I wanted to share a concrete illustrative example.
Scorbie wrote: ↑July 6th, 2023, 9:25 am
...
The bound glider pairs may change if we enclose a different region to serve as a dependent reflector, but it's okay to me as long as the explanation is consistent. If you think of the reflectors as a black box then the two different enclosings are different reflectors. ...
glider_rider wrote: ↑July 10th, 2023, 6:07 pm
... (Of course if you don't view it as a black box it obviously contains bit-carrying signals internally, but it's not inconceivable there could be a reflector with these properties that isn't just a self-sabotaging independent reflector, and that wouldn't have bit-carrying signals anywhere. This is why I like viewing things as black boxes.)
Pavgran wrote: ↑August 18th, 2023, 4:55 pm
...
With dependent reflectors, things are slightly more complicated. I would view a single reflector as a signal-processing device (with the gliders being the signal in the same local sense as with the Snark example), albeit with very low information entropy. It can essentially either continue operating, or fail to recieve an input signal and destruct. Essentially, the only information it can process is 'when to destruct', and in closed oscillator loop, the answer might be 'never', but that will be, in essence, 'locally never'. An information in the form of almost any glider from outside will destroy the loop, in one way or another.
...
Here's a large engineered
period-79 dependent reflector.
As long as this device is used for what it is advertised to do, the only things one needs to know are "physical":
- Where and when input gliders must appear? (timing mod 79)
- Where and when output gliders will appear? (timing mod 79)
- Does the device fit into the available space?
Code: Select all
x = 747, y = 828, rule = B3/S23
214b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o2b2o$214b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o3$214b2o78b2o$214b2o78b2o$229b2o$
229b2o$214b2o78b2o$214b2o78b2o3$214b2o20bo57b2o$214b2o10b2o8b3o8b2o45b
2o$226b2o4b2o5bo7bo$232bobo3b2o5bobo$214b2o18bo10b2o47b2o$214b2o18b2o
58b2o3$214b2o7b2o69b2o$214b2o7bo70b2o$220b2obo$220bo2bob2o$214b2o6b2ob
o68b2o$214b2o9bo13b3o52b2o$225b2o11bo3bo$237bo5bo7b2o$214b2o21bo5bo6b
2o42b2o$214b2o21bo5bo8bo41b2o$238bo3bo4b2o24b2o$239b3o5bobo24bo$214b2o
33bo22bo21b2o$214b2o21b2o10b2o21b5o17b2o$238bo37bo$235b3o32b4o$214b2o
19bo34bo2bo8b2o10b2o$214b2o66b2o10b2o2$289b2o$214b2o73b2o3b2o$214b2o
78b2o$281b2o$282bo$217bobo59b3o12b2o$217b2o41b2o17bo14b2o$218bo42bo21b
2o$261bobo3b3o13bo$262b2o2bo3bo10bobo10b2o$265bo5bo9b2o11b2o$265bo5bo$
265bo5bo$266bo3bo23b2o$267b3o24b2o2$280b2o$214b2o64bo13b2o$214b2o49b2o
14b3o10b2o$266bo16bo$263b3o$214b2o47bo4bo25b2o$214b2o52b2o24b2o$267bob
o$198bo$197bo16b2o78b2o$197b3o14b2o78b2o3$214b2o78b2o$214b2o78b2o3$
214b2o78b2o$214b2o78b2o3$214b2o78b2o$214b2o78b2o3$214b2o32b2o44b2o$
214b2o31bobo44b2o$249bo$179bo$177b2o35b2o78b2o$178b2o34b2o78b2o3$214b
2o2b2o2b2o2b2o2b2o2b2o14b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o$214b2o2b2o2b2o2b2o2b2o2b2o14b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o11$228b2o$229b2o$228bo$158bo$158bobo$158b2o15$208b3o$210bo$
209bo$138bobo$138b2o$139bo14$189bo$189b2o$188bobo$119bo$118bo$118b3o
12$76bo$76b3o$79bo$78b2o89b2o$168bobo$170bo$100bo$98b2o$99b2o15$149b2o
$150b2o$149bo$79bo47b2o$79bobo45bo$79b2o48bo$125b5o$125bo$128b4o$118b
2o8bo2bo$118b2o5$119b2o$119bo$120b3o$122bo17b2o$117b2o21bo$118bo13b3o
3bobo$118bobo10bo3bo2b2o$119b2o9bo5bo$59bobo68bo5bo$59b2o69bo5bo$60bo
4bo65bo3bo$63b3o66b3o$45bo16bo$45b3o14b2o56b2o$48bo72bo$47b2o69b3o14b
2o$118bo16bo$59b3o74b3o$58bo3bo70bo4bo$57bo5bo68b2o$57bo5bo68bobo$46b
2o9bo5bo$45bobo10bo3bo2b2o$45bo13b3o3bobo$44b2o21bo$49bo17b2o$47b3o$
46bo$40b2o4b2o$40b2o2$37b2o$38bo$35b3o7b2o$35bo9b2o8bo2bo$55b4o$52bo$
52b5o$56bo95b2o$54bo97bobo$54b2o96bo$76bo$77b2o$76b2o15$172b2o$171b2o$
173bo$97bo$95bobo$96b2o15$191b3o$191bo$192bo$115bobo$116b2o$111bo4bo$
111b3o$114bo16bo$113b2o14b3o$128bo$128b2o2$115b3o$114bo3bo$113bo5bo$
113bo5bo$113bo5bo9b2o$110b2o2bo3bo10bobo$109bobo3b3o13bo$109bo21b2o79b
o$108b2o17bo83b2o$127b3o81bobo$130bo$129b2o4b2o$135b2o4$130b2o$118bo2b
o8b2o$118b4o$124bo$120b5o$120bo$122bo$121b2o$100bo$98b2o$99b2o$231b2o$
231bobo$231bo15$79bo$79bobo$79b2o$251b2o$250b2o$252bo15$59bobo$59b2o$
60bo$270b3o$270bo$271bo14$40bo$39bo$39b3o$291bo$290b2o$290bobo15$21bo$
19b2o$20b2o$310b2o$310bobo$310bo15$o$obo$2o$330b2o$329b2o$331bo18$349b
3o$349bo$350bo17$370bo$369b2o$369bobo18$389b2o$389bobo$389bo18$409b2o$
408b2o$410bo18$428b3o$428bo$429bo17$449bo$448b2o$448bobo38$488b2o$487b
2o$489bo18$507b3o$507bo$508bo17$528bo$527b2o$527bobo18$547b2o$547bobo$
547bo18$567b2o$566b2o$568bo18$586b3o$586bo$587bo17$607bo$606b2o$606bob
o18$626b2o$626bobo$626bo18$646b2o$645b2o$647bo18$665b3o$665bo$666bo17$
686bo$685b2o$685bobo18$705b2o$705bobo$705bo18$725b2o$724b2o$726bo18$
744b3o$744bo$745bo!
As long as the incoming p79 glider stream is regular without holes / mistimed gliders, here's what happens:
- The incoming glider stream is redirected to a new glider stream, which enters the region surrounded by the blocks.
- The stream is further redirected twice. After that, gliders leave the part surrounded by blocks.
- The stream is further redirected twice, before leaving the engineered p79 dependent reflector.
However, when there is a hole in the incoming glider stream, the failure of the engineered p79 dependent reflector proceeds in a different way:
- A stray glider is created during destruction of the first elementary reflector in the chain.
- That stray glider creates a hole in the stream returning from the region surrounded by blocks.
- That hole reaches the penultimate elementary reflector in the chain, which fails.
- The stream going to the last elementary reflector in the chain ends, and the last elementary reflector fails.
Now, the seemingly paradoxical part is that
- As long as you use the device as a dependent reflector, you can increase or decrease the "total path length" (assuming that's meaningful), by moving the "trombone slide" part surrounded by blocks by 79 diagonals and adding/removing intermediate gliders as needed.
- However, when the device fails, it always fails the same way with the same timing, regardless of any "trombone slide adjustment".
In other words, it is confusing (if not outright contradictory) to view individual gliders as "signals" in this example.
To me, this example indicates that period-N dependent reflectors shouldn't be described as "signal devices". They are merely devices capable of redirecting uninterrupted period-N glider streams. The specific way of failing is not (and should not be) part of the definition of
dependent reflector.