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One of the other answers mentions "Uncontrollable bad thoughts about the object of anger, particularly ones that are not rational". I'd expand on this to put in the suggestion of simple, unreasonin...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/47722 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
One of the other answers mentions "Uncontrollable bad thoughts about the object of anger, particularly ones that are not rational". I'd expand on this to put in the suggestion of simple, unreasoning repetition. (E.g. "Damn him. He's wrong. He's wrong. He'd wrong. He's wrong.") It would signify the weakness of a character's reasoning that they can't expand a thought with logical justification, and just have to loop back on the assertion as if to establish their correctness by simple insistence. You could also vary the wording without real expansion ("What does he know? He doesn't know what he's talking about. He's an ignoramous. He has no clue." etc.); the shallowness of the variation would make it clear to the reader that that the character is unwilling to plumb the source of their contempt or hatred to any real depth. In my examples I deliberately left out exclamation points, in order to hint at a certain fearful self-doubt, but it could possibly build up to exclamation point punctuation. This repetition could be sprinkled through multiple paragraphs, maybe even as awkward self-interruptions of other thoughts.