This presentation discusses chaos theory and the butterfly effect. It begins with an introduction that defines the butterfly effect as how small variations can dramatically change the outcome of a system over time. There are three types of systems: linear, random, and chaotic, which are deterministic yet unpredictable long-term. The history section describes how meteorologist Edward Lorenz discovered the butterfly effect in 1961 when a small variation in input data led to vastly different weather model outputs. The term "butterfly effect" comes from a 1972 quote about whether a butterfly could cause a tornado. Applications of chaos theory discussed include weather prediction, stock markets, biology, physics, evolution, fractals, aviation safety, traffic patterns, psychology, and time travel

1. CHAOS THEORY and the butterflyeffect English presentation By: Assaad Moawad

2. Index Introduction History Applications Movies Quotes and moral conclusion Presentation by: Assaad Moawad CHAOS THEORY Slide: 2

3. Part 1 - Introduction – Butterfly effect When a tiny variationchanges 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 Moawad CHAOS THEORY Slide: 3

4. Part 1 - Introduction – 3 kinds of systems 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? Presentation by: Assaad Moawad CHAOS THEORY Slide: 4

5. System Input Output Presentation by: Assaad Moawad CHAOS THEORY Slide: 5 Part 1 - Introduction – 3 kinds of systems

6. System Input Output Presentation by: Assaad Moawad CHAOS THEORY Slide: 6 Part 1 - Introduction – 3 kinds of systems

7. System Input Output Presentation by: Assaad Moawad CHAOS THEORY Slide: 7 Part 1 - Introduction – 3 kinds of systems

8. Part 1 - Introduction – 3 kinds of systems System Input Output So that’s how the chaotic system is: Deterministic Highly sensitive (butterfly effect) Unpredictable on the long term Presentation by: Assaad Moawad CHAOS THEORY Slide: 8

9. 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!!! Presentation by: Assaad Moawad CHAOS THEORY Slide: 9

10. Part 2 - History of the Theory This is what he observed: Small difference of the input: 0.506 instead of 0.506127 Extreme Differences of the output After a period of time Presentation by: Assaad Moawad CHAOS THEORY Slide: 10

11. Part 2 - History of the Theory 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…. Presentation by: Assaad Moawad CHAOS THEORY Slide: 11

12. Part 3 - Applications 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. Presentation by: Assaad Moawad CHAOS THEORY Slide: 12

13. Part 3 - Applications 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 Moawad CHAOS THEORY Slide: 13

14. Part 3 - Applications 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 Moawad CHAOS THEORY Slide: 14

15. Part 3 - Applications 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. Presentation by: Assaad Moawad CHAOS THEORY Slide: 15

16. Part 4 - Movies Presentation by: Assaad Moawad CHAOS THEORY Slide: 16

17. Part 4 - Movies Presentation by: Assaad Moawad CHAOS THEORY Slide: 17

18. 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 Moawad CHAOS THEORY Slide: 18

19. Thank you for your attention. Assaad Moawad