First question: how is this so adorable? :3

A mystery. :3

Them legs.

There are quite many of them

Yes they are.

Best. Taur. Ever.

From FA's foremost taurficionado that means quite a lot! :D

The best taur is automatically the one with the most legs - this one has the most so is the best

How much does this character's body compress on itself from backwards motion? If they ever move forward then there must always be some part of their body that is moving forward, unless their universe has different rules.

Well, he can always produce more of himself from wherever he came from, so any forward movement would theoretically require no compression. But in practice, yeah, there is some stretch and squish but due to the length of his body, it averages out to almost nothing.
He's used to a lot of backtracking too, and this doesn't really compress the body much either, since all the legs can carry him backwards exactly along whatever route he took. It does look silly though. :P

If someone tickles your one of your paws a few lightyears away, do you feel it instantly or is there a light speed delay?

Great one! :D Universe-breaking and silly. This might require a whole comic to address.

My initial thoughts: I'm gonna assume that in order to be a functional infinite being in whatever universe he exists in (and our universe), the electrical impulses inside him have to travel at speeds far faster than light. And my favorite FTL copout is multidimensional trickery, the same kind that makes his additional floating eyeballs. So yes, he could feel it more or less instantly.

Ohh, that's what those are. So, a compound vision sort of thing going? Unless he can see infinitely, too. o.o

So, to keep track of where every part of his body is and account for the seemingly infinite gravitational pulls, his brain would have to be infinitely powerful to account for all of that, right? Not to mention a heck of a memory and other senses, if he can't see back, either!

At the very least, he wouldn't end up affecting planetary movements or anything like that...not unless he were to bunch up in one spot, maybe. If that were to happen, though, I'd think it'd affect him before it'd affect any planetary bodies?

Also, he'd have to be real careful of black holes and other such things, am I right? Unless he's capable of some truly astounding velocities through that multi-dimensional trickery of his...or just pops into another dimension to go 'around' it, so to speak.

I'm thinking it's most practical for him to have a brain going down the whole length of his body, or something like a chain of brains. And yeah, vision will be finite. He'll have enough sensation down the whole length of his body that he can swerve to avoid anything massive - planets, stars, black holes, etc.

Man, talk about a brain trust!

Hopefully nobody tries to exploit this feature to use him as an inter-planetary FTL communications relay! :P

Oh wow, I just noticed that when he blinks even his floating eyes blink.

Hehe, I thought it would be a nice alien touch. :D

So if he goes on his way into another universe but passes through ours, wouldn't he end up permanently taking up residence in our own universe? :O

Ahahaha yes, I did think about this. Initially I had him saying he would "find another exit and move onto the next universe". But you see exactly why this is a problem! This is why he says he's going to go back the way he came. That way he can just loop back on himself and slip back into his own universe without leaving any part of himself here.

It'd be fun too have a trail of moving legs that lives between two holes in our universe, forever. Also you could put a treadmill below them and get infinite power.

The problem with the treadmill is that it would essentially keep part of his body from moving. When he realizes this, he'll hop away from it.
There may be some other possibility though, some other kind of mill to harness his movement.

Oh! Something like a bunch of big paint rollers in a row that they could put on his back. That would produce energy and still allow him to move.

Well, if he managed to make a stopover back into his home universe between stops, he could use that as a taur-matter-sink to allow his butt (assuming he has one at the end of that infinitely-long body :P ) to enter and exit the previous universe via his original entry and exit points. Right? :D

You know, speaking of butts, this actually leads me to yet ANOTHER question! Thank you! :P

If he were finite, yes! But he ain't. :P

Actually if he were really infinite, would he not have a head as well, and instead be this never-ending body of legs with no front or back?

THIS IS TOO FUN TO THINK ABOUT, HUSH XD

Interestingly enough, a creature like that (let's call it the Infinitrain) would not be any bigger than the Infinitaur. Or at any rate, they would have the same number of legs.
This video explains why! http://ed.ted.com/lessons/how-big-is-infinity

But having a butt doesn't mean he would be finite, he still has an infinite amount of middle between the two ends! Which I assume is safely contained within his own infinitely-large homeworld :P

WELLLLLLLL fine, technically that's possible, and he could probably find his tail in a finite amount of time.
Weird thing is, these two parts of him need not move simultaneously or even in the same direction!

Does he have a tail? :O

If he did, he wouldn't be infinite!
Given the current model of a "brain chain" going down the length of his body, he can access and receive information going as far back as he wants. But even after all this time, he has not reached the end of himself. He's also tried looping around and physically following his body as far back as he can, but even then, his body JUST KEEPS GOING, disappearing into the fog.
So if he does have a tail, it's located at a point infinitely far away. :P

I do wonder, what's with those extra floating eyes?

is an alien. ouo

Maybe I should have elaborated....

Since those eyes are floating and disembodied, can he presumably "detach" them, hold them in his hands, move them, place them somewhere, etc? Or are they pretty much stuck and frozen?

They hover there, they have about as much give as any other part of the body if you were to tug it. Except don't. Nobody likes a poke in the eye. :P
(Modular stuff is fun though. Hex is adept!)

Yeah, I have to agree, modular stuff is pretty fun! We should speak to each other more sometime.

Love this idea! I think I already asked all of the questions I could think of though in the stream.

Brb... giving each body section a hug. This could take a while!

I might have forgotten most of them! Feel free to comment here if you've still got stuff that hasn't been answered above already.
Infinitaurhugs. <3

lol I think I've forgotten many of my questions too.

Is anything or even anyONE living on his back? Small or otherwise?

Well, I think Hex lives there now. :P
Other than that, he's probably picked up little critters in the places he's gone. We'll see!

I assume he doesn't mind having his lower body touched, laid on etc.? Not like he has much choice but to tolerate it in regards to the infinite majority of his body anyway.

And a headcanon: when people ask about his sex organs, he wryly says they're between his hindmost pair of legs.

He can squirm or kick off anything that bugs him too much, and he may not even realize it since his brain goes the length of his body and each segment is semi-independent.

Does he feel some coldness from outside space?
Will he die when somewhere his body gets "snapped" or cuts into two pieces?

Cold? Good question. Probably! Or maybe he generates enough warmth to withstand it. Haven't figured that out.
Your second question is answered here: https://www.furaffinity.net/view/18903386/

I saw some videos about what happen to body on outer space without space suit.
Like body gets boiling and holding breath damage its lungs... How does he breath trough outer space?

Do you saw my another question on that second part about Flatland and Planiverse?

The infinitaur is best at tickle fights. You should draw infinitaur tickling someone with his infinite amount of legs he has. Him tickling a persons belly, armpits and etc.

I'm thinking that he does have an end, but as he walks, more taur bodies sprout immediately to fill the gap.

Is their like a portal he came from, I can't think of another way an infinitely large being could work, especially in a finite universe.

:0 Hilbert hotel paradox reference? never thought i'd see one in the wild haha