• Complexity - Quotes about complexity
• Complexity - Reference

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An analog(ue) computer is a form of computer that uses electronic or mechanical phenomena to model the problem being solved by using one kind of physical quantity to represent another. The central concept among all analog computers can be better understood by examining the definition of an analogy. The similarities of an analogy define the salient characteristics of the comparison. But the differences in an analogy are important too. Modeling a real physi ...

Including:

• Analog computer - How analog computers work
• Analog computer - Analog computer components
• Analog computer - Limitations
• Analog computer - Current Research
• Analog computer - Practical analog computers
• Analog computer - Idealized analog computers
• Analog computer - Reference

Read more here: » Analog computer: Encyclopedia - Analog computer

In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by semi-random, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. Flow that is not turbulent is called laminar flow. The (dimensionless) Reynolds number characterizes whether flow conditions lead to laminar or turbulent flow; a reynolds number above a ...

Including:

• Turbulence - Examples of turbulence

Read more here: » Turbulence: Encyclopedia - Turbulence

Emergence is the process of complex pattern formation from simpler rules. This can be a dynamic process (occurring over time), such as the evolution of the human brain over thousands of successive generations; or emergence can happen over disparate size scales, such as the interactions between a great number of neurons producing a human brain capable of thought (even though the constituent neurons are not individually capable of thought). The original term wa ...

Including:

• Emergence - Emergent properties
• Emergence - Emergence in games
• Emergence - Emergent structures in nature
• Emergence - Emergence in culture and engineering
• Emergence - Emergence in physics
• Emergence - Bibliography

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Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newton's laws of motion and his law of universal gravitation. It is a specific and distinct branch of celestial mechanics, which focuses more broadly on Newtonian gravitation and includes the orbital motions of artificial and natural astronomical bodies such as planets, moons, and comets. Astrodynamics is principally concerned with spacecraft trajectories, from launch to atmospheric re-entry, including all orbital maneuvers, ...

Including:

• Astrodynamics - Laws of astrodynamics
• Astrodynamics - Formulae for ellipse
• Astrodynamics - Historical approaches
• Astrodynamics - Kepler's equation
• Astrodynamics - Perturbation theory
• Astrodynamics - Modern techniques
• Astrodynamics - Conic orbits
• Astrodynamics - Transfer orbits
• Astrodynamics - The patched conic approximation
• Astrodynamics - The universal variable formulation
• Astrodynamics - Perturbations
• Astrodynamics - Non-ideal orbits
• Astrodynamics - Interplanetary superhighway and fuzzy orbits
• Astrodynamics - Reference

Read more here: » Astrodynamics: Encyclopedia - Astrodynamics

The word random is used to express apparent lack of purpose, cause, or order. The term randomness is often used synonymously with a number of measurable statistical properties, such as lack of bias or correlation. Randomness has an important place in science and philosophy. Randomness - History. Humankind has been concerned with randomness since prehistoric times, mostly through divination (reading messages in random patterns) and gambling. The opposition between free will ...

Including:

• Randomness - History
• Randomness - Randomness versus unpredictability
• Randomness - Misconceptions/logical fallacies
• Randomness - A number is due
• Randomness - A number is cursed
• Randomness - Study of randomness
• Randomness - In philosophy
• Randomness - In biology
• Randomness - In the natural sciences
• Randomness - Source of randomness
• Randomness - In mathematics
• Randomness - In communication theory
• Randomness - In finance
• Randomness - Applications and use of randomness
• Randomness - Generating randomness
• Randomness - Quotations
• Randomness - Books

Read more here: » Randomness: Encyclopedia - Randomness

Determinism is the philosophical proposition that every event, including human cognition and action, is causally determined by an unbroken chain of prior occurrences. No mysterious miracles or wholly random events occur. If there has been even one indeterministic event since the beginning of time, then determinism is false. Determinism - Philosophy of determinism. The principal consequence of deterministic philosophy is that free will (except as defined in strict compatibilism) becomes an illusion. It is a ...

Including:

• Determinism - Philosophy of determinism
• Determinism - The nature of determinism
• Determinism - Determinism in Western tradition
• Determinism - Determinism in Eastern tradition
• Determinism - Arguments against determinism
• Determinism - Argument from morality
• Determinism - Determinism quantum mechanics and classical physics
• Determinism - First cause
• Determinism - A multi-deterministic position
• Determinism - Modern perspectives on determinism
• Determinism - Scientific determinism and first cause
• Determinism - Determinism and generative processes

Read more here: » Determinism: Encyclopedia - Determinism

The roots of chaos theory date back to about 1900, in the studies of Henri Poincaré on the problem of the motion of three objects in mutual gravitational attraction, the so-called three-body problem. Poincaré found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point. Later studies, also on the topic of nonlinear differential equations, were carried out by G.D. Birkhoff, A.N. Kolmogorov, M.L. Cartwright, J.E. Littlewood, and Stephen Smale. Except for Smale, who was perhaps the first p ...

See also:

Chaos theory, Chaos theory - Description of the theory, Chaos theory - Chaotic motion, Chaos theory - Attractors, Chaos theory - Strange attractors, Chaos theory - History, Chaos theory - Mathematical theory, Chaos theory - Minimum complexity of a chaotic system, Chaos theory - Other examples of chaotic systems, Chaos theory - Application

Read more here: » Chaos theory: Encyclopedia II - Chaos theory - History

Chaos Theory

science that focuses on sudden and fundamental change. (NAD)

(See also: Chaos Theory, New Age Spirituality, Body Mind and Soul)

The roots of chaos theory date back to about 1900, in the studies of Henri Poincaré on the problem of the motion of three objects in mutual gravitational attraction, the so-called three-body problem. Poincaré found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point. Later studies, also on the topic of nonlinear differential equations, were carried out by G.D. Birkhoff, A.N. Kolmogorov, M.L. Cartwright, J.E. Littlewood, and Stephen Smale. Except for Smale, who was perhaps the first p ...

See also:

Chaos theory, Chaos theory - Description of the theory, Chaos theory - Chaotic motion, Chaos theory - Attractors, Chaos theory - Strange attractors, Chaos theory - History, Chaos theory - Mathematical theory, Chaos theory - Minimum complexity of a chaotic system, Chaos theory - Other examples of chaotic systems

Read more here: » Chaos theory: Encyclopedia II - Chaos theory - History

Mathematicians have devised many additional ways to make quantitative statements about chaotic systems. These include: fractal dimension of the attractor Lyapunov exponents recurrence plots Poincaré maps bifurcation diagrams Transfer operator Chaos theory - Minimum complexity of a chaotic system. Many simple systems can also produce chaos without relying on differential equations, such as the logistic map, which is a difference equation (recurrence r ...

See also:

Chaos theory, Chaos theory - Description of the theory, Chaos theory - Chaotic motion, Chaos theory - Attractors, Chaos theory - Strange attractors, Chaos theory - History, Chaos theory - Mathematical theory, Chaos theory - Minimum complexity of a chaotic system, Chaos theory - Other examples of chaotic systems, Chaos theory - Application

Read more here: » Chaos theory: Encyclopedia II - Chaos theory - Mathematical theory

Chaos theory is a collection of results, methods, and visualization techniques used to study dynamical systems. A mathematical model of a natural or human system where numerical quantities are used to represent the state of the system is an example of a dynamical system. Some of these numerical quantities vary with time—they are dynamical—and others remain fixed—they are parameters. In a dynamical system, the numerical quantities are combined in a formula to determine how the dynamical quantities change after a short time period. The c ...

See also:

Chaos theory, Chaos theory - Description of the theory, Chaos theory - Chaotic motion, Chaos theory - Attractors, Chaos theory - Strange attractors, Chaos theory - History, Chaos theory - Mathematical theory, Chaos theory - Minimum complexity of a chaotic system, Chaos theory - Other examples of chaotic systems, Chaos theory - Application

Read more here: » Chaos theory: Encyclopedia II - Chaos theory - Description of the theory

Mathematicians have devised many additional ways to make quantitative statements about chaotic systems. These include: fractal dimension of the attractor Lyapunov exponents recurrence plots Poincaré maps bifurcation diagrams Transfer operator Chaos theory - Minimum complexity of a chaotic system. Many simple systems can also produce chaos without relying on differential equations, such as the logistic map, which is a difference equation (recurrence r ...

See also:

Chaos theory, Chaos theory - Description of the theory, Chaos theory - Chaotic motion, Chaos theory - Attractors, Chaos theory - Strange attractors, Chaos theory - History, Chaos theory - Mathematical theory, Chaos theory - Minimum complexity of a chaotic system, Chaos theory - Other examples of chaotic systems

Read more here: » Chaos theory: Encyclopedia II - Chaos theory - Mathematical theory

A non-linear dynamical system can exhibit one or more of the following types of behavior: forever at rest forever expanding (only for unbounded systems) periodic motion quasi-periodic motion chaotic motion The type of behavior a system may exhibit depends on the initial state of the system and the values of its parameters, if any. The most difficult type of behavior to characterize and predict is chaotic motion, a non-periodic complex motion, for which the theory is named.See also:

Chaos theory, Chaos theory - Description of the theory, Chaos theory - Chaotic motion, Chaos theory - Attractors, Chaos theory - Strange attractors, Chaos theory - History, Chaos theory - Mathematical theory, Chaos theory - Minimum complexity of a chaotic system, Chaos theory - Other examples of chaotic systems

Read more here: » Chaos theory: Encyclopedia II - Chaos theory - Description of the theory

Fractal mysticism is the loosest and least rigorous of the three types. In it, fractal artworks are used as a framework for spiritual journeys, much in the same way as are mandalas. The ideas, terms and concepts of chaos theory are used as inspiration, but little effort is made to create solid correlations. Recursive shapes such as fractals have been a favorite of mystics for quite a long time, as (for example) the "wheel within a wheel" of the Biblical prophet Ezekiel or ...

See also:

Fractal metaphysics, Fractal metaphysics - Fractal Mysticism, Fractal metaphysics - Fractal Metaphor, Fractal metaphysics - Fractal Philosophy, Fractal metaphysics - Fractal Theism

Read more here: » Fractal metaphysics: Encyclopedia II - Fractal metaphysics - Fractal Mysticism