

The Ystart challenge introduced the idea of using stablestate cell arrangements as an alternative goal for Maze of Life. As goals go, the stablestates are certainly a rather more appropriate (lifeorientated) choice. The inevitable question then arises... just how many stablestates can the bluecell manufacture from an arbitrary start state, such asYstart? 

It turns out that the bluecell is really quite good at generating stablesstates. Find out more below or discover a stablestate goal for yourself with this minichallenge:
From: SS<U<D>US/RS>/S
Find: a 14 cell stablestate (edgedependent) goal
in 4 moves
Note: this challenge has been preloaded for you, just
click on the grid to move the blue cell.
Controls Movement Keys 
Carl Hoff illustrated early on that a good number of stablesstates are indeed reachable from Ystart. An early collection can be seen here. It includes stablestate goals with 4 through 12 cells (some freestanding, some edgedependent) along with several multicluster arrangements. However, due to the limitations of the early V2 applet it was not easy to save and load move sequences and some were lost along the way, so for almost a year the collection included a number of lost goals. Eventually in March 2001 the gaps were filled by a Delphi search program written by Jacco Compier. Jacco's search program rapidly proved that our handcrafted collection of goals was only a tiny subset of possible statestates reachable from Ystart. The move sequences of all stablesstates reached in 20 moves or less is listed here.
One of the findings that came out of the early manual searches was that it was really quite easy to drop into a stablestate almost by accident, and often this was bad news for the bluecell. Effectively the stablestates fall into two catagories, the escapable and the inescapable. Inescapable stablestates are another sort of deadend. In effect the bluecell doesn't have to die in Maze of Life, it may simply be forced to retire, infact Ed Pegg referred to all such states as retirementhomes.
It is worth noting that Jacco's list of stablesstates (from Ystart in 20 moves) includes very few highorder stablestates, only 5 results with 20 or more cells. Carl Hoff once asked..."How many live cells can you put in a stable state on the board at once? I can put 30. Now require it be nonedge based. I can put 24. My gut tells me that 24 is the max in this case. Note if you could put 25 then the density of live cells would be above 50% and I think you can prove you can't do that on an infinite board. I'm not sure if 30 is the max in the other case or not". Is Carl right? Find out more on the Dense goals page.
Some remaining questions relating to stablestates:
Are all stablestate goals reachable from Ystart?
If yes... is it provable, and is this true for any size board?
If not... would another start do better?
Another way of looking at these question is to ask... given the global set of Life stablestates is it possible for the bluecell to manufacture any stablestate from at least one other stablestate? Ie. is the behaviour of the bluecell sufficiently powerful to create a connected tree of all stablestates?