Amazing formula

carl_ · 24-01-2007 2:41am #1

Have a look for yourselves. Anybody have a clue how such a thing can be constructed?!

Michael Collins · 24-01-2007 4:21am

And not a pixel out of place. That's really quite unbelievable...

carl_ · 27-01-2007 7:06pm

Thinking about it a little bit, it was probably done with some sort of evolutionary algorithm.

Professor_Fink · 28-01-2007 4:06pm

One way to do it would be to take a formula which outputs every possibility mod some number N, and then calculate what the answer, A, should be, so that when it is plotted it gives a picture of the furmula (p pixels across, q down). Then all you need to do is calculate the input that gives A. You could easily do this if you know the factorization of N.

Clearly this is not the approach taken in the above, but it would yield another self referential formula.

breadmonkey · 28-01-2007 6:39pm

I don't get what's going on. The formula generates the pic of the formula?

Professor_Fink · 29-01-2007 2:00am

Yes!

breadmonkey · 30-01-2007 11:55pm

How?!

Professor_Fink · 31-01-2007 12:36am

breadmonkey wrote:

How?!

Basically for a certain value of the input, the output can be represented as a picture giving the formula. The mathworld entry linked to in the original post contains a detailed explanation.

Tar.Aldarion · 31-01-2007 10:39am

That's pretty nifty!

deimos · 25-02-2007 2:49am

That's is cool.

Anti · 08-03-2007 12:23pm

that rocks my box !

sicruise · 08-03-2007 2:52pm

I can see how it is done alright...

but fair play to them doing it so we don't have to!

Roonels · 01-04-2007 11:37am

has any1 heard of fractal mathematics....its pretty new..relatively speaking! check it out, it may lead to some answers.

europerson · 25-04-2007 1:35pm

That formula's cool, all right.

carl_ · 30-05-2007 1:39pm

http://avitzur.hax.com/2007/01/the_library_of_babel_function.html

MathsManiac · 01-06-2007 9:32am

carl_ wrote:

http://avitzur.hax.com/2007/01/the_library_of_babel_function.html

Nice link, Carl.

For those who want a quicker summary of how the bould Mr Tupper might have gone about constructing this amazing formula, the gist is this:

He constructs a formula that for any given value of n can produce a graph in a particular region of the plane that mimics pixels on a grid, and he does it in such a way that you can figure out what value of n will turn particular pixels on and off. He then decides what pixels he wants to turn on in order to draw a picture of the formula itself, and finds the corresponding value of n.

Interestingly, he can use his formula to draw pictures of any other piece of text too, by looking at regions corresponding to other values of n.

Amazing formula

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