To create the Photoshop random color squares design, firstly, go for a layout and guides, so go to the view menu and new guide layout and set it to 4 and 4 to create 16 cells to work with for your grid. Click OK. Make certain the view menu and snap is ON and snap to guides is also ON.
Go to the rectangle tool and go to the options in the control bar and set to square. Set the type to pixels.
Go to the swatches panel which can be found via the window menu and select a swatch and you may like to use all the swatches in the panel or perhaps go for all the reds or all the greens etc. Drag with the rectangle tool over one of the cells and the pixels should snap to the guides. You can always undo if it goes slightly wrong and try again. You can always select from a vast library of swatches as well as add more libraries to your panel.
Change the fill to say pink or green and then apply in the next cell and repeat with different greens and blues etc but try to avoid getting the same fill next to another also try and avoid doing the same around the edge, all the edge fills should be different.
You can now define this design as a tile or perhaps define it as a brush stroke via the edit menu. You can also duplicate it and make it a layer and perhaps modify the layer and also save it to the CC libraries. Perhaps duplicate the layer and re-size and overlay the existing design.
You can also add an adjustment layer to the artwork such as HSL and change the design. Or just use the image menu and adjustments. The artwork should still remain seamless.
Create a guide layout of 4 and 4. Go to the rectangle tool (layer option) and snap to the cell. Hold down the alt / option key and drag and add the design to all the cells. Select each cell and select a swatch from the panel. Flatten image. You can then adjust things by using HSL or black and white or LUT etc