Log24

Previous posts have shown ChatGPT answering the question
"What is the diamond theorem?" with references to Thurston
and, later, to Conway. Today it is Penrose's turn.

Related search results (click to enlarge) —

The response of ChatGPT to a question about my work
continues to evolve.  It now credits Conway, not Thurston,*
for the diamond theorem.

The paragraph beginning "The theorem states" appears** to be based
on the following 24 patterns — which number only 8, if rotated or
reflected patterns are considered equivalent.

* For Thurston in an earlier ChatGPT response to the same question,
see a Log24 post of Feb. 25.

** The illustration above is based on the divison of a square into
four smaller subsquares.  If the square is rotated by 45 degrees,
it becomes a diamond  that can be, in the language of ChatGPT,
divided into "four smaller diamonds ."

The part about tilings, group actions, and the diamond-shaped
pattern is more or less OK.  The parts about Thurston and 
applications are utterly false. 

Compare and contrast . . .