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Amazing formula

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  • 24-01-2007 3:41am
    #1
    carl_
    Registered Users Posts: 179 ✭✭


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


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    #2
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,847 Mod ✭✭✭✭Michael Collins


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


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    #3
    carl_
    Registered Users Posts: 179 ✭✭carl_


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


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    #4
    Professor_Fink
    Registered Users Posts: 861 ✭✭✭Professor_Fink


    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.


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    #5
    breadmonkey
    Registered Users Posts: 3,608 ✭✭✭breadmonkey


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


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    #6
    Professor_Fink
    Registered Users Posts: 861 ✭✭✭Professor_Fink


    Yes!


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    #7
    breadmonkey
    Registered Users Posts: 3,608 ✭✭✭breadmonkey


    How?!


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    #8
    Professor_Fink
    Registered Users Posts: 861 ✭✭✭Professor_Fink


    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.


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    #9
    Tar.Aldarion
    Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,086 Mod ✭✭✭✭Tar.Aldarion


    That's pretty nifty!


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    #10
    deimos
    Closed Accounts Posts: 210 ✭✭deimos


    :)

    That's is cool.


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    #11
    Anti
    Closed Accounts Posts: 12,401 ✭✭✭✭Anti


    that rocks my box !


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    #12
    sicruise
    Registered Users Posts: 378 ✭✭sicruise


    I can see how it is done alright...

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


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    #13
    Roonels
    Registered Users Posts: 70 ✭✭Roonels


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


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    #14
    europerson
    Registered Users Posts: 2,909 ✭✭✭europerson


    That formula's cool, all right.


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    #15
    carl_
    Registered Users Posts: 179 ✭✭carl_


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


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    #16
    MathsManiac
    Registered Users Posts: 1,595 ✭✭✭MathsManiac


    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.


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