I'd like to quickly repeat it 4 times.
So the result would be:
Is there any automated way to do this in Photoshop, instead of resizing the workspace then copying and placing it three more times?
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Well you can actually make it a pattern in Photoshop.
With the tile open, select all and choose
Edit > Define Pattern. Then it's a pattern just like all the other built in Photoshop patterns.
If you know the tile size you can create a new document the size of 4 tiles, then just apply a pattern fill layer.
With a 500x500px tile, create a 1000x1000px document and choose
Layer > New Fill Layer > Pattern... selecting your pattern.
If you don't know the tile size, and it's already a pattern in Photoshop... You can turn on Tool Tips in the Preferences, then hover your mouse over a pattern and the tip will show you the tile size:
In the screenshot below, percentage input is selected and the result will be a 2x2 tiling of the original image.
No need to create (and presumably later delete) a pattern or worry about the exact dimensions of the source image (unless you want to, of course, in which case you can change the input units to pixels instead of percentages).