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  • Y g 2

    Hexxel Notation

    February 18, 2016 by Y g 2

    Alright. I've revised this, ended up accidentally turning it into something that closely resembles Aarex's Graham Generator, and cut it off before I got too weird with dots. I believe, based on what I've observed with other functions, that the basic White-Hex Level has a maximum growth rate of ω+3 in the fast-growing hierarchy, but the black hexagon might take it up to ω2.


    1. ab = a↑↑↑↑b

    2. anb = aan-1bb

    3/3b. a•(n)•b = a•(n-1)a↑↑↑↑bb

    5. anb = an-1((a↑↑↑↑b))•b

    Explanation:

    1. ab = a↑↑↑↑b, in Knuth up-arrow notation (hexation, hence the notation's defining shape)

    2. If, at the end of an expression, there is a number after a single hexagon, decrement the number by one and use the new expression as the number of up-arrows. (When th…


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