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  • Simply Beautiful Art

    So I made this Bump Funk, and the first version was basically defined as follows:

    (all ordinals in Cantor Normal Form)

    , we can even go further...

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  • Simply Beautiful Art

    So upon reading about the Fast growing hierarchy, I came up with this simple thing that avoids the use of ordinals:

    ? and d are either zero or involve @ symbols but don't involve # symbols.

    F a = a + 1

    F a # .... # b # d = F a # .... # b

    F a # b # .... # c = F[a] a # b - 1 # .... # c

    F[1] a # .... # b = F a # .... # b

    F[k] a # .... # b = F[k-1] (F a # .... # b ) # .... # b

    a # ? # .... # ? # 0 # b # .... # c = F a # ? # .... # ? # a # b - 1 # .... # c

    F a # ? # .... # ? # d # b # .... # c = F a # ? # .... # ? # O(d) # .... # O(d) # a # 1@0 # b-1 # .... # c, with a amount of # O(d)'s and d involves at least one @ symbol.

    Where we have the O function:

    O(e) = e - 1

    O(0@0) = a

    O(d@0) = O(d)@a, where a is the first number in the FAIL.

    O(d@e) = d@e-1

    The fu…

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