Nope, these are not miniature roses, neither are they some of the new "Carpet" roses I've seen advertised. They are moss roses, or portulacas.
Portulacas are a low growing (4" - 6") annual that flowers for months on end with little care. They come in both single and double flower forms. The doubles that I have remind me of carnations. My variety is known as the Sundial portulacas. The flowers close up at night and on cloudy days. The leaves are fleshy like most succulents, which explains why they do well in dry heat.
These great annuals are quite easily grown from seeds. Just dust the ground with them, water in, and watch grow. Many times they will re-seed themselves voluntarily in sundry neat places. In fact, the ones pictured in this post are all volunteers. The ones above are growing near the base of a mock orange I planted this year. I have no idea how the seeds got here.
Portulacas need full sun and good draining soil. They are perfect for an area that the hose won't reach. They also make wonderful "spillers" for containers. I recommend them to neglectful gardeners who are prone to forget watering their containers for a few days. The plants will spread to about 12" in diameter. They are great for rock gardens and sandy areas. Did I mention that they are an heirloom flower that your grandmother probably grew? Let us never forget these old time favorites.