CHAOS THEORY and the butterfly effect English presentation By: Assaad Moawad

CHAOS THEORY

and the butterfly effect

English presentation

By: Assaad Moawad

Index

Introduction

History

Applications

Movies

Quotes and moral conclusion

Presentation by: Assaad MoawadCHAOS THEORYSlide: 2

Part 1 - Introduction – Butterfly effect

When a tiny variation changes the results of a system dramatically (over a period of time), this sensitivity is what we call the butterfly effect.

Why was it called like that? Answer in the history section.


Linear (Normal) System• We can guess very precisely its behavior.• Ex: Almost all systems we use are linear…

Random Systems• We cannot guess at all! Ex: Throwing the dice.

Chaotic Systems• Deterministic with no random, but unpredictable on long

term because they are very complex and sensitive.• Seems to be illogical and paradoxal?

Part 1 - Introduction – 3 kinds of systems


Input Output of a normal system

Output of a random system

Output of a chaotic system

5 22.5 4 10

5.001 Can you predict? Can you predict? Can you predict?

SystemInput Output






5 22.5 4 10

5.001 22.503 25 (??) 37 (??)

10 Can you predict? Can you predict? Can you predict?

SystemInput Output






5 22.5 4 10

5.001 22.503 25 37

10 45 (value doubled) 9 (??) 29(??)

5 Can you predict? Can you predict? Can you predict?

SystemInput Output






5 22.5 4 (??) 10

5.001 22.503 25 37

10 45 9 29

5 22.5 46(??) 10

SystemInput Output


So that’s how the chaotic system is:1. Deterministic

2. Highly sensitive (butterfly effect)

3. Unpredictable on the long term


Part 2 - History of the Theory

Edward Lorenz in 1961 used a numerical computer model to run a weather prediction.

Lorenz was modeling the atmosphere with a set of three simple partial 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 scenario!!!


This is what he observed:

Small difference of the input:

0.506 instead of 0.506127

ExtremeDifferences

of the output



After a period of time

In 1972, Philip Merilees quoted Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?

This is why we call it butterfly effect….



1- The weather: Can you predict weather of the next year?

2- The stock market: Can you predict exchange rates?

3- Biology: Can you predict how a virus is going to spread?

4- Physics: Can you predict the motion of gas in vacuum?

5- Evolution of life: small changes in the chemistry of the early Earth gives rise to life.

Part 3 - Applications


http://en.wikipedia.org/wiki/The_Butterfly_Effect_2






6- Fractals: Even art has been touched with the chaos theory: A fractal is generally a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole, a property called "self-similarity. Fractals are often considered to be infinitely complex.



7- Aviation safety: The Swiss cheese model. The holes represent individual weaknesses and are

continually varying in size and position in all slices. The system produces failures when all of the holes in each

of the slices momentarily align.




8- Highway traffic jams: Unpredictable and very complex system.

9- Psychology: A small psychological fact in childhood can lead to problems or suicide in adolescence.

10- Time travel: The butterfly effect theory presents scenarios involving time travel with "what if " scenarios.

This fact attracts Hollywood which is always searching for basis to build stories.






Part 4 - Movies



Part 4 - Movies

Part 5 – Quotes inspired from the theory

You can stay at home and be happily introspective or you can make the choice, step out, and be the Butterfly that begins the tempest that changes the world. (John Sanford)

Sometimes it's the smallest decisions that can change your life forever. (Keri Russell)

Everything we do affects other people.


Thank you for your attention.

Assaad Moawad

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CHAOS THEORY and the butterfly effect English presentation By: Assaad Moawad