Thank you so much for your post! I have been fascinated by Pascal's triangle since learning about it in school when I was young. Beyond its connection to binomial coefficients and Sierpinski's triangle (which you mention), I think it's unbelievable how many other patterns emerge (related to triangular numbers, pyramidal numbers, Fibonacci's sequence, Catalan numbers, etc.). I have only recently seen how computer scientists are using code to explore the array, so I really appreciate the post. I actually just published a novel that uses Pascal's triangle as a structural framework. It's called The Right Amount of Brilliance and it's available here in Kindle and paperback formats: https://www.amazon.com/dp/B08F9FK9BP. I figured I'd post about the book in case it appeals to other people who find the triangle interesting.