How would I go about creating a scene that is "infinite" in the players perspective. like the amount of movement afforded to the player in any direction is unlimited and there is a texture that repeats infinitely.
"Infinite" map
That depends heavily on what type of game you're making. In a 2D scroller, you just scroll the background and maybe add new objects to avoid.
Look into parallax background. This will give you an infinite background.
https://gdscript.com/solutions/godot-parallax-background/
To make the map infinite takes more work. You can use TileMaps. This is like the kind of levels from the original Mario game. You can create 2 TileMaps next to each other, and when the player gets to a certain point, you move the one in the far side to the near side (adjacent to the one on the screen). This gives you a fake infinite map. Or you could do things totally random or procedural.
- Best Answerset by GunRose
Endless walking in all directions depends on what's the purpose. Could be a simple as walking a sphere, or a surface whose borders overlap to avoid gaps and you wander it modulo its size. It's repetitive, but offers endless walking in all directions. Or much more sophisticated approaches for huge datasets.
- Edited
Cool. I don't have a ready solution for that, but it shouldn't be difficult to find (or produce with the help of a noise generator) textures that wrap around the borders and can be tiled without visible seems. These can be used in Tile Maps, as described by cybereality .