FANDOM

  • B1mb0w

    Alpha Spreadsheet q4.0

    May 18, 2019 by B1mb0w

    Alpha Spreadsheet v4.0

    \(\alpha(5.1713438192857) = Q(t_{0}^{t_{0}^{t_{0}(1)}(Q^{2}(Q^{3}(Q^{t_{0}(0)}(1,t_{0}^{[1]}(0)_*))_*,t_{0}^{[1]}(0)))}(t_{0}(1,0)),3)\)

    \(\alpha(5.1713438222485) = Q(t_{0}^{t_{0}^{t_{0}(1)}(Q^{2}(Q(2,t_{0}^{[1]}(0))_*,t_{0}^{[1]}(0)))}(t_{0}(1,0)),3)\)

    \(\alpha(5.1713438252114) = Q(t_{0}^{t_{0}^{t_{0}(1)}(Q^{2}(Q^{2}(2,t_{0}^{[1]}(0)_*)_*,t_{0}^{[1]}(0)))}(t_{0}(1,0)),3)\)

    \(\alpha(5.1713438281742) = Q(t_{0}^{t_{0}^{t_{0}(1)}(Q^{2}(Q^{t_{0}(0)}(2,t_{0}^{[1]}(0)_*)_*,t_{0}^{[1]}(0)))}(t_{0}(1,0)),3)\)

    \(\alpha(5.171343831137) = Q(t_{0}^{t_{0}^{t_{0}(1)}(Q^{2}(Q^{t_{0}(0)}(1,Q^{t_{0}(0)}(2,t_{0}^{[1]}(0)_*)_*)_*,t_{0}^{[1]}(0)))}(t_{0}(1,0)),3)\)

    \(\alpha(5.1713438340999) = Q(Q(t_{0}(1,0)),3)\)



    \(\alpha(5.17133627) = Q(t_{0…

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  • B1mb0w

    I use short hand notation for recursion of nested functions. They are a further development of notation I use that is not in common use.



    Here is a summary review of my notation:

    Decremented Function \(C\) is short-hand notation. For any arbitrary function:

    \(M^{c + 1}(n)\) then \(C = M^{c}(n)\)

    e.g.

    \(M^{c + 1}(n) = M(C) = M(M^c(n))\)

    Parameter Subscript Brackets is shorthand for functions with multiple parameters:

    \(M(x,0_{[2]}) = M(x,0,0)\)

    \(M(x,y_{[2]}) = M(x,y_1,y_2)\)

    \(M(x,0_{[2]},y_{[3]},z) = M(x,0,0,y_1,y_2,y_3,z)\)

    Leading Zeros Assumption applies to any function I define which accepts a variable number of input parameters. All leading zeroes can then be ignored:

    \(M(0_{[x]},0_{[2]},y_{[3]},1) = M(0_{[x + 2]},y_{[3]},1) = t_0(y_{[3]},1) = M(y_…




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  • B1mb0w

    Alpha Spreadsheet q3.0

    February 7, 2019 by B1mb0w

    Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.



    You are free to use and copy the code as you like. Version 3.0 of the Javascript code in Google Sheets is available here:

    Alpha Function Spreadsheet

    This replaces the Version 2.0 spreadsheet.



    Some examples taken from the spreadsheet.

    \(\alpha(2) = Q(1,2) = 5\)

    \(\alpha(2.75) = Q^{2}(1,2_*) = 11\)

    \(\alpha(3.1) = Q^{Q(2)}(1,2_*) = 23\)

    \(\alpha(3.61) = Q^{Q^{2}(2)}(1,2_*) = 47\)

    \(\alpha(4.29) = Q(t_0(0),2) = 95\)

    \(\alpha(4.446) = Q(Q^{t_0(0)}(t_0(0)),2)\)

    \(\alpha(4.605) = Q(Q(1,t_0(0)),2)\)

    \(\alpha(4.9706) = Q^{Q(Q(1,2))}(Q(Q(t_0(0),t_0(0)),2))\)

    \(\alpha(5.8721) = Q(t_0(1),2)\)

    \(\alpha(6.143) = Q(Q(t_0(0),t_0(1)),2)\)

    \(\alpha(6.436) = Q(Q(t_0(1),t_0(1)…






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  • B1mb0w

    Alpha Function Code q2.0

    January 10, 2019 by B1mb0w

    Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.


    You are free to use and copy the code as you like. Version 2.0 of the Javascript code in Google Sheets is available here:

    Alpha Function Javascript

    This version replaces my previous Version 1.0 spreadsheet, but all versions are still available online.



    Some examples taken from the spreadsheet.


    \(\alpha(2) = Q(1,2) = 5\)

    \(\alpha(2.75) = Q^{2}(1,2_*) = 11\)

    \(\alpha(3.1) = Q^{Q(2)}(1,2_*) = 23\)

    \(\alpha(3.61) = Q^{Q^{2}(2)}(1,2_*) = 47\)

    \(\alpha(4.29) = Q(t_0(0),2) = 95\)

    \(\alpha(5.8721) = Q(Q(1,t_0(0)),2)\)

    \(\alpha(8.825) = Q(Q(t_0(0),t_0(0)),2)\)

    \(\alpha(11.3623) = Q(Q(Q^{t_0(0)}(t_0(0)),t_0(0)),2)\)

    \(\alpha(15.2982) = Q(Q(Q(1,t_0(0)),t_0(0)),2)\)

    \(\…






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  • B1mb0w

    Alpha Function Code q1.0

    December 8, 2018 by B1mb0w

    Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.


    You are free to use and copy the code as you like. Version 1.0 of the Javascript code in Google Sheets is available here:

    Alpha Function Javascript



    Some examples taken from the spreadsheet.

    \(\alpha(0) = 0\)

    \(\alpha(1) = 1\)

    \(\alpha(1.375) = 2\)

    \(\alpha(1.5) = Q(2) = 3\)

    \(\alpha(2) = Q(1,2) = 5\)

    \(\alpha(3.01) = Q^{Q^{2}(2)}(Q^{2}(1,2_*)) = Q^{4}(Q^{2}(1,2_*))\)

    \(\alpha(4.286) = Q(t_0(0),2)\)

    \(\alpha(4.3582) = Q^{Q^{Q^{2}(2)}(1,2_*)}(t_0(0),2_*)\)

    \(\alpha(4.3625) = Q(Q(t_0(0)),2)\)

    \(\alpha(4.44) = Q(Q^{t_0(0)}(t_0(0)),2)\)

    \(\alpha(4.605) = Q(Q(1,t_0(0)),2)\)

    \(\alpha(4.9695) = Q(Q(t_0(0),t_0(0)),2)\)

    \(\alpha(5.0687) = Q(Q(Q(t_0(0)),t_0(0)),2)\)

    \(\a…





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