What is the logic for an infinite scrolling background given an engine with basic tools?

Also, would this be similar to the logic for a procedural level?

In a basic explanation, anyone care to give it a go?

Right now I am thinking of it like a typewriter. When the head gets to the end, it jumps back to the first position and repeats that. Am I close?

It depends on your purpose.

Your typewriter example is a possible solution. You start with a given sequence and once it reaches the end, you start with the first one again. The advantage is that it is pretty straight forward, but could become repetitive.

You can also have a pool of different segments that get randomly spawned at the end of the last segment. It can create a more diverse feeling, but it can potentially be more work because you do want them to connect visually. This approach would be more semi procedural in a way.

Or perhaps a bit of both worlds: Have a basic background scroll and spawn various background objects based on whatever factor you want.

Okay. Cool! Thanks!

Another technique for horizontal and vertical background wrapping is to use UV linear wrapping state with the device so you only need to draw the background once and the hardware takes care of the wrapping.

First you need to figure out how to create a background that when wrapped - it won't appear to have seams. This can be done by copying the background to 4 layers with each layer moved to a corner with their tips touching in the center to expose the seams that would show when scrolling. Then with a 50% opaque stamp tool, smudge tricks and other art techniques to hide seams. Now this art can scroll without seams appearing.

Then when rendering a texture, you would want the sampler state to use linear wrapping and when you draw it:

(using SamplerState.LinearWrap)

Draw(background, screenRect, new Rectangle((int)background_pos.X, (int)background_pos.Y, background.Width, background.Height), ColorTint);

Where screenRect is your destination screen rectangle(always the same), and the other rectangle is the source rectangle (x,y, width, height). When the source sampling starts at x, y and exceeds the edges of the texture (cuz trying to go width and height), it will wrap the texture to continue sampling. So then when the player moves you just change background position in that direction.

For layers the same technique could be applied.

Hypothetically, for huge mapped backgrounds, you may want to seamlessly tile parts together and scroll through sections of the grid -- each tile in the grid can tell it which part of which background art to show. This way you could have extensive changes to background scenery as the foreground scrolls.

5 % 5 = 5
10% 5 = 5

These are incorrect. They should be:

5 % 5 = 0

10 % 5 = 0

The modulo operator returns the remainder of a division operation. 5 / 5 has no remainder, so 5 % 5 = 0