Modeling/Art non-related to Amnesia / SOMA

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I would say that this is probably the best I have gotten so far though it unfortunately did not turn out seamless enough to be tiled.

To make a tiled texture, I believe you quarter it into sections, move the sections to the opposite side of the image(So that the middle is now on the outside) and then fix the new center.

Jup, that's what you do! In Photoshop just use the offset filter and set the offset to half the pixel size of your texture. Then fix the seams in the middle. The quick n' dirty way would be simply using the healing brush, but that might give you blurry areas or ugly repeating "chunks" of picture.

Depending on the texture you're making tileable, you might have to manually paint over the seams or copy extra elements of the picture over them (Like bricks or stones).
If your texture is rather uniform with no big elements (like sand, short grass, concrete or gravel for example) a neat trick is to duplicate the layer and only offset one of the two copies. Then paint a layer mask onto the offsetted one that only covers the seams and fades out in a fitting way (furry brush for grass, rough brush for concrete... just don't use the standard blurry brush it looks...blurry ). That way it's done within minutes and it often works nicely!
Instead of copying the layer you can of course also use another fitting texture. For example you could take two square chunks of concrete out of a bigger photo and blend them together into one tiling piece using the same method.