Pentation fractal
(08/01/2022, 10:56 PM)JmsNxn Wrote: Kouznetsov refers to the regular iteration about \(b = e\), as the Kneser iteration. This is based on his manner of constructing the function. Which I'm sure you're well aware of. His manner on the real line is real valued, and is what he always calls regular iteration.

I see you mentioning the "regular Kouznetsov iteration" but can you exactly give me the pages where he makes that assumption?!
By just skimming his pdf it looks like he refers to regular iteration just as everyone else does ...
And anyways I would not suggest messing a well-defined term up only because Kouznetsov calls something else that way (what I doubt until I see the concrete passage)
Yes, you are entirely correct. He wrote natural tetration!

That's what I mixed up. I used to call natural iteration the schroder iteration in my head, so when I was mentally making the swap for regular iteration to natural iteration, I erroneously made a false equivalence. So, sorry you are absolutely right. He calls it natural tetration.

That's a dumb mix up, lol.

Greatest apologies again.

So NOW the words make way more sense, I definitely was confused why I thought regular iteration could somehow be extended into the Crescent, and I'd see contradicting data, but I wasn't sure. This makes far more sense! I'll try my best to not screw up the terminology from here on out Smile

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