THE BUTTERFLY EFFECT

Butterfly Effect

Sensitivity To Initial Conditions

*(sensitive dependence on initial conditions)*

Navier Stokes Equations

Lorenz Attractor

Chaos Theory, Disorder and Entropy

If*M* is the state space for the map , then displays sensitive dependence to initial conditions if for any x in *M* and any δ > 0, there are y in *M*, with such that

Sensitivity To Initial Conditions

Navier Stokes Equations

Lorenz Attractor

Chaos Theory, Disorder and Entropy

Although the butterfly effect may appear to be an esoteric and unlikely behavior, it is exhibited by very simple systems: for example, a ball placed at the crest of a hill may roll into any of several valleys depending on, among other things, slight differences in initial position. Similarly the direction a pencil falls when held on its tip, or an universe during its initial stages.

These attractors apply to social systems and economics showing jumps between potential wells, and showing the strategic scaling behavior of rotating and cyclic systems whether they be social, economic, or complex spin or rotation of planets affecting weather and climate or spin of galaxies or elementary particles, or even a rock on the end of a piece of string.

What Playing with numbers is all about :)

If

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