simsim314 wrote:Something more similar to bit coin: minimal cell configuration for quadratic growth of any totalistic rule (there is around 256K totalistic rules, each one of them has minimal configuration for quadratic growth, some of the totally not trivial like in GOL).

Unfortunately it's fairly difficult to define really interesting CA problems where a reasonably predictable amount of computation time is required to find an answer. Take the case of a true p14 glider gun in Conway's Life, for example, or a c/8 spaceship, or a p19 oscillator. It's true that these objects, once found, can be verified very quickly, so that sounds good so far... but there's no known way to define a search for any of these objects that is guaranteed to terminate before the sun burns out.

We can't really award Bitcoin-like points to incremental negative results, like "there is no p19 oscillator inside an 8x8 bounding box", because _that_ result can't be verified without doing exactly the same amount of work again, independently... and it seems to me that that would open the door for sending in false negative results as a claim for work accomplished.

So... you could offer a CAcoin for various goals in a series, such as a spaceship of each new slower speed c/8, c/9, c/10, and so on. But problems like that get exponentially harder with every speed, not just incrementally harder. Just a few CAcoins down the chain it's just not worth anyone's time to hunt for the next one in the series, because the odds are that the search will take decades if not millennia.

I think the recent experience with

quadratic-growth patterns in Serizawa seems to indicate that even finding the smallest quadratic-growth pattern in a wide range of rules might run up against all kinds of open-ended problems -- proving that there's no possibility of quadratic growth in some rules, and proving (with a reasonable-length calculation) that quadratic growth will inevitably continue, in smallest-case candidates in other rules.