User blog comment:QuasarBooster/Duplicative Array Notiation/@comment-213.8.10.13-20160322093627/@comment-24923514-20160328003559

I'll try to give some sense of growth, but I can't guarantee that the higher estimates are completely accurate.

As the base case is simply an exponential, and since the first array entry just iterates over this, I'd expect the rate of an expression with but a single array entry to be \(f_3(n)\)<\nowiki>.

Not entirely sure if I'm looking at further extensions correctly. Each further entry, while the parent array is just a 1-structure, more or less iterates the previous one, so I'd expect the limit of any level-1 parent array to be \(f_\omega(n)\)<\nowiki>.

Taking that estimation into mind- if the parent array were to have multiple level-1 structures within itself, then with each one basically providing another ω of growth, the limit of a 2-structure parent array could be \(f_{\omega^2}(n)\)<\nowiki>.

If this pattern continues, then we'd next be having ω^2 added together to make ω^3 for a level-3 parent, followed by ω^4 for a level-4, etc. Therefore, I suspect that the current limit of any multi-entry, multi-structure parent array to be \(f_{\omega^\omega}(n)\)<\nowiki>.

I don't really know.. It might just be ω^2 at maximum for all I know. However, if it really does go to ω^ω, then that'd basically be the same level as linear BEAF! It's kind of defeating knowing that all this 'duplication' stuff, multidimensional too, is likely beaten by a simple linear array.

If that's true though, I suppose it's not too big a deal. This function was still fun to make, and wasn't that really the point of all this?