Did you do any pinching back? Alyssum is one of the few flowers that benefits greatly from pinching to force branching. With the pictures you have seen that show a thicker carpet that is what was done - pinching. Keeps the plant short and multiple branches form.

If left to go to a single stem - even if thickly sowed - they just getty leggy and droop over.

6-8" makes them easy to use as transplants but yes you can sow them closer if you don't plan to transplant them. Still have to pinch though.

Dave

I bought 1/4 lb of alyssum seed along with my 1 lb of wildflower seeds last year from Wildseed Farms. When I sowed them (they are pretty small seeds) they were quite close, and I got areas here and there a few feet square with a very nice carpet effect and they smell wonderful. I didn't pinch them but there were so many seeds I guess they kind of layered on each other.
This year it was an extra 1/4 of poppy seed, but the alyssum either reseeded or the alyssum in the fall sowing of mixed seed is already blooming because some of them are out there already.

Their seeds are so tiny that I do not bother with trying to space them when sowing. I just sprinkle a bunch and thin later. When it comes to transplant then you can observe 6-8" spacing guide.
If you sow them in place, they also grow in clumps with no problem. They will keep flowering til frost. AND they will re seed.

I start them in plastic six paks by sprinkling seeds on top of soil. When planting out, I break apart the plants and plug them into the ground about 5" apart. I don't bother to thin out any plants. Each plug has up to six seedlings. They fill out nicely.

great responses, thank you! That helps a lot. I went ahead and sowed them more thickly. I'll do the pinching as suggested as well!