Thursday, January 18, 2007

Tupper's Self-Referential Formula

Thanks to the Minding The Planet blog, I just came across this incredible formula discovered/invented/pulled out of a hat by Jeff Tupper (who possibly works at the University of Toronto - I couldn't find much info on him.)

(Quick formula/graph lesson: Everyone remembers the formula for a parabola (y=x2), right? When plotted on graph paper, it resembles a smooth letter "v" extending upwards forever.)

So, why is the above formula (or inequality, to be exact) so amazing. Well, if you plot it on a very, very, very tall piece of graph paper, and look way-y-y up, you'll see this:

An image of the formula is found in the graph of the formula! (Wow!!) I'm a math geek so this kind of thing excites me.

Had these types of problems ("Roughly sketch the graph of this self-referential formula.") appeared in high school math class, I'm sure a lot of us would have done better.

I wonder if this could be applied to cryptography, ie. create a function which graphs a secret message somewhere in the x-y plane.

Formula images thanks to:
Weisstein, Eric W. "Tupper's Self-Referential Formula." From MathWorld--A Wolfram Web Resource.


Anonymous said...

way interesting, mathman!

Sean O'Hagan said...

I agree anonymous. Very very interesting!