Tetration

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About the Graphs

^ye^a for y in { 1, 3/4, 1/2, 1/4, 0, -1/4, -1/2, -3/4, -1 }

Most graphs, like the one above, will have color coded keys indicating what the different lines on the graph are. It has taken quite some time to prepare these. When I first started this website, I did not have a robust extension of tetration. It was partially due to my struggle in creating such graphs that I stumbled upon the Abel linearization. Once I found how to apply it to tetration, more attention went to developing it rather than doing these graphs, which was what it was for! Now that I have developed a way to produce these graphs, here are a few graphs that use my extension of tetraiton. I hope you enjoy these graphs as much as I do.

Graphs

Tetration

z = ^ye


z = Dⁿ_y (^ye) for n in { 0, 1, 2 }


z = Dⁿ_y (^y2 for n in { 0, 1, 2 }

Super-logarithm

y = slog_e(z)


y = Dⁿ_z slog_e(z) for n in { 0, 1, 2 }


y = Dⁿ_z slog₂(z) for n in { 0, 1, 2 }

Other

z = ^oox


z = ^yx for y in { 0, 1, 2, 3, 4 }


z = ^yx for x in { 2, e, 10 }


z = ^ye^a for y in { 1, 1/2, 0, -1/2, -1 }