 If you liked
Higurashi no Naku Koro ni
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 ...then you might like
Yojouhan Shinwa Taikei
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Both of these shows feature time loops where the same plot is acted out, taking a different turn each time, and frequently overlaps, with things being told slightly differently. Higurashi is a lot more bright colors and slapstick humor, whereas Tatami Galaxy is somewhat darker humor, with less emphasis on little kids killing each other and laughing.
The use of recurrence of time to make characters come to realizations about the world around them and themselves.
Both anime take on the "Parallel world" aspect, and yet tie them together in an extraordinary way.
That said, they're also completely different genre. But I enjoy them both.
Although the plots and settings of these two shows are completely different they both feature a Groundhog Day esque narrative structure.
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Recommended by LoveLikeBlood
Stories that basically repeat one more time, with each repetition giving you a slightly different perspective to reach the truth to the end. Although in Higurashi the stories repeat every few chapters, in Yojouhan the stories repeat each chapter. Both anime are good psychological thrillers, but Higurashi being more of a bloodbath and Yojouhan more of a Slice of Life.