A brief outlook on the beauty in chaos

Chaotic Systems

And then people say physics is not poetic and beautiful.

At first glance, this picture looks like a work of art( well technically it is art because it’s a pictorial representation) but this is a graphical representation of a so-called Lorenz system of ordinary differential equations studied by E. Lorenz, the first person ever to visually see the solution of a so-called 3 -body problem as seen in this picture.

And all that was from an accident as he fed very old weather graphing computer program, highly sensitive data.

What he got was a mathematical model of atmospheric convection., i.e. three ordinary differential equations having chaotic solutions. Chaotic solutions of a dynamical system that is highly sensitive to initial conditions.

And voilà Chaos theory was born( or rather discovered) Initial conditions, Infinitesimal Variations, Butterfly Effect.

It’s insane, it’s beautiful, it’s insanely beautiful.

It may be chaos theory but it represents order out of chaos and the fact that it was discovered from am accident (by a person who was not even looking to discover it) makes it even more alluring.

Chaotic systems exist all around us, from an ideal system of a double pendulum to the population of rabbits to the entire multiverse itself, all these dynamical systems are highly sensitive to initial conditions. All these systems are governed by difference and differential equations.

The best analogy is that these changes in initial conditions are like Domino strikes, one strike and the whole system topples down, but still, there is an order to the toppling, because the universe always finds its way. Then again this is just that an analogy.

To quote one of my favorite physicists Richard Feynman,

“Nature uses only the longest threads to weave her patterns so that each small piece of her fabric reveals the organization of the entire tapestry.”

P.S. - To understand more about the power of difference equations and how they are used to model dynamical systems and as to how chaos arises, please check out the following ‘Veritasium’ video. Credit- Veritasium