The Simpsons opening sequence is a callback to the film. Bart writes "I will not wait 20 years to make another movie" on the chalkboard and skateboards through Springfield, which is still recovering from the dome incident. Several movie characters reappear, including president Schwarzenegger, the Multi-Eyed Squirrel, Colin, Russ Cargill, and the Medicine Woman. We also see that the Simpsons' house is still under construction and the silo is strapped to Homer's car. Plopper the pig is also featured for the first time in the series, during the couch gag and Homer refers to him as "my summer love." A special opening sequence, featuring
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