The ants walking pattern would be random that or it will be trying to follow a chemical trail through the circle. There are a few reasons to explain why.
When a queen sends a ant for food they will walk around randomly until they find a food source. While walking they release a chemical trail telling the ants where the food is so more can come for the harvest. That's why an ant in a circle will do one of these tasks.
Only one type of ant can produce offspring and that is the queen. Once a queen mates with a male the males sperm is stored in a storage sack which will be used for all the ants she creates.
After she mates with a male she will burrow in the ground and tear off her wings. She will then immediately she will start the colony. On average the queen will lay thousands of ants a day.
Ants are an advanced group of species that has adapted to thrive and withstand the harsh conditions of the environment. They succeed with mass reproduction and out number the human race one to a million.