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There exists an 'orphan' pattern that cannot arise in any configuration after the first generation. When we look at large patterns, the proportion of them that
by OscarCunningham 4y ago
There exists an 'orphan' pattern that cannot arise in any configuration after the first generation. When we look at large patterns, the proportion of them that contain an orphan tends to 1.
On the other hand the smallest known orphan is 12 by 8, and we also know that all still lifes (unchanging patterns) with up to 21 cells can be built.
- enkid 4y ago21 cells would be a 3 by 7?
- OscarCunningham 4y agoGardens of Eden can be arbitrary patterns, whereas only the 21-cell still lifes are known to be constructible.
- enkid 4y agoOk, but what do you mean by a "still life" of 21 cells? Is that a rectangle in a larger field or is it an arbitrary set of cells?
- OscarCunningham 4y agoA pattern with 21 live cells in any bounding box.
- enkid 4y agoThanks for answering!
- dvgrn 4y ago(Not just any such pattern, though -- a still life also means that it doesn't change when you evolve it according to Life rules.)
- OscarCunningham 4y agoAlso we can only do the strict still lives (i.e. those which are connected https://conwaylife.com/wiki/Still_life#Strict_still_lifes https://conwaylife.com/wiki/Still_life#Strict_still_lifes). We can't necessarily put down a 10-cell still life and an 11-cell still life near to each other.
- dvgrn 4y agoHeh, not necessarily, that's true, in the sense that all the possible arrangements haven't been tested and shown to be constructible. On the other hand, pseudo-still-life and quasi-still-life arrangements are much easier to construct on average than strict still lifes with the same number of cells. I think the consensus is that someone could figure out how to construct any given stable 21-bit configuration. The non-strict cases are just a bit too numerous and not interesting enough, so nobody has gone through and formally checked them off the list.
- dvgrn 4y agoIf you want to see what these 21-bit still lifes look like, their glider construction recipes are all stored online, on Catagolue (no, that's not a misspelling): https://catagolue.appspot.com/census/b3s23/synthesis-costs/xs21 https://catagolue.appspot.com/census/b3s23/synthesis-costs/x...