Thanks for an interactive version. Using this, you can check the examples that Anders pointed out in his comment here: https://news.ycombinator.com/item?id=17104624 -- for example, with n=20, see that row 17, column 8 does indeed have a red dot instead of black, which does not match the claimed pattern. (Edit: I wrote more in this comment: https://news.ycombinator.com/item?id=17106193)

Yes, the thing is the claimed pattern IS the one with the dot etc. the mistake we made was seeing how close the GCD triangle version fit and thinking it was the same when in fact it was not. The only claim I am making is that this is an interesting way to transform the ulam spiral into something less chaotic.