CHAOS THEORY
and the butterfly effect
English presentation
By: Assaad Moawad
Index
 Introduction
 History
 Applications
 Movies
 Quotes
Slide: 2
and moral conclusion
CHAOS THEORY
Presentation by: Assaad Moawad
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
Slide: 3
was it called like that? Answer in the history section.
CHAOS THEORY
Presentation by: Assaad Moawad
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?
Slide: 4
CHAOS THEORY
Presentation by: Assaad Moawad
Part 1 - Introduction – 3 kinds of systems
Input
Output
System
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?
Slide: 5
CHAOS THEORY
Presentation by: Assaad Moawad
Part 1 - Introduction – 3 kinds of systems
Input
Output
System
Input
Output of a
normal system
Output of a
random system
Output of a
chaotic system
5
22.5
4
10
5.001
22.503
25 (??)
37 (??)
10
Can you predict?
Can you predict?
Can you predict?
Slide: 6
CHAOS THEORY
Presentation by: Assaad Moawad
Part 1 - Introduction – 3 kinds of systems
Input
Output
System
Input
Output of a
normal system
Output of a
random system
Output of a
chaotic system
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?
Slide: 7
CHAOS THEORY
Presentation by: Assaad Moawad
Part 1 - Introduction – 3 kinds of systems
Input
Output
System
Input
Output of a
normal system
Output of a
random system
Output of a
chaotic system
5
22.5
4 (??)
10
5.001
22.503
25
37
10
45
9
29
5
22.5
46(??)
10
So that’s how the chaotic system is:
1. Deterministic
2. Highly sensitive (butterfly effect)
3. Unpredictable on the long term
Slide: 8
CHAOS THEORY
Presentation by: Assaad Moawad
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
Slide: 9
result was a completely different weather scenario!!!
CHAOS THEORY
Presentation by: Assaad Moawad
Part 2 - History of the Theory
This is what he observed:
Small difference
of the input:
Extreme
Differences
of the output
0.506 instead
of 0.506127
After a period of time
Slide: 10
CHAOS THEORY
Presentation by: Assaad Moawad
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
Slide: 11
is why we call it butterfly effect….
CHAOS THEORY
Presentation by: Assaad Moawad
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.
Slide: 12
CHAOS THEORY
Presentation by: Assaad Moawad
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 "selfsimilarity. Fractals are often considered to be infinitely
complex.
Slide: 13
CHAOS THEORY
Presentation by: Assaad Moawad
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.
Slide: 14
CHAOS THEORY
Presentation by: Assaad Moawad
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.
Slide: 15
CHAOS THEORY
Presentation by: Assaad Moawad
Part 4 - Movies
Slide: 16
CHAOS THEORY
Presentation by: Assaad Moawad
Part 4 - Movies
Slide: 17
CHAOS THEORY
Presentation by: Assaad Moawad
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
Slide: 18
we do affects other people.
CHAOS THEORY
Presentation by: Assaad Moawad
Thank you for your attention.
Assaad Moawad