Thank you for a very interesting question to research. The following
is the result of my research:
"In 1960 a meteoroligist named Edward Lorenz was researching into the
possibilities of long term weather prediction. He created a basic
computer program using mathematical equations which could
theoretically predict what the weather might be. One day he wanted to
run a particular sequence again, and to save time he started it from
the middle of the sequence. After lettin gthe sequence run he returned
to find that the sequence had evolved completely different from the
original. At first he couldn't comprehend such different results but
then realised that he had started the sequence with his recorded
results to 3 decimal places, whereas the computer had recorded them to
6 d.p. As this program was theoretically deterministic we would expect
a sequence very close to the original, however this tiny difference in
initial conditions had given him completely different results.
This sensitivity to initial conditions became known as The Butterfly
Effect. This is because it compares to the idea that a butterfly
flapping its wings could produce a tiny change in the atmosphere, and
trigger a series of changes which could eventually lead to a hurricane
on the other side of the world. The Butterfly Effect is a key
characteristic to a choatic system."
Chaos In Our Lives
Although Chaos Theory may appear to be an abstract concept within
modern science, it has many applications within our lives.
*One washing machine manufacturer has used chaotic motion to improve
the performance of their machines. A tiny pump vibrates with chaotic
cycles to stir the water more efficiently.
*The stock market is a good example as although it is somewhat random
it does follow trends ie. has a ordered structure.
*Weather forecasting is chaotic, as we know from Lorenz's discoveries.
*The human heart also has a chaotic pattern. The time between beats
doesn't remain constant but also depends on a persons activity and
stress. This analysis of the heartbeat can help medical researchers in
controlling irregular heartbeats.
*The solar system contains many chaotic patterns.
*The motion of gas in a vacuum is chaotic. Although the particles are
flying everywhere, they follow structure and pattern.
*Fractals are used to produce many of the modern computer art we see
in latest films.
University of Bath: Chaos Theory
"The 'Butterfly Effect': This is one of the catch phrases of chaos
theory. It refers to sensitive dependence on initial conditions. In
nonlinear systems, making small changes in the initial input values
will have dramatic effects on the final outcome of the system. A
butterfly flaps its wings and the weather changes in China. This is
one of the catch phrases of chaos theory, called the butterfly effect.
It refers to sensitive dependence on initial conditions. In nonlinear
systems, making small changes in the initial input values will have
dramatic effects on the final outcome of the system.
Theories abound as to real-life examples of this phenomenon:
1. The weather: small changes in weather effect larger patterns.
2. The stock market: slight fluctuations in one market can effect many others.
3. Biology: A small change in a virus in monkeys in Africa creates a
"thunderstorm" of an effect on the human population around the world
with the appearance of the AIDs virus.
4. Evolution: small changes in the chemistry of the early Earth gives rise to life.
5. Psychology: Thought patterns and consciousness altered by small
changes in brain chemistry or small changes in physical environmental
The butterfly effect occurs under two conditions:
1. The system is nonlinear.
2. Each state of the sytem is determined by the previous state. In
other words, the output at each moment is repeatedly entered back into
the system for another cycle through the mathematical functions that
determine the system."
Here are some real-life examples of the Butterfly Effect and the Chaos Theory:
CHAOS WASHING MACHINE
STOCK MARKET CHAOS
THE COASTLINE OF BRITAIN
LONG RANGE FORECASTING
SOLAR SYSTEM CHAOS
THE LORENZIAN WATERWHEEL
ThinkQuest: In A World Of Order Chaos Reigns
Some interesting reading on The Butterfly Effect:
Marc Perkel: The Butterfly Effect
Ian McFadyen: CHAOS AND SOCIAL PREDICTION
Multiworld: When a Butterfly Flaps its Wings
SpinChaos: Chaos And It's Relation to the Cosmos
California Institute of Technology - Michael Cross: The Butterfly Effect
Fortune City: The Butterfly Effect
John Hopkins University - Larry Bradley: The Butterfly Effect
"The Butterfly Effect"
"The Butterfly Effect" examples
"The Butterfly Effect" "real life examples"
I hope the information provided is helpful. If you have any questions
regarding my answer please don't hesitate to ask before rating.