butterflyeffect-141115090247-conversion-gate02 (1).pptx

butterflyeffect-141115090247-conversion-gate02 (1).pptx

• 1.
  Butterfly Effect Every smallchange matters…
• 2.
  • The butterflyeffect 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.
• 3.
  • The theoryderives 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.
• 4.
  Talking of geometriclimits and dynamic process systems… FRACTAL THEORY
• 6.
  • If somethinghas 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.
• 7.
  Its not alwaysannoying to be chaotic… CHAOS THEORY
• 8.
  • It isa 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.
• 9.
  • This happenseven 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.
• 10.
  A double pendulumshowing the chaotic behavior being a product of simple initial manipulation The resulting pattern is an iteration of simple pattern being looped chaotically over time.
• 11.
  • Thethe ory wassummarized by Edward Lorenz as follows: “ C h a o s :W h e nt h ep r e s e n td e t e r m i n e st h e f u t u r e ,b u tt h ea p p r o x i m a t e p r e s e n td o e s n o t a p p r o x i m a t e l yd e t e r m i n et h e f u tu r e .“
• 12.
  Revisting the butterflies… HOWBUTTERFLIES MATTER…
• 13.
  • Real worldapplication of butterfly effect and its supplementing theories lies in the study of highly dynamic systems. Flight Simulations: Vortex Formations
• 14.
  Other applications • Meteorology •Satellite trajectories • Weather models • Climatic change observations • Hydrodynamics • Pure mathematics • Computing
• 15.
  • Still aresearch field • Awareness and interest amongst general masses is catching up • The next big thing after quantum sciences.