Sunday, April 29, 2012

Collatz Conjecture and Art

I'm probably only one of a handful of people on the planet who has an Undergraduate degree in Art as well as a degree in Mathematics and a Master's in Artificial Intelligence.

As such, I'm always thinking about ways to explore Math in Art... Hidden in the shadows of most of my drawings (shadows cast by bodies as well as shadows in the bodies themselves) are often to be found other figures and clues, and just as often mathematical equations, progressions, theorems, conjectures, etc.

One recurring and fascinating issue to me, buried in the shadows of a drawing that I sold last week in New York is the Collatz Conjecture:

Take any natural number and let's call it n.

If n is even, then we divide it by 2 to get n / 2.

If n is odd, then we multiply it by 3 and add 1 to obtain 3n + 1.

Repeat this division/multiplication indefinitely (and this is where "indefinitely" becomes an issue, as the British say).

The Collatz Conjecture is that no matter what number you start with, you will always and no matter what the starting number is, eventually reach 1.

This conjecture property has also been called "oneness."

Can art help represent this? I don't know - that's why I bury them in the shadows of the drawings and not try to solve them per say; but often it is the drawings themselves that trigger the specific mathematical clue/issue being associated with the piece.

1 comment:

Jesse said...

Lenny, it makes me think of meditative art. I've seen a number of works by artists who practice Jewish Mysticism produce art based on repetion.

I like the thought of oneness. There's a real interesting concept to study.