indestructible pattern

[calcyman]

Would if the "wall" being repaired were a 99.99999% slow-glider eater?

No, it's too fragile. The remaining 0.00001% would cause the entire thing to blow, and reaching 99.99999% results in an enormous configuration, tens of billions of cells on a side. The wall should be something closer to a sparse array of blocks, with some highway robbers to defend the weak points at the corners.

although, of course, the UCC used in the gemini may not be the best suited to this particular task

Agreed. Gemini is designed specifically for perpetual self-relocation, and nothing else. That's why it's so efficient -- my latest general-purpose UCC (as yet unpublished) would take about 10^16 generations to replicate. I only need to sort out the tape for self-replication, and that's mainly an automatic process. It uses some technology from Gemini, specifically the idea of colliding two perpendicular synchronised gliders.

[p46beth]

Would if the "wall" being repaired were a 99.99999% slow-glider eater?

No, it's too fragile. The remaining 0.00001% would cause the entire thing to blow, and reaching 99.99999% results in an enormous configuration, tens of billions of cells on a side. The wall should be something closer to a sparse array of blocks, with some highway robbers to defend the weak points at the corners.

Ah, I see. A wall of sparse blocks would need to be very thick in order to block every diagonal. The possible issue with that layout is that if a block in the outer-most row of blocks is destroyed, the universal constructor would need to send gliders through the entire layer, which would need to be impossible without a generous supply of reflectors on scattered throughout the wall, to get gliders fired from the inside around other blocks. But those reflectors would also be targets for gliders coming from outside the wall. Although, I suppose it would be possible for the UCC to construct all necassary reflectors after detecting that a block has been destroyed, then delete them after repairing the wall.
The other potential issue is in order to detect the absence of a block, it would need to send out signals to each block's location at regular intervals (making it a very high period oscillator). The possibility remains, then, of a glider from outside the wall coming just as a block on the outermost layer is being checked. The glider could disrupt the signal, and there would be a lot of possible debris left, making it difficult to program the UCC to be ready for every situation.

[calcyman]

which would need to be impossible without a generous supply of reflectors on scattered throughout the wall, to get gliders fired from the inside around other blocks.

The Universal Constructor could use a multi-jointed construction arm to reach around the blocks, instead of using reflectors.

The other potential issue is in order to detect the absence of a block, it would need to send out signals to each block's location at regular intervals (making it a very high period oscillator).

The idea is for the collision to initiate a chain reaction, sending gliders towards the UCC (in certain, predictable positions), which then trigger the repair mechanism. If we can guarantee that every incoming glider does eventually reach the UCC, the UCC can do the rest of the work, sensing to ascertain the lane of the incoming glider.

Of course, this configuration would itself be unwieldly large, and I am more interested in an existence proof than an explicit example.

[p46beth]

The idea is for the collision to initiate a chain reaction, sending gliders towards the UCC (in certain, predictable positions), which then trigger the repair mechanism. If we can guarantee that every incoming glider does eventually reach the UCC, the UCC can do the rest of the work, sensing to ascertain the lane of the incoming glider.

Ah, in that case the wall would need to be a bit more than

The wall should be something closer to a sparse array of blocks, with some highway robbers to defend the weak points at the corners.

Since a glider can easily destroy a block while releasing very little potential signals.

Of course, this configuration would itself be unwieldly large, and I am more interested in an existence proof than an explicit example.

Agreed, an actual slow glider-proof eater would likely be to large to use.

[p46beth]

The starwars rule 345/2/4 has a wall which is impenetrable from the inside:

Code: Select all

x = 28, y = 28, rule = 345/2/4
2.A22.A$.3A2.A2.A2.A2.A2.A2.A2.3A$2A.22A.2A$.2A22.2A$2.A22.A$2.A22.A$
.2A22.2A$2.A22.A$2.A22.A$.2A22.2A$2.A22.A$2.A22.A$.2A22.2A$2.A22.A$2.
A22.A$.2A22.2A$2.A10.2A10.A$2.A22.A$.2A22.2A$2.A22.A$2.A22.A$.2A22.2A
$2.A22.A$2.A22.A$.2A22.2A$2A.22A.2A$.3A2.A2.A2.A2.A2.A2.A2.3A$2.A22.A
!

As found in the thread for 345/2/4.

This is similar to the box mentioned earlier in this thread for b2/s2. It seems feasible that life could have a similar structure, although certainly not an orthogonal line of white cells...though allowing diagonal sides could work if there was a way to stabilize the corners.

[Batmanifestdestiny]

The starwars rule 345/2/4 has a wall which is impenetrable from the inside:

Code: Select all

x = 28, y = 28, rule = 345/2/4
2.A22.A$.3A2.A2.A2.A2.A2.A2.A2.3A$2A.22A.2A$.2A22.2A$2.A22.A$2.A22.A$
.2A22.2A$2.A22.A$2.A22.A$.2A22.2A$2.A22.A$2.A22.A$.2A22.2A$2.A22.A$2.
A22.A$.2A22.2A$2.A10.2A10.A$2.A22.A$.2A22.2A$2.A22.A$2.A22.A$.2A22.2A
$2.A22.A$2.A22.A$.2A22.2A$2A.22A.2A$.3A2.A2.A2.A2.A2.A2.A2.3A$2.A22.A
!

As found in the thread for 345/2/4.

This is similar to the box mentioned earlier in this thread for b2/s2. It seems feasible that life could have a similar structure, although certainly not an orthogonal line of white cells...though allowing diagonal sides could work if there was a way to stabilize the corners.

I just tried a diagonal line in a toroidal universe, and a glider running into it makes a rather large mess.

[Tropylium]

The T-tetromino replicator (found in a cylindrical Life universe of circumference 6) seems to make a fairly indestructible wall. Granted, it doesn't exactly stay put…

Edit: Nevermind, it doesn't defend very well against irregular superstring salvos (which in turn are easily block'd by a few, well, blocks).