Butterfly Effect

Every small change matters…

• The butterfly effect is the sensitive dependency on initial conditions in which a small change at one place in system can result in large differences in a later state of that system.

• This was first theorised by

Edward Lorenz.

• The theory derives its name from the example by Lorenz.

• He showed the details of a hurricane (exact time of formation, exact path taken) being influenced by minor perturbations equating to the flapping of the wings of a distant butterfly several weeks earlier.

• Thus he proposed that events of large scale could be largely influenced by insignificant seeming events of a very small scale.

FRACTAL THEORY

Talking of geometric limits and dynamic process systems…

• If something has complicated results, it does not necessarily mean that it had a complicated input. Chaos may have crept in (in something as simple as round-off error for a calculation), producing complicated results.

• Fractal Dimensions are used to measure the complexity of objects. Like in the geometry of snow flakes.

CHAOS THEORY

Its not always annoying to be chaotic…

• It is a mathematical order of the butterfly effect.

• Deals with the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect.

• Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general.

• This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.

• Thus its implementation lies

mostly in the interpretation

of philosophy and history.

A double pendulum showing the chaotic behavior being a product of simple initial

manipulation

The resulting pattern is an iteration of simple pattern being looped chaotically over time.

• The theory was summarized by Edward Lorenz as follows:

“Chaos: When the present determines the

future, but the approximate present does not approximately determine the future. “

HOW BUTTERFLIES MATTER…

Revisting the butterflies…

• Real world application of butterfly effect and its supplementing theories lies in the study of highly dynamic systems.

Flight Simulations: Vortex Formations

Other applications

• Meteorology

• Satellite trajectories

• Weather models

• Climatic change observations

• Hydrodynamics

• Pure mathematics

• Computing

• Still a research field

• Awareness and interest amongst general masses is catching up

• The next big thing after quantum sciences.