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"a character is basically a 2x2 grid"... Do you have any reference for this type of classification/composition?

N.B.: I am not implying that it is incorrect - I am a dabbler in Japanese Brush Calligraphy (without any fluency in the language, only as an art) and I would like to read more about this so if you have links or books (preferably in English) I would be very happy to learn more.

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The practice paper given to children learning kanji is commonly partitioned into a 2x2 grid, to help with proportions -- kind of like how children learning to write English are given paper with guidelines for baseline, ascenders, descenders, and mean line. You can see an example of the 2x2 grid in the Nintendo kanji game on the article's "Info" page, or by searching for "kanji practice paper".

The lines are meant more to help relative placement than to exactly divide characters, but many characters do divide into left-and-right or top-and-bottom portions -- see Jack Halpern's SKIP system for example:

https://en.wikipedia.org/wiki/Kodansha_Kanji_Learner%27s_Dic...

Characters are written, not drawn. First learn to write.

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