I was imprecise: I meant using the overall structure (moving tape, two construction sites, two construction and one destruction arm at each) and range of components used in Gemini.
Gemini, in its current form, can asymptotically approach, but not reach, (1,1)c/580, since the gliders can (apparently) be compressed to p576. The extra four generations are due to the fact that the block drifts away, in a phenomenon similar to the Doppler effect. Equivalently, Dieter's p120-driven slide gun hits the block every 124 generations.
Stable technology can be compressed to p466 (using one of my multi-stage reflectors), but it involves welded eaters with miscellaneous heads. That would facilitate everything up to, but not including, (1,1)c/470.
My other multi-stage reflector, which is composed of simple-to-construct still lifes, admits a compression of p487. However, it doesn't have a natural Herschel output, so it may be difficult to use it as anything other than a reflector.
It is definitely possible to use the Silver reflector and related glider-to-Herschel converter, which accepts gliders at p497. The resulting Gemini speed limit would be (1,1)c/501.
Yes, I've been hoping this phrase would catch on!
I wondered whether anyone would recognise that quotation -- it was what Bill Gosper would call an insurmountable opportunity.
This is the single most impressive pattern in Life that I have ever seen.
Agreed. It is made even more impressive by its elegance and simplicity; it doesn't use a Rube-Goldbergian design typical of my constructions (e.g. the Phi calculator).
The next step: a spaceship with three or more constructors for the program to pass through
That seems like a fairly pointless modification, unless you have four constructors in a rectangle.
and after that, a program capable of modifying its own speed/shape/direction.
Universal computation is actually easy to implement, now that Paul Chapman and myself have created usable components. I just need to make a clean Spartan version of my memory tape. (I only have a clean non-Spartan and dirty Spartan version so far.)
*starts plotting how to create a spaceship that can inject its own program into other Gemini spaceships*
A bacteriophage! I would like to see that, along with other biologically-inspired patterns.
You might want to draw inspiration from Langton's Loops. In fact, the four-constructor pattern could behave exactly
like Langton's Loops. Samaya made a version known as 'Evoloop', which allows genetic material to be injected into other loops, similar in principle to what you have described.
I've updated my Open Problems page after the discovery of an oblique spaceship (Gemini), arbitrary-speed spaceship (also Gemini), c/5 greyship (by Hartmut Holzwart), and my O(sqrt(log(t))) pattern.