When you hear “Sierpinski gasket”, what they’re talking about is the Sierpinski triangle. Mandelbrot coined the name and he was being a smart ass, and it stuck. But also, there was misunderstanding in how the name came about.. because he used different terminology and it became lost in translation since there was no English translation for the exact word he used. Actually, it’s complicated. But the Sierpinski triangle has many names. I don’t call it the Sierpinski gasket because I know a little about the history of the name, and also, I was talking with a guy in Munich (Andreas Hinz) and he was so disgusted by the name “gasket” that I never used it in our conversations. Well, we had so many conversations that eventually it became more natural for me to call it the Sierpinski triangle. If you ask me, Ian Stewart had it right when he called it.. Sierpinski’s Doily.