Fractal Noise's Offset Turbulence has maximum value. How can i keep going?

Going back through my old posts. A little older, a little wiser.
Now, reading through these responses again, they still don't make any sense.
A graphical representation:

This combination doesn't really make for seamless upward movement, does it?

I was asking about how to do an infinite upward movement, and why the expression maxes out at -33867.2, when clearly the offset turbulence value can keep decreasing.

I think perhaps once the commenters realized they understood the solution and I didn't, they ignored the question and just began conversing amongst themselves about the old days, and creating tiled, static noise patterns in Photoshop. The term match frame was mentioned repeatedly as though this was the magic solution. However google searches for it were futile.

In hindsight, the answer to my original posted question is simply:
No. There is no way to keep Fractal Noise sliding upward forever.

And the workaround was apparently also in my original post.
Fading in and out of a short loop.

I hope this thread was helpful to someone. Certainly not me.

I appreciate that you want to loop The offset. But you Cant loop this without also looping evolution. If evolution is not cycling, then you won’t be able to match your frame. No matter what your offset settings are. So the technique I suggested is to 1st of all make sure that your Evolution settings are looping properly (Using the cycle Option). Then deal with the offset. My suggestion, as I said, is to somehow find matching frames, Keyframe those and then loop these using an expression. My suggestion to find  matching frames is to try the extreme values. You may also try other values. I’m going to be on after affects today so I’ll give it a try for you and see if I can’s create a solution. I hope this helps.

Software has limits. So, now you know the constraints of the effect - find a way around it. Here are a few ideas, in no particular order.

If you haven't already, try starting it at the opposite end of this property's limit, instead of zero; you just doubled what it'll give you.

If you read Angie's post carefully, I believe she's actually suggesting using Evolution as well as the Offset Turbulence (which I would probably suggest as well). It's possible you'll be able to find a match frame that would work well enough.

Fire is flickery by nature - it seems like it would be easy enough to hide a quick fade to another layer of this effect. I'd randomize the time somewhat so it doesn't feel uniform if someone watches for a while.

Make a taller layer to put the effect on, and use a combination of Offset Turb + y position movement to give yourself more leeway. It's likely you could then duplicate this, push it later in time, and use a soft mask edge to simply blend the next instance in pretty seamlessly. If you find an amount of time that works well, you could then drop this comp into another and use time remapping to loop it infinitely.

As you've noticed, you can only animate a parameter up to its maximum value.  You'll want to animate to a match frame in order to create a loop cycle.

If you can get the look you want by animating the Evolution parameter, it's very easy to create the loop cycle (as Angie suggested) as you can enable Cycle Evolution under Evolution Options. With this enabled, you return to a visual match every 360 degrees.  Two keyframe and a loopOut() expression allow animations made this way to run forever (or 5 to 10 minutes easy).

With Cycle Evolution enabled, you could use a time expression instead of two keyframes and a loopOut(); however, the max value for Evolution is something like 2,147,483,648.  It's also more challenging to sync other layers if going the expression only route.

You e run into the pixel res limitation there. You can get around this by cycling the evolution and making sure the offset value matches up with that. Do you have cycle evolution turned on?