Not sure if this was to me (I hate that HN anonymizes so much, it doesn't understand the importance of personal context in communication), but I just looked up purity cycle and didn't find anything but found purity spiral, is that what you meant?

> A purity spiral is a theory which argues for the existence of a form of groupthink in which it becomes more beneficial to hold certain views than to not hold them, and more extreme views are rewarded while expressing doubt, nuance, or moderation is punished (a process sometimes called "moral outbidding").[1] It is argued that this feedback loop leads to members competing to demonstrate the zealotry or purity of their views.[2][3]

https://en.wikipedia.org/wiki/Purity_spiral

Sorry, that was directed at tsimionescu and their Hitler analogy.