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. Presentation by: Assaad MoawadCHAOS THEORYSlide: 3

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 Presentation by: Assaad MoawadCHAOS THEORYSlide: 4

InputOutput of a normal system Output of a random system Output of a chaotic system Can you predict? System Input Output Presentation by: Assaad MoawadCHAOS THEORYSlide: 5 Part 1 - Introduction – 3 kinds of systems

InputOutput of a normal system Output of a random system Output of a chaotic system (??)37 (??) 10Can you predict? System Input Output Presentation by: Assaad MoawadCHAOS THEORYSlide: 6 Part 1 - Introduction – 3 kinds of systems

InputOutput of a normal system Output of a random system Output of a chaotic system (value doubled)9 (??)29(??) 5Can you predict? System Input Output Presentation by: Assaad MoawadCHAOS THEORYSlide: 7 Part 1 - Introduction – 3 kinds of systems

InputOutput of a normal system Output of a random system Output of a chaotic system (??) (??)10 System Input Output Presentation by: Assaad MoawadCHAOS THEORYSlide: 8 So that’s how the chaotic system is: 1.Deterministic 2.Highly sensitive (butterfly effect) 3.Unpredictable on the long term Part 1 - Introduction – 3 kinds of systems

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 He entered expecting to continue on. The result was a completely different weather scenario!!! Presentation by: Assaad MoawadCHAOS THEORYSlide: 9

This is what he observed: Small difference of the input: instead of Extreme Differences of the output Part 2 - History of the Theory Presentation by: Assaad MoawadCHAOS THEORYSlide: 10 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…. Part 2 - History of the Theory Presentation by: Assaad MoawadCHAOS THEORYSlide: 11

1- The weather:1- The weather: Can you predict weather of the next year? 2- The stock market:2- The stock market: Can you predict exchange rates? 3- Biology:3- Biology: Can you predict how a virus is going to spread? 4- Physics:4- Physics: Can you predict the motion of gas in vacuum? 5- Evolution of life:5- Evolution of life: small changes in the chemistry of the early Earth gives rise to life. Part 3 - Applications Presentation by: Assaad MoawadCHAOS THEORYSlide: 12

Part 3 - Applications 6- Fractals: 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. Presentation by: Assaad MoawadCHAOS THEORYSlide: 13

7- Aviation safety: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. Presentation by: Assaad MoawadCHAOS THEORYSlide: 14 Part 3 - Applications

8- Highway traffic jams:8- Highway traffic jams: Unpredictable and very complex system. 9- Psychology:9- Psychology: A small psychological fact in childhood can lead to problems or suicide in adolescence. 10- Time travel: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. Presentation by: Assaad MoawadCHAOS THEORYSlide: 15 Part 3 - Applications

Part 4 - Movies Presentation by: Assaad MoawadCHAOS THEORYSlide: 16

Presentation by: Assaad MoawadCHAOS THEORYSlide: 17 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. Presentation by: Assaad MoawadCHAOS THEORYSlide: 18

Thank you for your attention. Assaad Moawad