Logistic Growth Model and the Butterfly Effect

If you are having trouble viewing the simulation or would like to embed the simulation into an app, use this LINK.

This model shows chaos, not randomness.

Adjust the growth rate (r) to 3. Run the simulation three times in a row. While the pattern is unpredictable (chaotic), every run the results are the same (deterministic, not random).

Adjusting the starting population even a little (by a hundredth), with the growth rate (r) at 3, will cause a drastic change in the final outcome. This is sensitive dependence on initial conditions, also known as the butterfly effect.

My short reflection on how to use the simulation to determine the butterfly effect, fixed-point attractors, logistic maps, and bifurcation diagrams. Here is a video on how to generate the bifurcation diagram: