A subtrope of Cheated Angle. Oftentimes in cartoons if a character is wearing clothes with a complex pattern, e.g. plaid, the pattern on the clothing will retain the same orientation regardless of the positioning of the character. It's as if the clothing the character is wearing isn't so much patterned as a cloth-based wormhole to a similarly patterned universe, or that the character's clothing has had a static pattern overlaid on it through Chroma Key techniques. This phenomenon is known as Unmoving Plaid (or for those who like jargon, perspective incorrect texturing).
This trope, like the Wheel o' Feet, Four-Fingered Hands and others, spawns from the Lazy Artist or a lack of budget. Patterned clothes are hard to animate correctly and take longer to do, so animators just don't bother animating the pattern. However, with the advent of more advanced digital animation tools to do such gruntwork, this trope may start falling by the wayside. Additionally, when intentionally used for lavishly animated content, it may transcend the notion of sheer laziness and become a distinct (if sometimes bizarre) visual style.
The effect is also sometimes seen in comic strips, with the pattern remaining the same orientation from panel to panel (and usually straight vertical and horizontal, regardless of the orientation of the fabric of which it supposedly is a part). Often this is because comics (especially manga) use tone paper to fill in the plaid article, which makes it rather difficult to show the proper orientation of the pattern. Most artists just don't bother.
Nothing to do with Plaid Cymru. See also Limited Animation.
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Anime and Manga
Gankutsuou is an extreme example that can only be described as an "acquired taste art style" - just about any detailed pattern or texture is screened in, including the characters' hair, creating an effect that's almost like an animated collage.
Mononoke uses this effect in a way similar to Gankutsuou, although not quite to such extremes.
Hell Girl's "kimono of exacting damnation" does the same thing as the two above anime titles. The pattern itself is animated, but still has incorrect perspective.
Bakemonogatari, by the same studio, also uses this technique for patterned clothing. It's stylistic choice (one of Akiyuki Shinbo's trademarks) rather than pure laziness, given how much they've embraced digital animation.
In an episode of Ouran High School Host Club, Tamaki wears an extremely elaborate designed tea kimono. The design - while not plaid - is static, which is made painfully (and probably deliberately) evident when he does a slow motion backward face fault.
Hiro's pink plaid pants from the Soul Eater anime, as well as manga character Tezca Tlipoca's plaid bear mask. Otherwise averted by Maka's plaid skirt and striped pajamas in the anime.
In Soul Eater Not!, Shaula Gorgon's hair is colored in with an elaborate pattern in this manner.
Paradise Kiss's anime uses this to animate the more elaborate dresses made by the characters, though the regular clothing is animated normally
Kiyohiko Azuma, the artist of Yotsuba&!, sometimes averts this by, for example, painstakingly drawing realistic plaid on Fuuka's pajamas, but other times embodies it by simply screen-toning the plaid on Yotsuba's pajamas or the pattern on Jumbo's Hawaiian shirts.
In Ranma ½, Ryouga Hibiki's headband demonstrates this.
In Seitokai Yakuindomo, the female characters wear plaid skirts and the pattern is either angled in an odd way during a still-shot, or doesn't move when the character does. With the ED "Aoi Haru", it is more obvious.
The Death Note manga took some very noticeable shortcuts when depicting plaid or striped clothes.
In Area no Kishi, the skirts for the girls' school uniform suffers from this. It's especially noticeable when the focus is on the potential love interest, Six.
MM The ending has this in their skirts and ties same color plaid, but the ties are angled. Watching them jump and turn around is very odd since the plaid only moves vertically.
Averted in Otoyomegatari. Not only does the author draw the patterns on their everything (dresses, fabrics, etc.), she draws it slightly differently between different panels depending on the angle you're supposed to be looking at, even on the same page.
Persona 4: The Animation has this for school uniforms and Naoto's plaid pants. The school uniforms are probably this way because there are upwards of 15 students in a shot at times, and drawing all that houndstooth would be fun.
Ojamajo Doremi has this during the second ending for the Dokkan! season, using floral patterns for the girls and other patterns for the boys that appear.
Shows up in the manga version of Axis Powers Hetalia and some of the artwork, although it's averted in the anime.
For truly unsettling effect, the Anti-Spiral's entire body in Tengen Toppa Gurren Lagann uses grayscale patterns and designs that constantly cut from one to the next. It really lets you know that this guy has abilities beyond your comprehension.
In Bokurano, Chizuru "Chizu" Honda wears a dress with a plaid pattern in the manga. It's a solid red color in the anime.
It was initially a limitation of the computer hardware (and, presumably, the patience of the animator) in Secret Of Monkey Island. Later games appeared on computers that COULD handle moving plaid, but kept the look as an homage to the original, since it was so iconic of Stan that it simply didn't look like Stan if it moved around.
Gaia in E.V.O.: Search for Eden also deliberately uses this effect, but with her hair; it's colored with a cloud pattern that scrolls on its own, giving her hair the appearance of shimmering clouds.
Touhou does a similar trick to EVO with Utsuho Reiuji's cape; the inside of it has a deep space pattern that, like Gaia's hair and Stan's suit, scrolls independently of Utsuho's own movement, giving the illusion that her cape is a portal to deep space.
League of Legends: Kassadin's Void Blade doesn't have a standard texture to it, instead it appears to be a hole into some oddly-patterned realm.
The complex colors of pants in The Fancy Pants Adventure: World 3 stay still when Fancy Pants Man moves. Since this game is a 2-D platformer, Brad Borne would not appreciate animating each of the 30 frames per second of this game for dozens of colors of pants.
Though not seen in-game, during the FMV intro for Metal Saga, the camouflage pattern on the main character does this, though one must be looking to see it. Here is said intro. You can most easily see the effect at 1:27 and 1:33.
Zebra Girl: After his ascension as a wizard, Jack the Plaid's 'totem' acquires a plaid pattern, as indicated on his jacket and most of his spells, creating the impression of a literal gateway to a plaid dimension.
Avoiding this was the reason that neither Zatanna nor Black Canary wore fishnets with their costumes in Justice League Unlimited.
Delta State really liked using this for Phillip. It was also done intentionally for the Rifters while in the Delta State: Their cloaks contained unmoving galaxies.
Along the same lines, the Thing in the animated Fantastic Four: World's Greatest Heroes had his bulky body drawn traditionally while the animators used computers to generate a hexagonal grid pattern over his skin to indicate the his rocky hide.
In My Little Pony: Friendship Is Magic, the Ursa Major's pelt is an Unmoving Star Field. While Princess Celestia's mane also flows, the colors on her mane don't flow the same way. And on one occasion, the colours on Rainbow Dash's tail continue to curve smoothly even where the end of the tail is ruffled into a zigzag.
Occasionally scene in Silly Symphonies shorts which involve objects with a checked pattern, although "Funny Little Bunnies" also used plaid at one point.
Battletech featured a wide variety of Battlemechs, many of which featured various camoflage patterns which would shift continuously whenever the 'mechs moved around.
Sheep in the Big City used this from time to time in its second season (most notably with General Specific's cousin General Lee Outrageous and his ridiculously flashy uniform).
Crops up occasionally among users of programs such as Photoshop, who decide to use background patterns with colours only in certain areas of their images (clothing being a common example).
Has been used deliberately, and to nice effect, in at least one Demoscene production.
Easy to pull off when making animations in POVRay to the degree that newer users will often do it by accident. Simply have the scene code for an object apply the transformations to it before applying the texture.
Certain skin conditions can hop from an arm to the chest without following the curvature of the body, giving the appearance that the rash was spray painted on. Most common (though still rare) with the bullseye rash characteristic of Lyme's Disease.
If one wears distinctly pure green or blue clothes, the unmoving plaid can be achieved via chroma keying.