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Ok, I know that clay only spawns when the X axis and the Z axis are the same, which means that there is a diagonal line where you can find clay between two corners of the map.
My question is, it it the line between the North West and South East corners? Or the line between the North East and South West corners?
Its not always in corners and I know this for a fact as I had found clay in 3 worlds and 2 out of the three it was not in a corner of the map. The whole X and Z thing may be right but I found clay in the middle left and top left of those to worlds.
Just forget all that cardinal direction noise... I don't even think the GAME knows which direction things are supposed to be in.
Looking at your map, that imaginary diagonal line should stretch from the upper-left corner of your map, down to your bottom-right corner. It'll only show up in areas with sand. So unless you really feel like scouring the entire line, stick to looking at sandy areas first, before you move on to the long shots of "that 2x6 section of sand in the snow!".