Clone of Clone of THE BUTTERFLY EFFECT
Butterfly Effect
Sensitivity To Initial Conditions
(sensitive dependence on 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 M is the state space for the map f^t, then f^t displays sensitive dependence to initial conditions if for any x in M and any δ > 0, there are y in M, with 0 < d(x, y) < \delta such that
d(f^\tau(x), f^\tau(y)) > \mathrm{e}^{a\tau} \, d(x,y).

Loading Insight Maker...
(This may take a few moments)