Chaos Theory and Computers

What is Chaos Theory ?

• It finds its roots in mathematics and physics.
• The study of complex, nonlinear dynamic systems as they tend to be difficult to predict.
• This study shows how sensitive events are to the initial conditions.
• Mainly people find this type of theory to be easy to observe in weather.

Chaos, for most people, conjures up notions of randomness and disorder. However, Chaos Theory describes systems that behave in both orderly and disorderly ways.

How Chaos Theory was born and why ?

• Edward Lorenz in 1961 used a numerical computer model to run a weather prediction.
• Lorenz was modeling the atmosphere with a set of differential equations.
• One day he wanted to restart his computations where he ended the day before. The previous day's last output was 0.506127.He entered 0.506 expecting to continue on.
• The result was a completely different weather, leading to what's called ""Butterfly Effect "".

The Butterfly Effect
"" Small variations of the initial conditions of a dynamical system may produce large variations in the long term behavior of the system.""

""When a butterfly flutters its wings in one part of the world, it can eventually cause a hurricane in another.""
-Edward Lorenz-

Butterfly is so strong, you must respect it.

Chaos Theory and the human behavior

• Human behavior is complex and unpredictable so it's subject to the Chaos theory.
• If a fluttering butterfly's wings can make a hurricane, so what about the effect of a human with his body, mind and talk.

""There are generations yet unborn, whose very lives will be shifted and shaped by the moves you make and the actions you take. ""
-Andy Andrews-

CHAOS THEORY AND EDUCATION
Pedersen (1988) has suggested that it is an error to oversimplify
the complex human dynamics involved in education.

COMPUTER IN EDUCATION

some of Chaos Theory constructs

• Sensitive dependence
• Phase space
• Iteration
• Turbulence
• Fractals

Sensitive Dependence

Sensitive dependence on initial conditions means that initially tiny differences grow rapidly to the order of the system size.

Phase Space


""Phase space is composed of as many variables as needed to describe a
system's movement"" (Stickel, 1992, p. 4).

Iteration



Repetition ensures the building of chaos theory and it means the same reactions on the same previous results.

Iteration II



Repetition help to learn about the developments between computers and chaos which are constantly changing and with repetition you write notes and we have a large
amount of information to help us improve.

Fractals



Fractals have received a great deal of attention by practitioners in many fields they are often shown to children in classrooms, and many children they can be used to display complex and irregular shapes such as tree leaves and clouds.

Use world wide web sites to learn more about the chaos theory.

what is the main focal point of this paper ?

• Give some examples of Chaos constructs and learn how to apply them to computer use.
• Showing some world wide web sites that may be helpful in providing information about Chaos Theory and its potential applications in education and other social science.

what is the ratio of contribution the author delivered to the related research field in this paper ?


In my opinion the article gave a glimpse of the history of the evolution of chaos theory as it explained the ways we benefit from that theory and how it helps us to develop and know the information that helps improve also the mathematical equations don't work without a test of chaos.

references

• Edil Torres-Rivera , Marlowe H. Smaby & Cleborne D Maddux PhD (1996) Chaos Theory and Computers, Computers in the Schools, 12:4, 55-61, DOI: 10.1300/J025v12n04_06

Untitled Slide

Untitled Slide