What causes these circular swirls of islands?
Near the Lake of the Woods, the island swirl or vortex is due to structures in bedrock beneath the lake.  The rocks in this area are old and have been folded by tectonic action. The area has either been folded into a dome or a basin, exposing different layers of bedrock. Glacial activity afterwards has 'flattened'the area, and differential erosion within the folded area formed valleys that flooded where the rock eroded faster. 

Geologic history of The Lake of the Woods.