As with many things with Photoshop, there are probably millions of ways of doing this - this is just one way. First, create a document 600 x 600 etc and
Tutorial by: Andrew Buckle
Works with: Photoshop CC and CS and standalone, Elements
Other tutorials: Tutorial links
Videos: Video tutorials
then set up some smart guides via the view menu and new guide layout. Set to 2 and 2 guides. You can then go to the view menu and set the snap to on and set the snap to only guides
You need to create four triangles with four different triangles. They don't have to be equal triangles but it works best when the corner points at least match for seamless reasons. The center can be in the center (mine generally are) but you can also set the guides to have them slightly shifted from the center. Of course, other combinations of guides can be set up as well to create other combinations of anchor points. Click the top left corner with the pen tool and then go to the bottom left corner and then click and then go to the center and then back to the start point to close. Go to the top right corner and then go to the top left and click and then go to the center and click and then to the start point for the second triangle. Do the same with the next triangle i.e. bottom left to center and then to bottom right and back to the start and so on. Create four shapes - all triangles. On finishing, you should have a complete filled square in a solid color.
You can now go to the layer's panel and you should see four triangle layers in the same color. Select the rectangle tool and then click each of the layers - 1, 2, 3 and 4. Set the color via the top fill color option - go for blue, another blue, a darker blue and then a lighter blue (that is one option) or have random colors such as red, green, blue etc or perhaps use the window menu extensions and Adobe color themes to set up harmonious colors and so on. Flatten the result (you can always undo and come back and change the colors)
Go to edit menu and define command. The tile is then stored in the preset's panel. You can then use it via the edit menu fill as well as layer and new fill layer as well as use it via layer styles / textures / pattern and much more.
You can select part of the artwork and re-color that and then define that. You can also combine them with adjustment layers such as hue and saturation to re-color the artwork or part of the art. Select parts of the design and fill with images. You can also use different sizes of structure as well such as rectangle themed one
Or use different origin points using the direct selection tool to shift the origin to create more abstract artwork
You can also just duplicate and rotate and scale (75% etc) the layer and then combine to create a new tile with the same color though you could use a different color or perhaps add effects to the second layer as that is not near the seams, it is not an issue for the seamless tile.
Or perhaps combine more than one additional colorful layer so all kinds of super colorful artworks can be created using the same approach
You can also combine effects such as blurs to the artwork (avoiding the seams) and create additional unusual tiles