# Glossary Of Terms And Phrases

This is a comprehensive glossary of terms and phrases relating to chaos theory, dynamic systems, and fractal geometry. Most of the difficult words used in these pages, and others relating to the subject are listed below. The words are in alphabetical order for ease of location. To search for a word or phrase, enter it in the form below. If no match is found, the closest match will be shown. To add a word, or buil upon the definition of a word already in the glossary, click below on the link which says Add A Word.

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# A

A super fractal

# B

butterfly effect- Submitted By The Authors
See sensitive dependance.

# C

cantor set- Submitted By The Authors
The Cantor Set is a fractal generated by repeatedly removing the center third from a line of unit length.

chaos theory- Submitted By The Authors

complex- Submitted By The Authors
The complexity of a system is defined by the comlexity of the model necessary to effectively predict the behavior of the system

converge- Submitted By The Athors
A point converges if it is stays withing a set boundry throughout iteration.

critical points- Submitted By The Authors
The critical points of an equation is defined as the point where the graph of a function changes from increasing to decreasing

# D

diverge- Submitted By The Authors
A point diverges if it escapes from a set boundry, or goes to infinity, when the equation is iterated.

# E

euclidean geometry- Submitted By The Authors
Euclidean geometry is geometry based on Euclid's axioms and is the geometry of Euclidean space. Throughout these documents, it is used in reference with objects of an integer dimension.

# F

feigenbaun's constant- Submitted By The Authors
In a period doubling situation, such as the logisitc equation, the ratio of distances between the consecutive doubling parameter values of the equation is iterated to infity is called Feignbaun's constant. It is aproximately 4.669201609102990671853

fractal- Submitted By The Authors

fractal attractor- Submitted By The Authors
See Strange Attractor.

fractal dimension- Submitted By The Authors

fractal geometry- Submitted By The Authors

# J

julia set- Submitted By The Authors
The Julia Set, closely related to the Mandelbrot Set, is the set of converging points in a plane when tested with equation z=z2+c, using varying z values.

# K

koch curve- Submitted By The Authors
The Koch Curve is a fractal generated by removing the center third from a line segment of unit length and replacing it with an equilateral triangle, which has its base removed.

koch snowflake- Submitted By The Authors
The Koch Snowflake is a fractal, similiar to the Koch Curve, which is generated by removing the center third from each line segment of and equilateral triangle and replacing it with an equilateral triangle which is missing its base.

# L

logistic equation- Submitted By The Authors
The Logistic Equation, t =c(1-t), is a model for animal population

lorenz model- Submitted By The Authors
The Lorenz Model is a model for the convection of thermal engergy.

# M

mandelbrot set- Submitted By The Authors
The Mandelbrot Set is the set of converging points of a plane when tested with the equation z=z2+c, with varying c values.

# N

nonlinear- Submitted By The Authors
Nonlinear implies that a set of data does not fit linear model

# S

self similiar- Submitted By The Authors
Self-similiarity is the property of invariance under a change of scale. In other words, a magnified image is virtually indistinguisahble from the whole.

sensitive dependance- Submitted By The Authors
Sensitive dependance, otherwise known as the butterfly effect, is one of the key elements in a complex system, stating that complex systems have extreme sensitivity upon initial conditions

sierpinski triangle- Submitted By The Authors
The Sierpinski Triangle, or the Sierpinski Sieve is a fractal which is generated in the following manner: A triangle is repeatedly divided into four conguent triangles and the center triangle is removed.

strange attractor- Submitted By The Authors
A Strange Attractor is the limit set of a chaotic trajectory. A Strange Attractor is an attractor that is topologically from a periodic orbit or a limit cycle. It can also be considered a fractal attractor.

system- Submitted By The Authors
The understanding of the relationship between things which interact. For example, a pile of stones is a system based upon how they are piled. This site deals mainly with chaotic systems.

# Z

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