Treehouse of Horror VI

Krusty, as the Headless Horseman from The Legend of Sleepy Hollow, holds his laughing head and hurls it at the camera, making the title, "The Simpsons Halloween Special VI", appear on screen in blood.

Homer goes to Lard Lad Donuts to get a "colossal doughnut". Upon realizing that the colossal doughnut is the name of the doughnut that Lard Lad holds and actual doughnuts that size do not exist, he denounces the store and vows to get a colossal doughnut. He returns that night and steals the giant doughnut from the Lard Lad statue in front of the store. In the midst of a freak storm, Lard Lad and the other giant advertising statues come to life to terrorize Springfield. At Marge's insistence, Homer eventually returns the doughnut to Lard Lad, but that does not stop Lard Lad and his friends from causing destruction. Lisa goes to the ad agency that created those advertising characters, and an executive suggests the citizens stop paying attention to the monsters as they are advertising gimmicks, and attention is what keeps them motivated. He suggests a jingle will help distract people from watching the monsters. Lisa and Paul Anka later perform a catchy song and the citizens of Springfield stop looking at the monsters, who lose their powers and become lifeless (although Homer has to be dragged away from the Lard Lad statue, holding a sign reading "Now With Sprinkles"). Homer is distracted and Lard Lad drops the doughnut, which rolls past Kang and Kodos, who are trying to hitchhike to Earth's capital. Kent Brockman signs off by warning of the dangers of advertising and Homer says "We'll be right back."

Bart has a nightmare that Groundskeeper Willie is out to kill him. He is slashed with a rake, and the scratches are still on his body after he wakes up. Many other students at Springfield Elementary School also say they were terrorized by Willie in their nightmares. When the students take a test, Martin - having finished his test first - falls asleep and is strangled to death by Willie in his dream, before waking up and dying in the real world. After Bart and Lisa tell Marge about the incident, she explains Willie burned to death after the thermostat was turned too high, his suffering drawn out by the spendthrift disrepair of the school and the parents of the students looking on and doing nothing; Willie swore that he would take his revenge out on their children in their dreams where their parents could not protect them. Bart, Lisa, and Maggie try not to fall asleep for several days, but eventually, Bart decides that he is going to have to go to sleep and fight Willie in his dream. Bart falls asleep and attempts to find Willie, who appears as a lawn mower. Bart manages to trick Willie into mowing a sandbox containing quicksand, and Willie sinks. Willie recovers and turns into a giant bagpipe spider and is about to kill Bart as well as Lisa, who has entered the dream after also falling asleep. Suddenly, Maggie appears and uses her pacifier to seal the vent on Willie's spider body, resulting in Willie exploding. The Simpsons children awaken and despite being pleased to be alive, Lisa fears that Willie might still be around "out there, and could back, any time, in any form." As it turns out, a very much alive and well Willie exits a bus and tries to scare the children, but loses a shoe as he chases the bus to retrieve a gun he left aboard.

Patty and Selma visit the Simpsons, driving Bart, Lisa, and even the pets to evade them and consequently leave almost no place for Homer to hide. Desperate to avoid his wife's sisters, he looks behind a bookcase and enters a mysterious new world in which everything is in 3D. Homer explores the peculiar area, and finds that he is trapped within (the rest of the family can only hear his voice). He seeks help from them, but their attempts to rescue him are fruitless.

After a cone hits Homer, he throws it into the floor and accidentally pierces the fabric of the space-time continuum, creating a blackhole that threatens to pull Homer and the rest of the dimension into it. Bart takes command and enters the third dimension to save Homer. Bart is unable to help, however, and the universe collapses on itself. Bart is pulled back into the house and Marge is sad that her husband is gone; Reverend Lovejoy attempts to console her by saying he has gone to "a better place". Homer is sent into the real world, landing in a dumpster in a live-action Sherman Oaks, Los Angeles. He walks around, frightened as people stare at him, but then is pleased to find an erotic cake store.

In what Bill Oakley considers the "money shot", Homer steps into the 3D world

A large portion of "Homer³" was three dimensional and computer-animated. Supervising director David Silverman was aiming for something better than the computer animation. The animation was provided by Pacific Data Images (PDI) and overseen by Tim Johnson. The animators at PDI worked closely with the 2D animators on The Simpsons and worked hard not to "reinvent the character[s]". The animators storyboarded the segments and showed the PDI animators how they would have handled the scenes. While designing the 3D model of Bart, the animators did not know how they would show Bart's hair. However, they realized that there were vinyl Bart dolls in production and purchased one to use as a model. One of the most difficult parts for the PDI animators was to make Homer and Bart move properly without making them look robotic.[7]

One of the key shots in the segment was where Homer steps into the 3D world and his design transitions into 3D. Executive producer Bill Oakley considers the shot to be the "money shot" and had a difficult time communicating his idea to the animators.[7]

An edited version of Homer³ appeared alongside several other shorts in the 2000 American 3-D animated anthology film, CyberWorld shown in IMAX and IMAX 3D.

Several background jokes were inserted into "Homer³". The PDI animators inserted a Utah teapot, which was the first object to be rendered in 3D, and the numbers 734 (which on a phone pad correspond to PDI).[7] Several math equations were also inserted in the background. One of the equations that appears is 1782¹² + 1841¹²=1922¹². Although a false statement, it appears to be true when evaluated on a typical calculator with 10 digits of precision. The answer is incorrect by approximately 7 x 10²⁹. If it were true, it would disprove Fermat's Last Theorem, which had just been proven when this episode first aired. Cohen generated this "Fermat near-miss" with a computer program.[8] Other equations that appear are Euler's identity and P = NP which is a reference to the famous P vs NP problem, and similarly contradicts the general belief that in fact P ≠ NP.[5] The code 46 72 69 6E 6B 20 72 75 6C 65 73 21 is a string of hexadecimal numbers that, when interpreted as ASCII codes, decodes to "Frink rules!".[9] There is a signpost with x, y, and z, and many basic shapes littered across the screen.[5] While wandering around, Homer walks past a building that is identical to the library from the 1993 computer game Myst, complete with a musical homage to the game's soundtrack.[10] In The Simpsons and Their Mathematical Secrets, Simon Singh notes "we glimpse a cosmological equation (ρ_m0 > 3H₀² /8πG) that describes the density of Homer's universe. Provided by one of Cohen's oldest friends, the astronomer David Schiminovich, the equation implies a high density, which means that the resulting gravitational attraction will ultimately force Homer's universe to collapse. Indeed, this is exactly what happens toward the end of the segment."[11] Cohen told Entertainment Weekly that the equation predicts "the universe is going to one day collapse in on itself, and that was to represent the fact that the 3-D world collapses in on itself at the end." The fate of the universe was an unsolved problem at the time, though Cohen noted in 2018 that “astronomers now believe that our universe will not collapse back in on itself."[10] Cohen would later include references to Fermat's Last Theorem in "The Wizard of Evergreen Terrace", where solutions to it appear on a chalkboard.

In 1996, the "Homer³" segment was awarded the Ottawa International Animation Festival grand prize.[24] The episode was also submitted for the Primetime Emmy Award in the "Outstanding Animated Program (For Programming less than One Hour)" category because it had a 3D animation sequence, which the staff felt would have given it the edge.[25] The episode did not win the award, which went to A Pinky and the Brain Christmas.[26] Bill Oakley, speaking in 2005 on the DVD commentary for the episode, expressed regret about not submitting "Mother Simpson," an episode with a more emotionally driven plot and felt that it would have easily won had it been submitted.[27]