I started growing basil about two years ago, and once I overcame the initial difficulties, it has been a smooth experience ever since. Basil is actually a very resistant plant, and to my surprise it lasts incredibly long and can withstand even the most powerful storms.
The little plant pictured here is the third generation from my very first basil plant, it's now about 20 cm high and has been growing for about 4 weeks. Its 'mother' is now about 10 months old, pretty huge (80cm diameter) and healthy, pictured at the end of this post. The first generation actually died eaten by caterpillars, after growing for about 4 months.
Once it's up, basil produces flowers and lots of seeds, and you will see dozens of little basil plants sprouting up. It's then just a matter of potting some of them, if you wish to extend your basil plantation. Some claim that you should always trim the flowers to prevent the plant from dying, but I found that my basil has been growing more healthily since I stopped chopping its flowers, and it hasn't died yet (it has been sprouting flowers for at least 6 months).
It's great to have such a plant in your terrace. You can just pluck a few leaves if you want to make some fresh pesto, and I guarantee it tastes better than the basil you buy at the supermarket. I am now planning to start growing other herbs such as rosemary and shiso. Hopefully I will soon be able to show how beautifully they have grown.