This pattern is called "Patchwork" and appears in Mary Konior's Tatting with Visual Patterns. The original pattern is a small repeatable square that can be connected to other squares to make a large mat. I transformed it into a magic square by adding trefoils to the corners of the small squares.
For those who would like to try this pattern adaptation, here are my notes. As you tat this, keep in mind that the central flowers have a slightly different stitch count so they can attach to the trefoils. I've also changed a lot of the original stitch counts to suit my tatting style:
Right clicking and opening the photo in a new tab should make the stitch counts large enough to read. Numbers in the diagram show one repeat. The flower in the lower left corner (where numbering begins) is a good place to start tatting this pattern.
If you are really ambitious, you could make the square much larger. I digitally altered the photo to give an idea of what a larger magic square would look like:
I'd recommend starting in the corner and working your way around like this:
This larger square is all done in one pass, but it is quite a maze and careful attention is needed to keep your place!