p29 dependent reflector

[Sokwe]

I'm surprised this wasn't found earlier:

Code: Select all

x = 56, y = 53, rule = B3/S23
2bo$obo$b2o5$8bo$9b2o$8b2o5$16bo$17bo$15b3o6$22bobo$23b2o$23bo5$31bo$
29bobo5b2o5b2o$30b2o5b2o5bo$42bobo$42b2o$38b2o$38bobo5bo$39bo5bobo$46b
o7$32b2o4b3o3b3o4b2o$32bo5bobo3bobo5bo$29b2obo5b3o3b3o5bob2o$29bo2bob
2o13b2obo2bo$31b2obo15bob2o$34bo15bo$34b2o3b2o3b2o3b2o$38bo2bobo2bo$
39b2o3b2o!

[Freywa]

It's not actually new. This merely replaces the 15-tick mechanism in pre-pulsar shuttle 29 with a "pump" - my term for a dependent reflector reaction. What would be interesting is a p23 pre-pulsar shuttle made up of an 11-tick mechanism (found in Bellman One) and a 12-tick mechanism (which we are to find).

[Sokwe]

It is certainly new, although it does use old components. Specifically, the standard boat-based reflector reaction was found by Noam Elkies in September 1998 and the p29 pre-pulsar shuttle was found by David Buckingham in January 1983 (although an large p29 pre-pulsar shuttle found by Buckingham in August 1980 would have also worked). However, the fact that the p29 could support the reflector reaction was not previously known (see Jason Summers' status page which hasn't been updated yet). On a side note, I was inspired by Jason Summers' use of the p29 pre pulsar shuttle to support these two reactions:

Code: Select all

x = 119, y = 53, rule = B3/S23
73b2o$74bo$10b2o3b2o19b2o3b2o29bo29b2o3b2o$9bo2bobo2bo17bo2bobo2bo28b
5o24bo2bobo2bo$5b2o3b2o3b2o3b2o9b2o3b2o3b2o3b2o28bo20b2o3b2o3b2o3b2o$
5bo15bo9bo15bo22b4o23bo15bo$2b2obo15bob2o3b2obo15bob2o19bo2bo20b2obo
15bob2o$o2bob2o13b2obo5bob2o13b2obo2bo39bo2bob2o13b2obo2bo$2obo5b3o3b
3o5bo2bo2bo5b3o3b3o5bob2o31bo7b2obo5b3o3b3o5bob2o$3bo5bobo3bobo5bobobo
bo5bobo3bobo5bo19bo4b3o6bobo9bo5bobo3bobo5bo$3b2o4b3o3b3o4b2obobob2o4b
3o3b3o4b2o18bobo3bobo7bo10b2o4b3o3b3o4b2o$26bo41bobo3b3o$69bo2$22bo7bo
38bo$21bobo5bobo36bobo3b3o$22bo7bo37bobo3bobo$9bo33bo25bo4b3o10bo21bo$
8bobo31bobo41b4o18bobo$9bo33bo41bo2b2o6b4o9bo$17bo4b2o5b2o4bo34bo2bo
11b2o2b2o4b4obo$16bobo3b3o3b3o3bobo33b4o11b3o6b2obo2b2o$17bo4b2o5b2o4b
o40bo8b2ob2o5b2o2b2o$11b2o27b2o30b5o9b3o7bob3o$10bobo27bobo29bo14bo10b
o$10bo31bo31bo$9b2o31b2o29b2o35b2o$7bo2bobo27bobo2bo64bo$7b2o2b2o27b2o
2b2o40bo10bo14bo$17bo4b2o5b2o4bo48b3obo7b3o9b5o$16bobo3b3o3b3o3bobo47b
2o2b2o5b2ob2o8bo$17bo4b2o5b2o4bo47b2o2bob2o6b3o11b4o$9bo33bo40bob4o4b
2o2b2o11bo2bo$8bobo31bobo30bo9b4o6b2o2bo$9bo33bo30bobo18b4o$22bo7bo44b
o21bo10b3o4bo$21bobo5bobo76bobo3bobo$22bo7bo77b3o3bobo$115bo2$26bo88bo
$3b2o4b3o3b3o4b2obobob2o4b3o3b3o4b2o58b3o3bobo$3bo5bobo3bobo5bobobobo
5bobo3bobo5bo19b2o4b3o3b3o4b2o10bo7bobo3bobo$2obo5b3o3b3o5bo2bo2bo5b3o
3b3o5bob2o16bo5bobo3bobo5bo9bobo6b3o4bo$o2bob2o13b2obo5bob2o13b2obo2bo
13b2obo5b3o3b3o5bob2o7bo$2b2obo15bob2o3b2obo15bob2o15bo2bob2o13b2obo2b
o$5bo15bo9bo15bo20b2obo15bob2o20bo2bo$5b2o3b2o3b2o3b2o9b2o3b2o3b2o3b2o
23bo15bo23b4o$9bo2bobo2bo17bo2bobo2bo27b2o3b2o3b2o3b2o20bo$10b2o3b2o
19b2o3b2o32bo2bobo2bo24b5o$76b2o3b2o29bo$110bo$110b2o!

[Sokwe]

One of the tubs in a skewed pre-pulsar shuttle can be replaced by a block. This creates a domino spark that allows the construction of a period-29 independent reflector:

Code: Select all

x = 53, y = 58, rule = B3/S23
10b2o$9bobo$9bo$7b2ob4o$6bobobo2bo$6bobo$4b2o2bo$3bo4b2o$3b5o$b2o4bo
12bo$o2b2o8b3o3bobo$2obo9bobo4bo$3bo9b3o$3b2o3$7b2o6b3o3b2o$7b2o6bobo
3b2o$15b3o3$10b2o$11bo$8b3o5bo$8bo6bobo$16b2o$12b2o7b3o$11bobo7bo$11bo
5b2o3bo$10b2o5b2o4$29b2o$28b2o$30bo5$36b2o$36bobo$36bo5$44bo$43b2o$43b
obo6$50b3o$50bo$51bo!