Chaos and Fractals

Chaos and Fractals

Chaos deals with nonlinear dynamical systems. Learn about Chaos Theory or discuss topics such as lotenz systems, the butterfly effect, and modeling turbulent fluid systems such as the climate and weather. Fractals are used especially in... [more]

Chaos deals with nonlinear dynamical systems. Learn about Chaos Theory or discuss topics such as lotenz systems, the butterfly effect, and modeling turbulent fluid systems such as the climate and weather. Fractals are used especially in computer modeling of irregular patterns and structures in nature.

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The Heart of Trading Futures Contracts: Fractals Defined

Written by trader7757 on
Source of some of this article is Wikipedia. A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A fractal often has the following features: * It has a fine structure at arbitrarily small scales. * It is too irregular to be easily described in traditional Euclidean geometric language. * It is self-similar (at least approximately or stochastically). * It has ... Read Full Story

Fractals

Written by rafoarc on
Some experiments with fractals, using chaoscope and gaston. Both applications can generate fractal formations in 3d. However, the models are made out of (millions of) points, so I suppose that it would be impossible to export in any standard 3d format... Read Full Story

Chaos Theory and Fractals

Written by trader7757 on
It is fitting that chaos theory got its start in the humble but frustrating field of meteorology. Why does it seem impossible for all our hot-shot meteorologists, armed as they are with ever more efficient computers and ever greater masses of data, to predict the weather? Two decades ago, Edward Lorenz, a meteorologist at MIT stumbled onto chaos theory by making the discovery that ever so tiny changes in climate could bring about enormous and volatile changes in weather. Calling it the Butterfly Effect, he pointed out that if a butterfly flapped its wings in Brazil, it could well produce a tornado in Texas. ... Read Full Story

Fractal Dimension and Analysis of Chaotic System Predictions

Written by HouwLiong on
By: Acep Purqon Advisor: Prof. Dr. The Houw Liong Departemen Fisika - ITB : Jl. Ganesa 10, Bandung Created: 2005-01-27 , with 1 file(s). Master Theses from JBPTITBFI / 2005-02-08 14:16:05 In 1963 Edward Lorenz successfully formulated chaotic behavior in weather. Lorenz simplified model of 2D thermal convection known as Rayleigh-Benard convection into three simultaneous ordinary differential equations called Lorenz equations. Lorenz noticed that, in his simplified mathematical model of Rayleigh-Benard convection, very small differences in the initial conditions blew up and quickly led to enormous differences in the final behavior. He reasoned that if this type of behavior could occur in such a ... Read Full Story

Free Fractal generation using Gnofract 4D

Written by mriza on
What is fractal A fractal is generally "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured". A fractal often has the following features: It has a fine structure at arbitrarily small scales. It is too irregular to be easily described in traditional Euclidean geometric language. It is self-similar (at least approximately or stochastically). It has a Hausdorff dimension which is greater than its topological ... Read Full Story
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Fraqtive 0.4.5
Fraqtive 0.4.5 (KDE Education)Fraqtive is an open source, multi-platform generator of the Mandelbrot family fractals. It uses very fast algorithms supporting SSE2 and multi-core processors. It generates high quality anti-aliased images and renders 3D scenes using OpenGL. It allows real-time navigation and dynamic generation of the Julia fractal preview.changelog:0.4.5 (2009-12-18) This release adds the possibility to generate fractal images...  
From kde.org ()
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Explore Fractals on Your iPhone or iPod Touch
© Pomegranate Software Normally costing US$2.99, for the rest of 2009, Pomegranate Software is offering its Fractals app for free. Fractals are graphic images based on mathematical equations, and are a lot of fun to explore. The Fractals app is a neat way to explore both Madelbrot and Julia fractals in your spare time, and you can save any of the fractals as images on your device. Fractals 1.0 is the first fractal app for iPhone that...  
From z.about.com ()
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Corel Painter Growth Effect: A Fascinating Fractal
Originally created as far back as Painter version 4, the Growth effect is a fascinating effect that you will want to explore further. The Growth effect was discovered by exploring fractal algorithms, and is based on 2 dimensional fractals. The Growth effect can be found on all versions of Painter and is located in the Esoterica grouping of effects. Just in time for the holidays, let us explore this fascinating fractal! • Corel Painter Growth...  
From z.about.com ()
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3D fractal video
axis.mundi shares a 3D fractal video: From the maker: The wide variety of organic forms resulting from relatively simple configuration of iterative functions illustrates the concept that complex results can arise from simple conditions. It is my belief that nature expresses itself on every level through fractals, limits, feedback loops, and iterative functions.From www.phidelity.com. Posted by jamesk.  
From dosenation.com ()
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Mandelbulb: 3D Mandelbrot
The Mandelbulb is an attempt to extrude the classic Mandelbrot Set fractal into three dimensions. I'm not enough of a mathematician to say whether it accomplishes this feat, but it is utterly arresting. Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal: (via /.) Previously:Benoit Mandelbrot - Boing Boing Findings fractals in the stock market - Boing Boing Fractal weather - Boing Boing Fractal art contest winners - Boing Boing...  
From boingboing.net ()
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Links
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  1
Sprott's Fractal Gallery
  2
Chaos And Fractals: A Computer Graphical Journey
  3
The Science House - Chaos & Fractals
  4
Sci.Fractals Faq
  5
Efg's Fractals And Chaos -- Fractals Show 2 Lab Report
  6
Open Directory - Science: Math: Chaos And Fractals
  7
Chaos, Fractals And Dynamics
  8
Fractals
  9
A.3 Internet Resources
 10
Chaos Theory: A Brief Introduction
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