Tetration

	Main	Identities	Code	Graphs	Paper
	History	Definitions	Error	Tables	Links

About the Graphs

^ye^a for y in { 1, ¾, ½, ¼, 0, -¼, -½, -¾, -1 }


         Most graphs, like the one above, will have color coded keys indicating what the different lines on the graph are. Unlike the one above, however, most graphs will have a white background. If you would like to see more graphs with a black background, let me know. My email address can be found at the bottom of each page.
         It has taken quite some time to prepare these. When I first started this website, I didn't 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! 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 = ^∞x


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, ½, 0, -½, -1 }