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Chaos Game Sagabutterfly

Butterfly Effect

About the saga...

Chaos Theory was a concept popularized by the film series Jurassic Park where the 'hero' of the story (mathematician Ian Malcolm) surmised that tiny, unpredictable, immeasurable instabilities in a 'system' (like Jurasic Park) would add up, compounding in such a way as to lead to outcomes beyond anyone's imagination. (Watch a movie clip!)

Another short story, A Sound of Thunder by Ray Bradbury, extended the concept of The Butterfly Effect: A butterly flaps it's wings in Peking and changes the weather in New York.

Our app shows how random numbers can be generated in a simple quadratic system using nothing more than the concept of mathematical feedback: output becomes input becomes output becomes input....

Tiny, microscopic changes in the original input produces wildly varying output over time...just by feedback amplification.

It gives one a sense of how pseudo-random numbers could be generated in a computer environment.

Let's step on some butterflies!

Note: If you just can't wait until we finish this saga, we have an older version of Chaos Game in Past Blasts that works but isn't as pretty as it will be in Processing.

Last update: 09/28/25


Current Development Stages:

Chaos Game via Copilot: Stage 1

It's been nearly 6 years since we looked at Stage 4 below. Since then, we've been getting sassy with Copilot! With minimal prompts (and we helped by supplying some Grid code in JavaScript) we were jarred by what a good job our 'helper' did in generating this version!


Webplot via Slider - Stage 4: Late January 2020

The previous stage required tediously pushing a button to see the webplot evolve into a chaotic mess. This version lets you quickly load multiple iterations almost instantaneously.


Webplot with Tabular Values - Stage 3: Late January 2020

Although Developer Tools listed our 'random numbers' in Stage 2, it would have been nice to have them 'front and center' in a handy HTML table. We provide that in this stage. You're welcome.


Webplot 101 - Stage 2: Late January 2020

With our quadratic and linear in place, we can create a 'webplot' - the trail of input/output cycles using the quadratic to generate input, generated one click at a time.


The Quadratic and the Linear - Stage 1: Late January 2020

This stage creates the quadratic feedback function and the linear 'reflection' line that takes output and makes it input.