The Logistic Map

Benoit Mandlebrot's fractal is known all over the world but very few know its source as Chaos quietly connects the tiny as per Quantum and the vast as per Relativity ... and yes, the Logistic Map equation, as depicted by this amazing video, will change how one views the world. :)

The Mandlebrot Set

The logistic map connects fluid convection, neuron firing, the Mandelbrot set and so much more. Fasthosts Techie Test competition is now closed! Learn more about Fasthosts here: https://www.fasthosts.co.uk/veritasium Code for interactives is available below...

Animations, coding, interactives in this video by Jonny Hyman 🙌

Try the code yourself: https://github.com/jonnyhyman/Chaos

References:

James Gleick, Chaos

Steven Strogatz, Nonlinear Dynamics and Chaos

May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976). https://doi.org/10.1038/261459a0

Robert Shaw, The Dripping Faucet as a Model Chaotic System

https://archive.org/details/ShawRober

Pendulum, orbits, water flows, etc, etc, Chaos resides everywhere, including in BRT. :)

When the present determines the future, but the approximate present does not approximately determine the future. - Edward Lorenz

Chaos theory is a branch of mathematics focusing on the study of chaos—states of dynamical systems whose apparently random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions. 

For example ...

The butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

End result ... initial conditions rule ...

Evolution of different initial conditions as a function of r