Rule 110 is known to be Turing-complete. https://en.wikipedia.org/wiki/Rule_110
I have a feeling that Rule 90 is the most efficient algorithm: the Sierpiński Triangle, self-sacrifice, infinite recursion to a perfect pattern. I'm not mathematically talented enough to prove that though.
https://mathworld.wolfram.com/Rule90.html
Please come to chat about A New Kind of Science on Facebook! A couple of weeks ago I noticed that the page didn't exist, so created it. Hopefully Wolfram doesn't mind. We stand on the shoulders of giants.
https://www.facebook.com/A-New-Kind-of-Science-1004052657757...