The Butterfly Effect is the idea that some systems exhibit unpredictable behaviors for small variances in the initial conditions. Because of the sensitivity of these systems, outcomes are unpredictable. This phenomenon is captured by the speculation that the flap of a butterfly’s wings in Brazil might ultimately set off a tornado in Texas.
I have prepared a video which demonstrates the Butterfly Effect with Excel. The dynamical system is a simple one–
- Start with one tenth
- Multiply by eleven and then subtract one. You should be back at one tenth.
- Keep repeating step 2.
In this demonstration we use Excel for the simple deterministic system given above. And something surprising happens. Click here to watch the video.
This idea became the basis for a branch of mathematics known as chaos theory, which has been applied in countless scenarios since its introduction.