User blog:B1mb0w/Alpha Spreadsheet q3.0

Alpha function code (Spreadsheet) version 3.0
Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.

Javascript code 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

DRAFT Version 3.0 Examples
I have started working on a new version. Here is some work in progress:

\(\alpha(2.75) = Q(1,3) = 7\)

\(\alpha(3.2) = Q^{2}(1,3_*) = 15\)

\(\alpha(3.61) = Q^{3}(1,3_*) = 31\)

\(\alpha(3.76) = Q^{Q(3)}(1,3_*) = 63\)

\(\alpha(3.95) = Q^{Q^{2}(3)}(1,3_*) = 127\)

\(\alpha(4.14) = Q^{Q^{3}(3)}(1,3_*) = 255\)

\(\alpha(4.3) = Q(2,3) = 511\)

\(\alpha(4.75) = Q(1,Q(2,3)) = 1023\)

\(\alpha(5.3) = Q^{2}(2,3_*) = Q^{1023}(1,Q(2,3)_*)\)

\(\alpha(6.65) = Q^{3}(2,3_*) = Q^{(1,Q^{2}(2,3_*))}(1,Q^{2}(2,3_*)_*)\)

\(\alpha(7.61) = Q^{Q(1,3)}(2,3_*)\)

\(\alpha(8.714) = Q^{Q^{Q^{3}(3)}(1,3_*)}(2,3_*)\)

\(\alpha(8.8) = Q^{Q^{Q(3)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)\)

\(\alpha(8.82) = Q^{Q^{Q^{3}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)\)

\(\alpha(8.824) = Q^{2}(Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*))\)

\(\alpha(8.8247) = Q^{Q^{2}(Q^{2}(1,3_*))}(Q^{Q^{Q^{3}(3)}(1,Q(2,3)_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*))\)

\(\alpha(8.82474) = Q^{Q^{Q^{Q^{2}(2,3_*)}(Q(1,Q^{2}(2,3_*)))}(Q^{Q^{2}(1,3_*)}(2,3_*))}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.824746) = Q^{Q^{3}(Q^{Q^{Q^{Q^{2}(3)}(1,3_*)}(Q^{Q^{2}(3)}(1,3_*))}(2,3_*))}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.8247469) = Q^{Q^{Q^{Q^{Q(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.82474692) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.824746928) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.8247469282) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.82474692824) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.8247469282402) = Q^{Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)}(1,Q^{Q^{Q^{Q^{3}(3)}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(2,3_*)_*)\)

\(\alpha(8.8247469282403) = Q(t_0(0),3)\)

\(\alpha(9.0591) = Q(Q(1,t_0(0)),3)\)

\(\alpha(9.55914) = Q(Q(t_0(0),t_0(0)),3)\)

\(\alpha(9.826235) = Q(Q(Q(1,t_0(0)),t_0(0)),3)\)

\(\alpha(10.39809) = Q(Q(Q^{2}(t_0(0)_*,t_0(0)),3))\)

\(\alpha(11.3622) = Q(t_0(1),3)\)

\(\alpha(11.3624) = Q(Q(t_0(1),3))\)

\(\alpha(11.3626) = Q^{2}(Q(t_0(1),3))\)

\(\alpha(11.36262) = Q^{Q(3)}(Q(t_0(1),3))\)

\(\alpha(11.36263) = Q^{Q^{3}(3)}(Q(t_0(1),3))\)

\(\alpha(11.36264) = Q^{Q^{2}(Q(1,3))}(Q(t_0(1),3))\)

\(\alpha(11.36265) = Q^{Q^{3}(Q^{2}(1,3_*))}(Q(t_0(1),3))\)

\(\alpha(11.36266) = Q^{Q^{Q^{2}(1,3_*)}(Q^{Q^{3}(3)}(1,3_*))}(Q(t_0(1),3))\)

\(\alpha(11.36267) = Q^{Q(Q^{2}(2,3_*))}(Q(t_0(1),3))\)

\(\alpha(11.36268) = Q^{Q^{Q^{3}(3)}(2,3_*)}(Q(t_0(1),3))\)

\(\alpha(11.36269) = Q^{Q^{Q(t_0(0),Q^{2}(Q(Q(1,t_0(0))),3_*))}(2,Q^{Q^{Q(Q(1,3))}(Q^{2}(1,3_*))}(Q(3),Q^{2}(Q^{2}(1,Q^{2}(2,Q^{2}(Q^{t_0(0)}(t_0(0)),3_*)_*)_*),Q(Q^{2}(Q(1,t_0(0))),Q^{2}(Q^{Q^{t_0(0)}(t_0(0))}(Q(1,t_0(0))),3_*))_*)_*)_*)}(Q(t_0(1),3))\)

\(\alpha(11.3627) = Q^{Q(Q(1,Q(Q^{2}(3),Q(Q^{t_0(0)}(t_0(0)),Q^{Q(3)}(Q^{Q(Q^{t_0(0)}(t_0(0)),t_0(0))}(Q(Q^{t_0(0)}(t_0(0)),t_0(0))),3_*)))))}(Q(t_0(1),3))\)

\(\alpha(11.36271) = Q^{Q(Q^{t_0(0)}(Q^{Q^{2}(Q^{2}(Q(t_0(0)),Q(Q(Q^{Q^{2}(t_0(0))}(1,t_0(0)_*)),t_0(0))_*))}(2,Q^{Q^{t_0(0)}(t_0(0))}(Q^{Q^{t_0(0)}(t_0(0))}(Q(1,t_0(0))),Q(Q^{Q^{t_0(0)}(t_0(0))}(Q(1,Q^{Q^{Q(1,t_0(0))}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))),t_0(0))_*)_*)),3)}(Q(t_0(1),3))\)

\(\alpha(11.36272) = Q^{Q(Q(Q(Q^{2}(2,Q(t_0(0),t_0(0))_*),Q^{2}(Q(Q^{Q(t_0(0))}(1,t_0(0)_*))_*,t_0(0))),3),Q^{2}(Q^{Q(1,Q(t_0(0),t_0(0)))}(Q^{2}(Q^{2}(Q(Q^{2}(1,t_0(0)_*)),Q^{[1]}(Q^{2}(Q(1,Q^{2}(2,t_0(0)_*)))_*,t_0(0))_*)_*,t_0(0))),3_*))}(Q(t_0(1),3))\)

\(\alpha(11.362721) = Q^{Q(Q^{Q^{2}(Q(t_0(0),Q^{[1]}(Q(2,t_0(0))_*,t_0(0)))_*,t_0(0))}(Q(Q(1,Q(Q^{Q^{t_0(0)}(1,t_0(0)_*)}(Q^{Q(t_0(0))}(1,t_0(0)_*)),t_0(0)))),Q(Q^{2}(Q(Q^{2}(2,t_0(0)_*),t_0(0))),Q^{2}(Q^{Q^{t_0(0)}(t_0(0))}(2,t_0(0)_*)_*,t_0(0)))_*),3)}(Q(t_0(1),3))\)

\(\alpha(11.362722) = Q^{Q(Q^{2}(Q^{Q^{Q^{Q(t_0(0))}(Q^{2}(1,t_0(0)_*))}(Q(Q^{Q^{2}(2,t_0(0)_*)}(t_0(0),Q(Q^{2}(t_0(0)),t_0(0))_*),Q^{[1]}(Q^{2}(Q(1,t_0(0)))_*,t_0(0)))_*,t_0(0))}(Q^{[1]}(Q^{Q^{2}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(Q^{Q^{Q^{2}(1,t_0(0)_*)}(Q^{2}(1,t_0(0)_*))}(2,t_0(0)_*))_*,t_0(0)))_*,t_0(0)),3)}(Q(t_0(1),3))\)

\(\alpha(11.362723) = Q^{Q(t_0(1),3)}(Q(t_0(1),3))\)

\(\alpha(11.36276) = Q(1,Q(t_0(1),3))\)

\(\alpha(21.837) = Q(t_0^{2}(0),3)\)

\(\alpha(117.3063) = Q(t_0^{t_0(0)}(0),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{t_0(0)}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{t_0(0)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{t_0(0)}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{Q^{t_0(0)}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*)_*,t_0(0)),3)\)

\(\alpha(11.3621611517856) \approx Q(Q^{2}(Q^{Q^{Q^{t_0(0)}(1,t_0(0)_*)}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*))_*,t_0(0)),3)\)

\(\alpha(11.3622) = Q(t_0(1),3)\)

\(\alpha(21.8367923498238) \approx Q(Q^{Q^{t_0(0)}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(21.8367923498238) \approx Q(Q^{Q^{Q^{2}(Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(2,t_0(0)_*)_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(21.8367923498238) \approx Q(Q^{Q^{Q^{2}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(21.8367923498238) = Q(Q^{Q^{Q^{2}(Q^{Q^{t_0(0)}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*))_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2)),3)\)

\(\alpha(21.837) = Q(t_0^{2}(0),3)\)

\(\alpha(117.3060621482) \approx Q(Q^{Q^{t_0(0)}(t_0^{2}(1)_*,t_0^{2}(1))}(t_0^{2}(2)_*,t_0^{2}(2)),3)\)

\(\alpha(117.3060621482) \approx Q(Q^{Q^{Q^{Q^{Q^{Q^{2}(Q^{t_0(0)}(2,t_0(0)_*)_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2))}(t_0^{2}(0)_*,t_0^{2}(0))}(t_0^{2}(1)_*,t_0^{2}(1))}(t_0^{2}(2)_*,t_0^{2}(2)),3)\)

\(\alpha(117.3060621482) \approx Q(Q^{Q^{Q^{Q^{Q^{Q^{2}(Q^{Q^{Q^{t_0(0)}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2))}(t_0^{2}(0)_*,t_0^{2}(0))}(t_0^{2}(1)_*,t_0^{2}(1))}(t_0^{2}(2)_*,t_0^{2}(2)),3)\)

\(\alpha(117.3060621482) = Q(Q^{Q^{Q^{Q^{Q^{Q^{2}(Q(Q(Q^{Q^{t_0(0)}(t_0(0))}(2,t_0(0)_*),t_0(0)),Q^{[1]}(Q^{Q^{Q^{t_0(0)}(t_0(0))}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(Q^{Q^{Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)}(Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*))}(1,Q^{Q^{Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*)}(Q^{Q^{t_0(0)}(t_0(0))}(1,t_0(0)_*))}(2,t_0(0)_*)_*))_*,t_0(0)))_*,t_0(0))}(t_0(1)_*,t_0(1))}(t_0(2)_*,t_0(2))}(t_0^{2}(0)_*,t_0^{2}(0))}(t_0^{2}(1)_*,t_0^{2}(1))}(t_0^{2}(2)_*,t_0^{2}(2)),3)\)

\(\alpha(117.3063) = Q(t_0^{t_0(0)}(0),3)\)

Further References
Further references to relevant blogs can be found here: User:B1mb0w