Chaos Theory

Elaine A. Walker |
2 min readJul 25, 2022
Initiator, x, and generator, 1-rx squared. Replace x with the generator over and over.
Recursive mathematics shown graphically.

August, 2015

Chaos theory is a mathematical mirror of the natural world that allows us to inspect otherwise unnoticed or under-appreciated dynamical patterns within the complexity and to make important, objective statements about our world and many areas of our lives. It is still highly misunderstood by the general public, partly because of the poor choice in names. “Chaos” was traditionally used to refer to randomness, but by definition there is nothing random in chaos theory, or in any of the patterns it relates to such as fractals or spontaneous orders (the self-organization of large groups of individual agents, whether molecules, birds, people, or galaxies).

We are drenched in a wonderful world of chaos and fractals — mammoth cobwebs of clustering galaxies, infinitesimal webs of neurons zapping data around in our brains, splitting streams of rain running down windshields, bifurcating branches, roots, veins, lightening, river valleys, cascading consequences of human actions, evolving trends in society, and even our meandering moral behavior. Whether a process involves a superabundance of factors like weather or is a simple system like a dripping faucet or pendulum; whether it involves growing and shrinking of gaps like those between cars flowing like waves on the highway or our ever changing knowledge gaps; whether it’s the pattern on a bee’s wing, or the entire swarm, or the forming of a snowflake, or even the sound of a windblown snow flurry — chaos theory peels away any illusion of randomness and reveals the deterministic inner workings of these diverse and interconnected systems. Chaos theory also demonstrates how complexity is never predictable to an exact degree even though it is deterministic.

Our natural world is an intimate mix of unpredictability and order. Things, processes, people, ideas, and even sounds and smells are all connected through a flow of cause and effect, acting and reacting to each other in a constant mingling. So of course it results in many unpredictable outcomes. But for the most part, it is the kind of unpredictability that we shouldn’t worry about so much.

It is actually counter productive to worry about most of the things that we expend so much energy trying to “manage”. It is one thing to manage our individual lives or a system of machines, or a small group such as a family or small business. But managing highly nonlinear things that involve multitudes of individual agents such as societies or ecosystems always backfires to some degree. If we ever do attempt to control the weather it will drive the point home, if we survive to talk about it.

If you like this, you may love my book! Matter Over Mind: Cosmos, Chaos, and Curiosity. See also



Elaine A. Walker |

I’m an electronic musician and microtonal composer, with an interest in visual math, physics, neuroscience, longevity, and the future of humanity.