The previous app explored 'chaotic' behavior when a feedback loop of input and output from a quadratic yielded seemingly 'random' numbers in the interval [0, 1] (ish).
We get it: simple 'systems' can give way to chaotic behavior when feedback is utilized.
However, what happens when a purely random process is employed with a simple algorithm that is repeated in a computer loop? Wouldn't that be completely random?
One would think so, until we dance the Mathematician's Mambo from the disco era gone by.
What's the Mathematician's Mambo you ask?
Well, glad you asked. Imagine an electronic dance floor with 3 lights (red, green and blue) arranged level on the floor in a shape like an equilateral triangle. Our 'groovy' mathematician steps on the floor and activates this process:
- The floor registers his initial location and records it
- One of the lights turns on briefly (twinkles, flashes), signalling the mambo dancer to move half-way between his current location and the twinkling light
- Upon arrival, the 'smart' dance floor activates a smaller light underneath the dancer's feet with the same color of light that triggered his movement to that location
- That new light stays on and then the process repeats: another light twinkles and the dancer moves to the midpoint between his current location and the location of that twinkling light
What would this look like over time? A bunch of random dots? It would seem so until you do the dance....
Note: We wrote this software years ago in Flash and it was awesome, but...Flash is no longer widely supported and was never supported by the iPhone ecosystem. So? We needed an upgrade. If you want to see that legacy app, assuming you can run it these days, here it is, complete with disco music. (We just loved Flash with ActionScript!)
Disappointed if you couldn't get Flash to run? No worries, we made a movie of the disco...just for you!
Boogie Down!
Last update: 01/24/20
