The Simpsons opening sequence a main title for the show. Jean said Banksy "sent back boards for pretty much what you saw." Series creator Matt Groening gave the idea his blessing, and helped try to make the sequence as close to Banksy's original storyboards as possible. Approximately the first half minute of the opening sequence remains the same, with a few oddities: the word "BANKSY" is sprayed onto a number of walls and other public spaces. The chalkboard gag ("I must not write all over the walls") is written all over the classroom walls, clock, door, and floor. After the Simpsons arrive at home,
Automatic sequence is a fixed point of φ—that is, if "w" = φ("w")—then "s" = τ("w") is a "k"-automatic sequence. This result is due to Cobham, and it is referred to in the literature as "Cobham's theorem". Conversely, every "k"-automatic sequence is obtainable in this way. Let "k" ≥ 2. The "k-kernel" of the sequence "s"("n") is the set of subsequences In most cases, the "k"-kernel of a sequence is infinite. However, if the "k"-kernel is finite, then the sequence "s"("n") is "k"-automatic. It follows that a "k"-automatic sequence is necessarily a sequence on a finite alphabet. Let "u"("n") be a sequence