While working with Recursion, why do we need a base case? What will happen if we remove it? Explain with example

Give a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.

Using recursion and java, please make a sierpenski carpet Please also comment the code just like the image below. Do not make it fill of hastags