Butterfly effect

A brief slideshow on the Butterfly effect and its sister theories , the Chaos theory and The Catastrophe theory and how they affect the real world and its outcomes. Meant for beginners.

1. Butterfly Effect Every small change matters… A presentation by Punit Goswami On…

2.   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.

3. 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.

4. Fractal Theory Talking of geometric limits and dynamic process systems…

5. A fractal is a representation of complex physical processes and dynamic system. Simple process that goes through many iterations becomes a very complex system on the whole. Fractals can look very complicated. Yet, usually they are very simple processes that produce complicated results. And this property transfers over to Chaos Theory.

6. 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.

7. Chaos Theory Its not always annoying to be chaotic…

8. 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.

9. 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.

10. 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.

11. 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. “

12. How butterflies matter… Revisting the butterflies…

13. Real world application 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 a research field Awareness and interest amongst general masses is catching up The next big thing after quantum sciences.

16. Questions ?