It's not so much a matter of how TG "animates" anything, but how *you* choose to animate something in TG.
If you animate a camera and nothing else in the scene, the flames (or other fractal-based phenomena) should *not* change (except in terms of specific noise pattern which is just due to random sampling and is a render detail issue, not an actual change to the underlying noise function, e.g. the flame pattern). However, noises are mostly defined in, or "anchored" in, World Space by default. So if you move the object/shader that is using a noise function as input, the *object* is moving *relative* to the noise function (which stays static), and therefore the pattern changes. Basically the "slice" of the noise function that is being visualized by e.g. a cloud node changes based on where that cloud node is positioned and sampling the noise in that location. Unless, of course, "Move textures with cloud" is enabled.
So with all that in mind, you can animate noise functions in a wide variety of ways to achieve different effects. You can Translate in X or Z, which would keep the *shapes* the same but simply move them horizontally. You could also Translate in Y which in most cases gives the appearance of an "evolving" animation where the shapes slowly change to other shapes. This is because you are always seeing either a 2D projection of the noise function - like a "slice" - as in the case of a noise function on a surface, or you are seeing a limited area volumetric representation, as in the case of a cloud layer. In either case when you move the noise function relative to this slice or finite volume, the noise function appears to change because the "slice" you are taking is moving through the 3D noise function itself and the shapes vary throughout the function (which is what makes it a 3D noise function basically).
You can also animate with "4D Noise", which is a relatively newer function which actually *does* attempt to literally animate the noise along the 4th (time) dimension. So you get "evolving" shapes with this too, but the shapes are *actually* changing, rather than just the result of seeing a different part of the noise function.
You can also animate any other setting of a noise function and get useful and interesting results. Warping, scale, etc, etc. So there is no one simple answer to this.
- Oshyan