Grammar is a term that us usually used in the context of a natural language, such as English. We also use grammars in computing (although it is usually called syntax). And we can use grammars to control the process of generating art with software.
What is a grammar?
The English language contains thousands of words, but the words alone don't define the language. There are also rules about how the words can be combined so that the combination of words can be understood. These rules are called grammar.
Computer programming languages are usually simpler and more rigid than natural languages, but they are also usually recursive. For example in Python, here is an example of an expression:
x + 3
Here is another example of an expression:
x + 3 if y + 1 < z and z ** (a + b) == 7 else n + m
Here the main expression is a conditional expression (the ternary operator) but each of the parts is also an expression. This also happens in natural languages but very complex sentence structures are less common.
Generative art grammars
When we use grammars in generative art, we often work with individual symbols rather than words or variable names. For example in an L system we might define a grammar that only uses the symbols A, B and C.
The grammar defines which combinations of A, B and C are valid.
In addition, each symbol might represent a particular drawing operation.
We can apply the grammar rules to create a complex string of symbols, then we can translate those symbols into drawing operations to create an image based on the symbols.
Using grammars to create art
The grammar itself only tells us if a particular sequence of symbols is valid or not. The grammar itself won't create art.
Some grammars have fixed rules that can be applied automatically. Starting with an initial set of symbols, the rules can be applied to create a new, usually more complex, set of symbols. Eventually the symbols will be converted into drawing operations.
There are other systems where the grammar is less rigid, and at any point there may be several choices available. In that case it is common to use random or semi-random selections to create forms.