I find every interesting the following problem: what is the minimum universal constructor with a linear string, that is, a sequence of gliders that encode information efficiently (not using exponential space, but using a combinatorial combination of N gliders, for O(N) bits)?

Bonus question: can this string be "folded" so that it occupies a radius of O(sqrt(N))?

(now we have a close analogue of DNA! It's fascinating that indicates the universality of DNA and life -- we seem to be somewhat limited universal constructors)

Other questions: are there "Constructor classes" -- non-universal constructors specialized in building a certain "chemistry", a useful subset of all structures? What is the minimum (restricted) efficient contructor capable of building (a) A copy of itself; (b) A Turing machines; (c) Turing machine and construction tapes.

Also I've been thinking about reliability. Is there a constructor that can tolerate a flip ("error") anywhere inside? That can tolerate any single glider collision? Or can tolerate "most" bit flips? An interesting difference between CGoL and our universe is that we live in a thermal and quantum bath. So in a sense (that's up to QM metaphysics) there is inherent randomness in particles, and of course all particles chaotically "wiggle" at positive temperatures (it might be argued CGoL also has wiggle, but in CGoL you can have non-chaotic, periodic large systems -- it's essentially easy to have 0 temperature systems).

I've been playing with simulation of CGoL that have a proportion of random flips each generation. I've been investigating whether interesting structures come out of the "soup" -- this is more interesting, I believe, that just starting from a soup and seeing if something survives (in a deterministic universe), because you can have "multi-step evolution": maybe some small structure comes up, and then random perturbations slowly make more interesting structures emerge -- in a faint analogue to the origin of life, or just faint analogues of chemistry/proto-evolution -- the population of patterns evolves with time. It would be really cool to have a crowdsourced set of long-time simulations of such a field.

Another important open problem related is how to define a 'Life detector' (in Life). A Life detector is an algorithms that given a pattern and a few generations, tells you how complex, interesting, and 'alive' that pattern is. Very fun and significant problem I believe. Together, this means we can run massive crowdsourced searches to understand environments that tend to evolve interesting patterns (although of course anything close to a bona fide lifeform is probably still far out of reach of our computing power, and might benefit from other kinds of analysis)..