Blondie, it's really hard to tell from a photo, but I think I'm seeing a lot of herbs here. I know creeping thyme is good for getting this effect - varieties vary depending what zone you're in. Herbs are perennials which come back year after year - there's more maintenance in weeding than there is in caring for them. I would print this out and take it to my local nursery to get some help finding whatever is similar and available in my area. Be sure to check the tag for height, spread, where to plant and care. You are most likely to find the plants in spring - plant them after there is no more threat of frost.

Thanks, Becky!

The little white flowers on the steps are Sweet allysum. The grey-leafed plant on the left is Santolina. Both easy, draught tolerant and wonderful.

Love that self-seeding allysum. It smells of honey.

Does anyone know if it requires full sun or shade?

I guess you could do this in a shady space with different ground covering plants. But regularly spray some vinegar (about one cup vinegar in 5 cups water) on the steps to prevent slippery alges. The picture above looks sunny/half shade to me.