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The following diagonal line pattern in Life 1.06 format contains cells whose y value exceeds 2147483648 (2^31), and when loaded in Golly it is split into two distant parts instead of one continuous line.
#Life 1.06
0 2147483646
1 2147483647
2 2147483648
3 2147483649
4 2147483650
5 2147483651
Is ...

Selected 3-glider collisions including a synthesis for the xq36 and many for the xq21.
x = 304, y = 25, rule = B34jy/S2-i34q
296bo$297b2o$296b2o4$272bo$9bo15bo33bo4bo199bo7bobo$9bobo14bo31bo5bobo
198b2o5b2o$9b2o13b3o31b3o3b2o24b2o42bo129b2o$29bobo3bo54bobo40bo$29b2o
4bobo48bo3bo19bo22b3o ...

Extremely sparky p36 Megapulsar:
x = 14, y = 14, rule = B34jy/S2-i34q
2b2o6b2o$4bo4bo$o2bo6bo2bo$obo8bobo$bo10bo5$bo10bo$obo8bobo$o2bo6bo2bo
$4bo4bo$2b2o6b2o!


Unfortunately the sparks are a lot more sensitive than one would imagine, so I couldn't find a 2-engine gun. :( Hopefully it's still ...

xs23_c4go0e93zwmdzx113 and xs23_c4go0e96zwmdzx113 can be synthesized from known components.
x = 64, y = 56, rule = B3/S23
6b2o48b2o$5bobo47bobo$2o3bo44b2o3bo$o2bob2o43bo2bob2o$2b2o48b2o$3bo49b
o$2bo49bo$2b2o48b2o2$52b2o8bo$4b2o46b2o7bo$3b2o56b3o$5bo36b2o$43b2o2b
3o$42bo4bo11b2o$38b2o8bo10bobo ...

Has the sierpinski wolfram rule been proven TC?
Just curious, cuz otherwise this could be a counterexample:
x = 1, y = 1, rule = B15k/S012-i3-a45-kr678
o!



If you mean an XOR rule that produces Sierpinski-like patterns, each generation is just a linear combination of the previous one, so ...

This functionally stable p8 rectifier variant might be easier to construct than the stable one:
x = 34, y = 44, rule = B3/S23
21bo$bo17b3o$2bo15bo$3o15b2o6$28bo$b2o23b3o$o2bo21bo$b2o22b2o8$15b2o$
15b2o9$23b2o$22bo2bo$22bobo3b2o$23bo3bo2bo2$22bo8bo$19bo3bo4bo2bo$18bo
4bo5b2ob2o$18bo3bo8b3o ...

Multiple-of-8 displacements are ubiquitous, but odd-multiple-of-4 displacements are rarer. Here is a spaceship with speed 4c/56 using the old double-cross design:

#C [[ TRACKLOOP 56 0 -4/56 ]]
x = 221, y = 549, rule = B3-ckr5y/S2-i3-aek4ci5c
13b3o$3bo3bo5bo$2b3ob3o5bo$4bobo$4bobo$o9bo188b3o ...

A natural reaction between a snake, a block, and a honey farm can be stabilized in at least 8 ways.
x = 346, y = 45, rule = B3/S23
110bobo$110b2o$111bo4$61bo38bo$61bobo34bobo$61b2o36b2o2$101bo161bobo
37bobo$100bo162b2o38b2o$b2o9bobo26b2o9bobo26b2o17b3o18b2o9bobo26b2o9bo ...

Still there are other possibilities.
x = 39, y = 42, rule = B3-cjky4it5ekq6in7c8/S23-ack4ity5ce6-ak78History
22.2A$3D19.A15.D$D.D20.A12.D.D$D21.2A12.3D3$13.D.D$13.2D.D$15.D$18.3D
$18.D.D$18.D3$31.2A$31.A$31.3A24$16.3A$17.A!


A stable reflector with repeat time 422 has been hiding in plain ...

With higher repeat time or period of drive gun, there are two other H-to-B conduits that allows for the block factory reaction, namely HL141B (from Lx200 ) for >= 90 and HRx135B (from HRx93E+EF42B ) for >= 124.
x = 81, y = 97, rule = B3/S23
62bo$62b3o$65bo$64b2o4bo$68bo$69bo$66bob2o2$59bob2o ...

An oscillator with period 16, xp16_wgbbobaq4ozw11y02525t2sgzgk2gb3y0c97066z11 , where xp10_mm0u13z034b8l90cx8ozy11255d1dd is rephased by a pair of domino sparks from a figure eight .
x = 32, y = 16, rule = B3/S23
30b2o$28bob2o$4b2o14b2o5bo$2obobo10b2obobo8bo$2obo12b2obo6b2obo$3b2o
14b2o5b2o ...

A reduction for guntrue_265 from 3942 to 2808 cells made by putting together a p5 G-to-H , a NW14T181 and a p5 bouncer in a fixed loop.
x = 54, y = 52, rule = B3/S23
25b2o$24bo2bo$19b2o2bob2obo$19bo3bo2bobo$20b3o2bo2b2o$22bobobo2bo$24b
2ob2o$24b2o$13b2o9bo2b2o2b2o$13b2o9bobo2bo2bo$15bobo4bo5b2obo ...

This is one of the rules where I learnt about replicator engineering; unexpectedly there are still some low-hanging fruits of mirror-symmetric interactions between replicator pair and objects.

Two oscillators with period 128, one of which is adapted to a base-4 counter.
x = 137, y = 61, rule = B3 ...

This rule has a reaction where a tub splits a c/2 spaceship into eight, another reaction where a tub reflects a 4c/28 spaceship, and an oscillator made of two spaceships with period 102.
x = 67, y = 11, rule = B3aein4cit5ey6ce78/S23-kn4cirt67e8
2bo29bo$bobo27bobo29bo$2bo29bo29b2o$63bobo$65b2o$65bo ...

[...] replicator-like signal [...]


I don't get the idea behind the quoted phrase. Can you explain what exactly you mean by it?
(I saw the same phrase in a few of other your posts. I didn't see the same phrase anywhere else.)

I looked at the patterns. The patterns apparently contain some ...

Although omniperiodicity has been proven, it is worth noting that the replicator-like signal can be made into a loop with repeat time 9.
x = 123, y = 79, rule = B2ac3q5-i67/S03i45-q6-ac78History
3.A4.A45.A47.A$53.3A45.3A$A2.A5.A42.3A.B43.3A.B$2.3A3.3A40.3A.B.A41.
3A.B.A$3.3A3.3A40.A.B.A.A41.A.B.A.A ...

There are two 2-engine 9c/112 glider backrakes, one 9c/112 block puffer, and five reactions where the 9c/112 reflects a glider coming from front.
x = 312, y = 70, rule = B34e5ack6n8/S23-ey
48b2o6b2o$48b2o6b2o$5b2o6b2o28bobo4b2o2b2o4bobo$5b2o6b2o28bo2bo3bo4bo
3bo2bo ...

I removed the LifeWiki <code> tag style from MediaWiki:Common.css so that they would revert to the standard MediaWiki style. In particular, this makes text inside <code> tags inline, rather than a separate block. I did this so that I could use <code> tags in the LLSSS tutorial I'm writing. I'm not ...

Category:Pages needing cleanup states that "Template {{cleanup}} automatically adds pages to this category", but at the moment (see archived copy ) there are excessively many pages in the category without explicit inclusion of said template. Please verify if all of the 1,282 pages in the category ...

Earlier this month, the largest known prime number is updated to 2^136279841-1, also known as M136279841. (The exponent could easily be a row in a standard 9x9 sudoku had one of the 1's be a 5.) A possible predecessor for the corresponding large prime oscillator has been built by yours truly, ahead ...

The true repeat time of former replicator-like signal to c/4 diagonal spaceship is 21 ticks, as can be seen in the following reflector.

x = 17, y = 28, rule = B2ce4t6-i/S145-r6-ei7c8
14bo$14bobo4$9bo$9bo$10bo2$b2o$4o$4o$b2o$4bo2$o2b2o7b2o$b5o5b4o$b2o2b
2o4b4o$o5b2o4b2o$7b2o$8b2o$9b2o$10b2o$11b2o ...

Duplicators of the c/4 diagonal spaceship at repeat time 24. Once triggered, the replicator-like signal may be transported further, rotated, flipped, duplicated, before converting back.
x = 233, y = 38, rule = B2ce4t6-i/S145-r6-ei7c8
30bo49bo49bo49bo49bo$30bobo47bobo47bobo47bobo47bobo2$203bo ...

The beehive, pond and snake can be used as catalysts, for instance in the following conduits.
...
Still life factories, which may be the start or end of a stable T reflector.
...

An engineered eater to demonstrate the idea.
x = 65, y = 70, rule = B3-cjky4it5ekq6in7c8/S23-ack4ity5ce6-ak78History ...

GUYTU6J sent me these two patterns to celebrate the holiday in China today. The first is a sparky oscillator with period 140, shown with a warm theme color.

#C [[ THEME Fire ]]
x = 37, y = 29, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7cHistory
16.B3.B$15.3B.3B$6.B8.3B.3B8.B$5.3B3.2B.9B.2B3.3B$5.3B2 ...

The beehive, pond and snake can be used as catalysts, for instance in the following conduits.
x = 170, y = 50, rule = B3-cjky4it5ekq6in7c8/S23-ack4ity5ce6-ak78
42bobo27b2o88b3o$42bobo26bo2bo15bob2o$44bo27b2o16b2obo68b2o2$97b2o$72b
o$70bobo23b3o$70bobo$45b2o119bob2o$44bo2bo76bobo39b2obo ...