For general discussion about Conway's Game of Life.
biggiemac
Posts: 504
Joined: September 17th, 2014, 12:21 am
Location: California, USA

It's a valid statement in the sense that once a pattern reproduces itself with an offset, it can be said to have momentum in that direction, and it will continue to reproduce with the same offset until acted on by something external. Collisions don't have obvious conservation laws though, so it's certainly not straightforward to define a momentum conservation law for the whole universe. Just isolated spaceships, which isn't really useful.
Physics: sophistication from simplicity.

muzik
Posts: 3910
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Are there any gardens of Eden which are also still lifes?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

calcyman
Posts: 2316
Joined: June 1st, 2009, 4:32 pm

muzik wrote:Are there any gardens of Eden which are also still lifes?
No. Any still life is its own parent.
What do you do with ill crystallographers? Take them to the mono-clinic!

blah
Posts: 283
Joined: April 9th, 2016, 7:22 pm

calcyman wrote:No. Any still life is its own parent.
What about a still life which has no parent other than itself? If one exists, it would prove that not all still lifes are glider-constructible (which I think is currently an unsolved problem?).
succ

dvgrn
Moderator
Posts: 7281
Joined: May 17th, 2009, 11:00 pm
Contact:

blah wrote:
calcyman wrote:No. Any still life is its own parent.
What about a still life which has no parent other than itself? If one exists, it would prove that not all still lifes are glider-constructible (which I think is currently an unsolved problem?).
It would certainly be nice to find a still life that could be proven to have no parent other than itself. Unfortunately I suspect that there is no such thing. Still lifes are fairly highly constrained -- no ON cell can have less than two neighbors, or more than three -- but the parents of still lifes have no such constraints.

It may be possible to prove, let's say by exhaustive enumeration of all 6x6 areas that are compatible with being part of a still life, that in each possible 6x6 tile there's a predecessor tile that's different by at least one cell in the central 4x4 area, that becomes the still-life-compatible tile in one tick. EDIT: Nope -- counterexample below...

It's often very easy to make this kind of modification. For low-population tiles you can always just add a spark somewhere, and for tiles more densely packed with ON cells, you can generally find a few cells to swap around somehow:

Code: Select all

x = 12, y = 6, rule = B3/S23
o2bo4bo2bo$4o4b4o2$4o3bob3o$o2bo4bo2bo$9bo!
So it might possibly be within range of an (ambitious) automated search, to definitely disprove this conjecture. For any candidate self-is-only-parent still life, you'd be able to pick any 6x6 (or whatever size -- maybe 5x5 is big enough!) tile in the middle of it, look that tile up in the search program's results, and show that it can be replaced with a different subpattern that becomes identical to it in one tick.

EDIT: Coming back for another look at this, I don't think this is a workable approach. We might need to analyze say 3x3 areas inside a 7x7 block, to make sure that the hypothetical 3x3 replacement has no effect on the cells around it (in a 5x5 ring).

But where an exhaustive 6x6 analysis would be marginally within reach of an exhaustive search -- 2^36 is "only" 68 billion, and that can be reduced quite a bit -- 7x7 is a taller order, with 563 trillion possibilities to check. And a non-trivial predecessor search would have to be done on each one.

It's easy to show that 2x2 is too small a central tile area to always have an alternate replacement tile. The empty area inside a 4x4 ON onion ring, for example, has no alternative: if you turn on any cells in the middle, you break the onion ring on the next tick. So there are no "hot-swappable" tiles at that size.

3x3 isn't much harder -- again, there's no alternative to the empty tile, here:

Code: Select all

x = 7, y = 7, rule = LifeHistory
.2A$.2C2DCA$.D3.CA$.D3.D$AC3.D$AC2D2C$4.2A!

(We'd need something that would turn into empty space in one tick without breaking the blocks, and there ain't no such thing.)

So we're already up to trying to analyze all still-life-compatible 8x8 tiles. In 8x8 there are eighteen quintillion different arrangements of cells, minus rotations and reflections. Without a lot of very clever shortcuts that's going to be well outside of the range even of a distributed computing effort.

... Oops, and I think that the following pattern shows that a 4x4 central area isn't big enough. Again there's no alternative to the 4x4 empty-space tile:

Code: Select all

x = 8, y = 8, rule = LifeHistory
2.2A$.D2C3D$.D4.CA$.D4.CA$AC4.D$AC4.D$.3D2CD$4.2A! So now we're up to 2.4 septillion 9x9 patterns, minus shortcuts. I think at that size it's safe enough to say this method is not going to produce a proof by exhaustive analysis, any time soon. A for awesome Posts: 2122 Joined: September 13th, 2014, 5:36 pm Location: Pembina University, Home of the Gliders Contact: Re: Thread for basic questions I've noticed that this still life seems to be the rarest one inside its bounding box, having only five occurrences on Catagolue. It's possible some periodic arrangement of these could suffice: Code: Select all x = 6, y = 5, rule = B3/S23 2o2b2o$o2bobo$2b2o$obo2bo$2o2b2o! Code: Select all x = 11, y = 31, rule = B3/S23 3b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$4b3o$3bo3bo$3b2ob2o!
praosylen#5847 (Discord)

x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

toroidalet
Posts: 1153
Joined: August 7th, 2016, 1:48 pm
Location: My computer
Contact:

A for awesome wrote:I've noticed that this still life seems to be the rarest one inside its bounding box, having only five occurrences on Catagolue. It's possible some periodic arrangement of these could suffice:

Code: Select all

x = 6, y = 5, rule = B3/S23
2o2b2o$o2bobo$2b2o$obo2bo$2o2b2o!

Code: Select all

x = 11, y = 31, rule = B3/S23
3b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$4b3o$3bo3bo$3b2ob2o! What about this? Code: Select all x = 11, y = 32, rule = B3/S23 3b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b
3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o
2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bo
bo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$4b3o$3bo3bo$4bobo$4bobo!  The predecessor is different at the bottom. "I'm sure we all agree that we ought to love one another, and I know there are people in the world who do not love their fellow human beings, and I hate people like that!" -Tom Lehrer dvgrn Moderator Posts: 7281 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Contact: Re: Thread for basic questions toroidalet wrote:What about this? Code: Select all x = 11, y = 32, rule = B3/S23 3b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b
3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o
2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bo
bo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$4b3o$3bo3bo$4bobo$4bobo!  The predecessor is different at the bottom. There's one other option, which doesn't need any cells outside the original still life. This works for longer chains of this still life as well, but here's a short alternate predecessor: Code: Select all x = 11, y = 19, rule = B3/S23 3b2ob2o$4b2obo$5b2o2$2o3b2o2b2o$o2bobo2bobo$2b2obob2o$obo4bo2bo$2o2b2o
3b2o$5bo$2o3b2o2b2o$o2bo4bobo$2b2obob2o$obo2bobo2bo$2o2b2o3b2o2$4b2o$
3bob2o$3b2ob2o! This is surprisingly close to being the only option, though! Here's the JDF file for JavaLifeSearch, used to find the above -- and it only finds 5 solutions: one- and two-sided versions of this predecessor, plus the original still life. Code: Select all # JavaLifeSearch status file, automatically generated # # Any changes to it, including changing order of lines, may cause # any kinds of strange behaviour after loading it to JLS # including errors, deadlocks, or crashes. [Properties] columns=15 rows=21 generations=2 periods={2,1,2,3,4,5,6} outer_space_unset=No symmetry=None tile_horizontal=No tile_horizontal_shift_down=0 tile_horizontal_shift_future=0 tile_vertical=No tile_vertical_shift_right=0 tile_vertical_shift_future=0 tile_temporal=No tile_temporal_shift_right=0 tile_temporal_shift_down=0 translation=None rule_birth={No,No,No,Yes,No,No,No,No,No} rule_survival={No,No,Yes,Yes,No,No,No,No,No} [SearchOptions] sort_generations_first=Yes sort_to_future=Yes sort_start_column=0 sort_start_row=0 sort_type=Circle sort_reverse=No prepare_in_background=Yes ignore_subperiods=No prune_with_combination=No pause_each_iteration=No pause_on_solution=Yes save_solutions=No save_solutions_file= save_solutions_spacing=20 save_solutions_all_generations=No save_status=No save_status_file= save_status_period=60 display_status=Yes display_status_period=5 limit_generation_0=No limit_generation_0_cells=1 limit_generation_0_variables_only=No layers_live_constraint=No layers_live_cells=1 layers_live_cells_variables_only=No layers_active_constraint=No layers_active_cells=1 layers_active_cells_variables_only=No layers_from_sorting=Yes layers_start_column=0 layers_start_row=0 layers_type=Circles [CellArray] read_only=Yes cells{0,0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{0,1}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,2}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,3}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,4}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,5}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,6}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,7}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,8}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,9}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,10}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,11}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,12}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,13}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,14}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,15}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,16}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,17}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,18}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,19}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,20}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,1}={0,0,0,0,0,1,1,0,1,1,0,0,0,0,0} cells{1,2}={0,0,0,0,0,1,0,0,0,1,0,0,0,0,0} cells{1,3}={0,0,0,0,0,0,1,1,1,0,0,0,0,0,0} cells{1,4}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,5}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0} cells{1,6}={0,0,1,0,0,1,0,1,0,0,1,0,1,0,0} cells{1,7}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0} cells{1,8}={0,0,1,0,1,0,0,1,0,1,0,0,1,0,0} cells{1,9}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0} cells{1,10}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,11}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0} cells{1,12}={0,0,1,0,0,1,0,1,0,0,1,0,1,0,0} cells{1,13}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0} cells{1,14}={0,0,1,0,1,0,0,1,0,1,0,0,1,0,0} cells{1,15}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0} cells{1,16}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,17}={0,0,0,0,0,0,1,1,1,0,0,0,0,0,0} cells{1,18}={0,0,0,0,0,1,0,0,0,1,0,0,0,0,0} cells{1,19}={0,0,0,0,0,1,1,0,1,1,0,0,0,0,0} cells{1,20}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{1}={0,0,0,0,0,16,16,16,16,16,0,0,0,0,0} stacks{2}={0,0,0,0,0,16,16,16,16,16,0,0,0,0,0} stacks{3}={0,0,0,0,0,16,16,16,16,16,0,0,0,0,0} stacks{4}={0,0,0,0,0,16,16,16,16,16,0,0,0,0,0} stacks{5}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{6}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{7}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{8}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{9}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{10}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{11}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{12}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{13}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{14}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{15}={0,0,16,16,16,16,16,16,16,16,16,16,16,0,0} stacks{16}={0,0,0,0,0,16,16,16,16,16,0,0,0,0,0} stacks{17}={0,0,0,0,0,16,16,16,16,16,0,0,0,0,0} stacks{18}={0,0,0,0,0,16,16,16,16,16,0,0,0,0,0} stacks{19}={0,0,0,0,0,16,16,16,16,16,0,0,0,0,0} stacks{20}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} [Search] cell_count=630 search_mode=Yes variable_count=161 time_passed_ns=4413498 iterations_done=1529 solutions_found=3 cells{0,0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{0,1}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,2}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,3}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,4}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,5}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,6}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,7}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,8}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,9}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,10}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,11}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,12}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,13}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,14}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,15}={0,0,2,2,2,2,2,2,2,2,2,2,2,0,0} cells{0,16}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,17}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,18}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,19}={0,0,0,0,0,2,2,2,2,2,0,0,0,0,0} cells{0,20}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,1}={0,0,0,0,0,1,1,0,1,1,0,0,0,0,0} cells{1,2}={0,0,0,0,0,1,0,0,0,1,0,0,0,0,0} cells{1,3}={0,0,0,0,0,0,1,1,1,0,0,0,0,0,0} cells{1,4}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,5}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0} cells{1,6}={0,0,1,0,0,1,0,1,0,0,1,0,1,0,0} cells{1,7}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0} cells{1,8}={0,0,1,0,1,0,0,1,0,1,0,0,1,0,0} cells{1,9}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0} cells{1,10}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,11}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0} cells{1,12}={0,0,1,0,0,1,0,1,0,0,1,0,1,0,0} cells{1,13}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0} cells{1,14}={0,0,1,0,1,0,0,1,0,1,0,0,1,0,0} cells{1,15}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0} cells{1,16}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} cells{1,17}={0,0,0,0,0,0,1,1,1,0,0,0,0,0,0} cells{1,18}={0,0,0,0,0,1,0,0,0,1,0,0,0,0,0} cells{1,19}={0,0,0,0,0,1,1,0,1,1,0,0,0,0,0} cells{1,20}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{1}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{2}={0,0,0,0,0,16,16,16,0,0,0,0,0,0,0} stacks{3}={0,0,0,0,0,0,16,0,0,0,0,0,0,0,0} stacks{4}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{5}={0,0,0,0,0,0,16,0,0,0,0,0,0,0,0} stacks{6}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{7}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0} stacks{8}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0} stacks{9}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0} stacks{10}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0} stacks{11}={0,0,0,0,0,0,16,0,0,0,0,0,0,0,0} stacks{12}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0} stacks{13}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0} stacks{14}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{15}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0} stacks{16}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{17}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0} stacks{18}={0,0,0,0,0,0,0,16,16,16,0,0,0,0,0} stacks{19}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} stacks{20}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} # Representatives: # Variable index for each cell, -1 for cells without a variable representative{0,0}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{0,1}={-1,-1,-1,-1,-1,160,159,158,157,156,-1,-1,-1,-1,-1} representative{0,2}={-1,-1,-1,-1,-1,155,154,153,152,151,-1,-1,-1,-1,-1} representative{0,3}={-1,-1,-1,-1,-1,150,149,148,147,146,-1,-1,-1,-1,-1} representative{0,4}={-1,-1,-1,-1,-1,145,144,143,142,141,-1,-1,-1,-1,-1} representative{0,5}={-1,-1,140,139,138,137,136,135,134,133,132,131,130,-1,-1} representative{0,6}={-1,-1,129,128,127,126,125,124,123,122,121,120,119,-1,-1} representative{0,7}={-1,-1,118,117,116,115,114,113,112,111,110,109,108,-1,-1} representative{0,8}={-1,-1,107,106,105,104,103,102,101,100,99,98,97,-1,-1} representative{0,9}={-1,-1,96,95,94,93,92,91,90,89,88,87,86,-1,-1} representative{0,10}={-1,-1,85,84,83,82,81,80,79,78,77,76,75,-1,-1} representative{0,11}={-1,-1,74,73,72,71,70,69,68,67,66,65,64,-1,-1} representative{0,12}={-1,-1,63,62,61,60,59,58,57,56,55,54,53,-1,-1} representative{0,13}={-1,-1,52,51,50,49,48,47,46,45,44,43,42,-1,-1} representative{0,14}={-1,-1,41,40,39,38,37,36,35,34,33,32,31,-1,-1} representative{0,15}={-1,-1,30,29,28,27,26,25,24,23,22,21,20,-1,-1} representative{0,16}={-1,-1,-1,-1,-1,19,18,17,16,15,-1,-1,-1,-1,-1} representative{0,17}={-1,-1,-1,-1,-1,14,13,12,11,10,-1,-1,-1,-1,-1} representative{0,18}={-1,-1,-1,-1,-1,9,8,7,6,5,-1,-1,-1,-1,-1} representative{0,19}={-1,-1,-1,-1,-1,4,3,2,1,0,-1,-1,-1,-1,-1} representative{0,20}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,0}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,1}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,2}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,3}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,4}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,5}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,6}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,7}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,8}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,9}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,10}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,11}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,12}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,13}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,14}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,15}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,16}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,17}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,18}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,19}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} representative{1,20}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1} # Variable combination states: combination{0}={1,1,0,1,1,2,2,2,0,1,0,2,1,1,0,0,0,0,0,0,1,1,0,0,2,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,0,2,0,1,1,0,0,1,0,1,0,0,2,0,1,0,0,1,1,1,0,0,1,1,2,0,0,1,1,0,0,0,0,0,2,0,0,0,0,0,1,1,0,0,2,1,1,0,0,1,1,1,0,0} combination{100}={1,0,2,0,0,1,0,1,0,0,1,1,0,2,0,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,1,0,1,1,0,1,1,0,1,1} # Stack: # - Variable index # - Variable value, 0 = OFF, 1 = ON # - Item type, 0 = closed, 1 = open (i.e. the other state was not tried yet) stack{0}={160,1,0} stack{1}={140,1,0} stack{2}={155,0,1} stack{3}={154,1,0} stack{4}={149,0,0} stack{5}={150,0,0} stack{6}={148,1,0} stack{7}={153,1,0} stack{8}={143,0,0} stack{9}={144,0,0} stack{10}={145,0,0} stack{11}={139,1,0} stack{12}={138,0,0} stack{13}={129,1,0} stack{14}={118,0,0} stack{15}={128,0,1} stack{16}={137,0,1} stack{17}={127,0,1} stack{18}={117,0,1} stack{19}={116,1,0} stack{20}={126,1,0} stack{21}={115,1,0} stack{22}={136,0,1} stack{23}={107,1,0} stack{24}={106,0,0} stack{25}={105,1,0} stack{26}={95,1,0} stack{27}={104,0,0} stack{28}={103,0,0} stack{29}={93,0,0} stack{30}={96,1,0} stack{31}={114,0,0} stack{32}={94,0,0} stack{33}={85,0,0} stack{34}={83,0,0} stack{35}={125,0,0} stack{36}={92,1,0} stack{37}={84,0,0} stack{38}={124,1,0} stack{39}={82,0,0} stack{40}={135,1,0} stack{41}={81,0,0} stack{42}={152,0,1} stack{43}={156,1,0} stack{44}={151,1,0} stack{45}={146,0,0} stack{46}={141,0,0} stack{47}={142,0,0} stack{48}={147,1,0} stack{49}={134,1,0} stack{50}={113,1,0} stack{51}={112,0,0} stack{52}={123,0,0} stack{53}={101,0,0} stack{54}={102,0,0} stack{55}={91,1,0} stack{56}={80,1,0} stack{57}={90,0,0} stack{58}={133,0,1} stack{59}={132,0,0} stack{60}={122,0,1} stack{61}={74,1,0} stack{62}={73,1,0} stack{63}={111,1,0} stack{64}={100,1,0} stack{65}={78,0,0} stack{66}={79,0,0} stack{67}={89,0,0} stack{68}={121,1,0} stack{69}={110,1,0} stack{70}={98,0,0} stack{71}={99,0,0} stack{72}={109,0,0} stack{73}={120,0,0} stack{74}={130,1,0} stack{75}={119,1,0} stack{76}={131,1,0} stack{77}={108,0,0} stack{78}={97,1,0} stack{79}={86,1,0} stack{80}={87,1,0} stack{81}={75,0,0} stack{82}={72,0,1} stack{83}={71,0,0} stack{84}={63,1,0} stack{85}={52,0,0} stack{86}={62,0,1} stack{87}={70,0,1} stack{88}={69,1,0} stack{89}={68,1,0} stack{90}={61,0,1} stack{91}={60,1,0} stack{92}={58,0,0} stack{93}={59,0,0} stack{94}={51,0,1} stack{95}={50,1,0} stack{96}={49,1,0} stack{97}={88,0,1} stack{98}={41,1,0} stack{99}={40,0,0} stack{100}={39,1,0} stack{101}={29,1,0} stack{102}={30,1,0} stack{103}={38,0,0} stack{104}={37,0,0} stack{105}={27,0,0} stack{106}={28,0,0} stack{107}={48,0,0} stack{108}={19,0,0} stack{109}={47,1,0} stack{110}={26,1,0} stack{111}={46,0,0} stack{112}={36,1,0} stack{113}={18,0,0} stack{114}={57,0,0} stack{115}={35,0,0} stack{116}={77,0,1} stack{117}={76,0,0} stack{118}={67,0,1} stack{119}={66,0,1} stack{120}={56,0,1} stack{121}={45,1,0} stack{122}={34,1,0} stack{123}={65,1,0} stack{124}={64,1,0} stack{125}={55,1,0} stack{126}={54,0,0} stack{127}={44,1,0} stack{128}={32,0,0} stack{129}={53,1,0} stack{130}={43,0,0} stack{131}={33,0,0} stack{132}={20,1,0} stack{133}={42,0,0} stack{134}={21,1,0} stack{135}={31,1,0} stack{136}={22,0,0} stack{137}={25,1,0} stack{138}={24,0,0} stack{139}={15,0,0} stack{140}={16,0,0} stack{141}={23,0,0} stack{142}={17,0,0} stack{143}={14,0,1} stack{144}={13,1,0} stack{145}={12,1,0} stack{146}={9,1,0} stack{147}={8,0,0} stack{148}={4,1,0} stack{149}={11,0,1} stack{150}={10,0,0} stack{151}={7,1,0} stack{152}={6,1,0} stack{153}={5,0,0} stack{154}={0,1,0} A for awesome Posts: 2122 Joined: September 13th, 2014, 5:36 pm Location: Pembina University, Home of the Gliders Contact: Re: Thread for basic questions dvgrn wrote:There's one other option, which doesn't need any cells outside the original still life. This works for longer chains of this still life as well, but here's a short alternate predecessor: Code: Select all x = 11, y = 19, rule = B3/S23 3b2ob2o$4b2obo$5b2o2$2o3b2o2b2o$o2bobo2bobo$2b2obob2o$obo4bo2bo$2o2b2o
3b2o$5bo$2o3b2o2b2o$o2bo4bobo$2b2obob2o$obo2bobo2bo$2o2b2o3b2o2$4b2o$
3bob2o$3b2ob2o! This is surprisingly close to being the only option, though! What about mixing in the cis-siamese version?: Code: Select all x = 11, y = 43, rule = B3/S23 3b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b
3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o
2b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bo
bo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobobo2bo$2b2o3b2o$ob o2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b 3o2b2o2$4b3o$3bo3bo$3b2ob2o!
praosylen#5847 (Discord)

x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

toroidalet
Posts: 1153
Joined: August 7th, 2016, 1:48 pm
Location: My computer
Contact:

A for awesome wrote:
dvgrn wrote:There's one other option, which doesn't need any cells outside the original still life. This works for longer chains of this still life as well, but here's a short alternate predecessor:

Code: Select all

x = 11, y = 19, rule = B3/S23
3b2ob2o$4b2obo$5b2o2$2o3b2o2b2o$o2bobo2bobo$2b2obob2o$obo4bo2bo$2o2b2o 3b2o$5bo$2o3b2o2b2o$o2bo4bobo$2b2obob2o$obo2bobo2bo$2o2b2o3b2o2$4b2o$3bob2o$3b2ob2o!
This is surprisingly close to being the only option, though!
What about mixing in the cis-siamese version?:

Code: Select all

x = 11, y = 43, rule = B3/S23
3b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b 3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o 2b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bo bo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobobo2bo$2b2o3b2o$ob
o2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b
3o2b2o2$4b3o$3bo3bo$3b2ob2o! Still, the original goal was to find a still life that has predecessors other than itself... Code: Select all x = 20, y = 44, rule = B3/S23 12b2ob2o$12bo3bo$13b3o$5bobo$9b2o2b3o2b2o$5bobobo2bobo2bobo$5bobo3b2o 3b2o$9bobo2bobo2bo$5bobob2o2b3o2b2o$5bobo$9b2o2b3o2b2o$5bobobo2bobo2bo
bo$5bobo3b2o3b2o$9bobo2bobo2bo$5bobob2o2b3o2b2o$5bobo$9b2o2b3o2b2o$5bo
bobo2bobobo2bo$5bobo3b2o3b2o$9bobo2bo2bobo$5bobob2o2b3o2b2o$5bobo$9b2o 2b3o2b2o$5bobobo2bobo2bobo$5bobo3b2o3b2o$9bobo2bobo2bo$5bobob2o2b3o2b 2o$5bobo$9b2o2b3o2b2o$5bobobo2bobobo2bo$5bobo3b2o3b2o$9bobo2bo2bobo$5b obob2o2b3o2b2o$5bobo$9b2o2b3o2b2o$o4bobobo2bobo2bobo$2b2o4bo2b2o3b2o$b
9obo2bobo2bo$b7o2bo2b3o2b2o$2b2o$o4b2obo4b3o$12bo3bo$13bobo$13bobo!

This might work better:

Code: Select all

x = 23, y = 15, rule = B3/S23
14bo2bo$14b4o$6bo2bobo8bo$6b4ob10o2$6b4ob2o2bob4o$6bo2bobo2bob2o3bo$bo
2bobobo4b2o4b3o$b4obob2obobo2b3o$6bo3b3o2b2o2b3o$b3obob2o10bo2bo$o2bob
o2b9o4b2o$bobob2o9bo$2bo7b4o$10bo2bo!  "I'm sure we all agree that we ought to love one another, and I know there are people in the world who do not love their fellow human beings, and I hate people like that!" -Tom Lehrer A for awesome Posts: 2122 Joined: September 13th, 2014, 5:36 pm Location: Pembina University, Home of the Gliders Contact: Re: Thread for basic questions toroidalet wrote:This might work better: Code: Select all x = 23, y = 15, rule = B3/S23 14bo2bo$14b4o$6bo2bobo8bo$6b4ob10o2$6b4ob2o2bob4o$6bo2bobo2bob2o3bo$bo 2bobobo4b2o4b3o$b4obob2obobo2b3o$6bo3b3o2b2o2b3o$b3obob2o10bo2bo$o2bob o2b9o4b2o$bobob2o9bo$2bo7b4o$10bo2bo!

I doubt it:

Code: Select all

x = 23, y = 15, rule = B3/S23
15bo$14bo$7bo6b5o$6bo4bo8b2o$6b14o2$6b4ob2o2bob2obo$6bo2bobo2bob2obobo$bo 2bobobo4b2o4b2obo$b4obob2obobo2b3o$6bo3b3o2b2o2b3o$b3obob2o10bo2bo$o2bob o2b9o4bo$bobob2o5bo3bo5bo$2bo7bo3bo$9bobobo$9bo$11bo!

praosylen#5847 (Discord)

x₁=ηx
V*_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

dvgrn
Moderator
Posts: 7281
Joined: May 17th, 2009, 11:00 pm
Contact:

toroidalet wrote:
A for awesome wrote:
dvgrn wrote:This is surprisingly close to being the only option, though!
What about mixing in the cis-siamese version?
Still, the original goal was to find a still life that has predecessors other than itself...What about changing the outside instead?
Seems like it would be nice to find a still life where you couldn't change any internal cells to make a predecessor. I'm pretty sure there are always going to be sparks you can add around the edges to change the state of one cell at the edge of a still life. At least, the odds seem good that that could be proved by an exhaustive enumeration of cases at the corners.

For the cis-siamese version, it turns out that JavaLifeSearch finds a few more options in that case:

Code: Select all

x = 11, y = 43, rule = B3/S23
3b2ob2o$4b2obo$5b2o2$2o3b2o2b2o$o2bobo2bobo$2b2obob2o$obo4bo2bo$2o2b2o 3b2o$5bo$2o3b2o2b2o$o2bo4bobo$2b2obob2o$obo2bobo2bo$2o2b2o3b2o2$2o2b2o
3b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bo
bo$2b2o3b2o$obo2bobo2bo$2o2b2o3b2o2$2o2b2o3b2o$o2bobobo2bo$2b2o3b2o$ob o2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b 2o3b2o2$4b2o$3bob2o$3b2ob2o!
The following JDF file finds 20 solutions:

Code: Select all

# JavaLifeSearch status file, automatically generated
#
# Any changes to it, including changing order of lines, may cause
# including errors, deadlocks, or crashes.

[Properties]

columns=15
rows=45
generations=2
periods={2,1,2,3,4,5,6}
outer_space_unset=No
symmetry=None
tile_horizontal=No
tile_horizontal_shift_down=0
tile_horizontal_shift_future=0
tile_vertical=No
tile_vertical_shift_right=0
tile_vertical_shift_future=0
tile_temporal=No
tile_temporal_shift_right=0
tile_temporal_shift_down=0
translation=None
rule_birth={No,No,No,Yes,No,No,No,No,No}
rule_survival={No,No,Yes,Yes,No,No,No,No,No}

[SearchOptions]

sort_generations_first=Yes
sort_to_future=Yes
sort_start_column=0
sort_start_row=0
sort_type=Circle
sort_reverse=No
prepare_in_background=Yes
ignore_subperiods=No
prune_with_combination=No
pause_each_iteration=No
pause_on_solution=Yes
save_solutions=No
save_solutions_file=
save_solutions_spacing=20
save_solutions_all_generations=No
save_status=No
save_status_file=
save_status_period=60
display_status=Yes
display_status_period=5
limit_generation_0=No
limit_generation_0_cells=1
limit_generation_0_variables_only=No
layers_live_constraint=No
layers_live_cells=1
layers_live_cells_variables_only=No
layers_active_constraint=No
layers_active_cells=1
layers_active_cells_variables_only=No
layers_from_sorting=Yes
layers_start_column=0
layers_start_row=0
layers_type=Circles

[CellArray]

cells{0,0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
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stacks{0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
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[Search]

cell_count=1350
search_mode=Yes
variable_count=425
time_passed_ns=7978480
iterations_done=2351
solutions_found=9

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cells{0,44}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

cells{1,0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
cells{1,1}={0,0,0,0,0,1,1,0,1,1,0,0,0,0,0}
cells{1,2}={0,0,0,0,0,1,0,0,0,1,0,0,0,0,0}
cells{1,3}={0,0,0,0,0,0,1,1,1,0,0,0,0,0,0}
cells{1,4}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
cells{1,5}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,6}={0,0,1,0,0,1,0,1,0,0,1,0,1,0,0}
cells{1,7}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0}
cells{1,8}={0,0,1,0,1,0,0,1,0,1,0,0,1,0,0}
cells{1,9}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,10}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
cells{1,11}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,12}={0,0,1,0,0,1,0,1,0,0,1,0,1,0,0}
cells{1,13}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0}
cells{1,14}={0,0,1,0,1,0,0,1,0,1,0,0,1,0,0}
cells{1,15}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,16}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
cells{1,17}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,18}={0,0,1,0,0,1,0,1,0,1,0,0,1,0,0}
cells{1,19}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0}
cells{1,20}={0,0,1,0,1,0,0,1,0,0,1,0,1,0,0}
cells{1,21}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,22}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
cells{1,23}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,24}={0,0,1,0,0,1,0,1,0,0,1,0,1,0,0}
cells{1,25}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0}
cells{1,26}={0,0,1,0,1,0,0,1,0,1,0,0,1,0,0}
cells{1,27}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,28}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
cells{1,29}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,30}={0,0,1,0,0,1,0,1,0,1,0,0,1,0,0}
cells{1,31}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0}
cells{1,32}={0,0,1,0,1,0,0,1,0,0,1,0,1,0,0}
cells{1,33}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,34}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
cells{1,35}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,36}={0,0,1,0,0,1,0,1,0,0,1,0,1,0,0}
cells{1,37}={0,0,0,0,1,1,0,0,0,1,1,0,0,0,0}
cells{1,38}={0,0,1,0,1,0,0,1,0,1,0,0,1,0,0}
cells{1,39}={0,0,1,1,0,0,1,1,1,0,0,1,1,0,0}
cells{1,40}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
cells{1,41}={0,0,0,0,0,0,1,1,1,0,0,0,0,0,0}
cells{1,42}={0,0,0,0,0,1,0,0,0,1,0,0,0,0,0}
cells{1,43}={0,0,0,0,0,1,1,0,1,1,0,0,0,0,0}
cells{1,44}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

stacks{0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{1}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{2}={0,0,0,0,0,16,16,16,0,0,0,0,0,0,0}
stacks{3}={0,0,0,0,0,0,16,0,0,0,0,0,0,0,0}
stacks{4}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{5}={0,0,0,0,0,0,16,0,0,0,0,0,0,0,0}
stacks{6}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{7}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0}
stacks{8}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0}
stacks{9}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0}
stacks{10}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0}
stacks{11}={0,0,0,0,0,0,16,0,0,0,0,0,0,0,0}
stacks{12}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0}
stacks{13}={0,0,0,0,0,0,0,16,0,0,0,0,0,0,0}
stacks{14}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{15}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0}
stacks{16}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{17}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0}
stacks{18}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{19}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{20}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{21}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{22}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{23}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{24}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{25}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{26}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{27}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0}
stacks{28}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{29}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0}
stacks{30}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{31}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{32}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{33}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{34}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{35}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{36}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{37}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{38}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{39}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0}
stacks{40}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{41}={0,0,0,0,0,0,0,0,16,0,0,0,0,0,0}
stacks{42}={0,0,0,0,0,0,0,16,16,16,0,0,0,0,0}
stacks{43}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
stacks{44}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

# Representatives:
# Variable index for each cell, -1 for cells without a variable

representative{0,0}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{0,1}={-1,-1,-1,-1,-1,424,423,422,421,420,-1,-1,-1,-1,-1}
representative{0,2}={-1,-1,-1,-1,-1,419,418,417,416,415,-1,-1,-1,-1,-1}
representative{0,3}={-1,-1,-1,-1,-1,414,413,412,411,410,-1,-1,-1,-1,-1}
representative{0,4}={-1,-1,-1,-1,-1,409,408,407,406,405,-1,-1,-1,-1,-1}
representative{0,5}={-1,-1,404,403,402,401,400,399,398,397,396,395,394,-1,-1}
representative{0,6}={-1,-1,393,392,391,390,389,388,387,386,385,384,383,-1,-1}
representative{0,7}={-1,-1,382,381,380,379,378,377,376,375,374,373,372,-1,-1}
representative{0,8}={-1,-1,371,370,369,368,367,366,365,364,363,362,361,-1,-1}
representative{0,9}={-1,-1,360,359,358,357,356,355,354,353,352,351,350,-1,-1}
representative{0,10}={-1,-1,349,348,347,346,345,344,343,342,341,340,339,-1,-1}
representative{0,11}={-1,-1,338,337,336,335,334,333,332,331,330,329,328,-1,-1}
representative{0,12}={-1,-1,327,326,325,324,323,322,321,320,319,318,317,-1,-1}
representative{0,13}={-1,-1,316,315,314,313,312,311,310,309,308,307,306,-1,-1}
representative{0,14}={-1,-1,305,304,303,302,301,300,299,298,297,296,295,-1,-1}
representative{0,15}={-1,-1,294,293,292,291,290,289,288,287,286,285,284,-1,-1}
representative{0,16}={-1,-1,283,282,281,280,279,278,277,276,275,274,273,-1,-1}
representative{0,17}={-1,-1,272,271,270,269,268,267,266,265,264,263,262,-1,-1}
representative{0,18}={-1,-1,261,260,259,258,257,256,255,254,253,252,251,-1,-1}
representative{0,19}={-1,-1,250,249,248,247,246,245,244,243,242,241,240,-1,-1}
representative{0,20}={-1,-1,239,238,237,236,235,234,233,232,231,230,229,-1,-1}
representative{0,21}={-1,-1,228,227,226,225,224,223,222,221,220,219,218,-1,-1}
representative{0,22}={-1,-1,217,216,215,214,213,212,211,210,209,208,207,-1,-1}
representative{0,23}={-1,-1,206,205,204,203,202,201,200,199,198,197,196,-1,-1}
representative{0,24}={-1,-1,195,194,193,192,191,190,189,188,187,186,185,-1,-1}
representative{0,25}={-1,-1,184,183,182,181,180,179,178,177,176,175,174,-1,-1}
representative{0,26}={-1,-1,173,172,171,170,169,168,167,166,165,164,163,-1,-1}
representative{0,27}={-1,-1,162,161,160,159,158,157,156,155,154,153,152,-1,-1}
representative{0,28}={-1,-1,151,150,149,148,147,146,145,144,143,142,141,-1,-1}
representative{0,29}={-1,-1,140,139,138,137,136,135,134,133,132,131,130,-1,-1}
representative{0,30}={-1,-1,129,128,127,126,125,124,123,122,121,120,119,-1,-1}
representative{0,31}={-1,-1,118,117,116,115,114,113,112,111,110,109,108,-1,-1}
representative{0,32}={-1,-1,107,106,105,104,103,102,101,100,99,98,97,-1,-1}
representative{0,33}={-1,-1,96,95,94,93,92,91,90,89,88,87,86,-1,-1}
representative{0,34}={-1,-1,85,84,83,82,81,80,79,78,77,76,75,-1,-1}
representative{0,35}={-1,-1,74,73,72,71,70,69,68,67,66,65,64,-1,-1}
representative{0,36}={-1,-1,63,62,61,60,59,58,57,56,55,54,53,-1,-1}
representative{0,37}={-1,-1,52,51,50,49,48,47,46,45,44,43,42,-1,-1}
representative{0,38}={-1,-1,41,40,39,38,37,36,35,34,33,32,31,-1,-1}
representative{0,39}={-1,-1,30,29,28,27,26,25,24,23,22,21,20,-1,-1}
representative{0,40}={-1,-1,-1,-1,-1,19,18,17,16,15,-1,-1,-1,-1,-1}
representative{0,41}={-1,-1,-1,-1,-1,14,13,12,11,10,-1,-1,-1,-1,-1}
representative{0,42}={-1,-1,-1,-1,-1,9,8,7,6,5,-1,-1,-1,-1,-1}
representative{0,43}={-1,-1,-1,-1,-1,4,3,2,1,0,-1,-1,-1,-1,-1}
representative{0,44}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

representative{1,0}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,1}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,2}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,3}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,4}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,5}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,6}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,7}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,8}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,9}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,10}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,11}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,12}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,13}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,14}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,15}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,16}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,17}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,18}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,19}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,20}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,21}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,22}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,23}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,24}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,25}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,26}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,27}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,28}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,29}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,30}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,31}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,32}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,33}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,34}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,35}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,36}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,37}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,38}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,39}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,40}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,41}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,42}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,43}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}
representative{1,44}={-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1}

# Variable combination states:

combination{0}={1,1,0,1,1,2,2,2,0,1,0,2,1,1,0,0,0,0,0,0,1,1,0,0,2,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,1}
combination{100}={0,0,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0,1,1,1,0,0,2,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,2,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,0,0}
combination{200}={1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0,0,1,1,1,0,0,2,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,2,1,1,0,0,1,1,1,0,0,1,0}
combination{300}={1,0,0,1,0,1,0,0,1,1,0,2,0,1,1,0,0,1,0,1,0,0,2,0,1,0,0,1,1,1,0,0,1,1,2,0,0,1,1,0,0,0,0,0,2,0,0,0,0,0,1,1,0,0,2,1,1,0,0,1,1,1,0,0,1,0,2,0,0,1,0,1,0,0,1,1,0,2,0,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,0,0,1,1}
combination{400}={0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,1,0,1,1,0,1,1,0,1,1}

# Stack:
# - Variable index
# - Variable value, 0 = OFF, 1 = ON
# - Item type, 0 = closed, 1 = open (i.e. the other state was not tried yet)

stack{0}={424,1,0}
stack{1}={404,1,0}
stack{2}={419,0,1}
stack{3}={418,1,0}
stack{4}={413,0,0}
stack{5}={414,0,0}
stack{6}={412,1,0}
stack{7}={417,1,0}
stack{8}={407,0,0}
stack{9}={408,0,0}
stack{10}={409,0,0}
stack{11}={403,1,0}
stack{12}={402,0,0}
stack{13}={393,1,0}
stack{14}={382,0,0}
stack{15}={392,0,1}
stack{16}={401,0,1}
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stack{18}={381,0,1}
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stack{20}={390,1,0}
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stack{22}={400,0,1}
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stack{44}={415,1,0}
stack{45}={410,0,0}
stack{46}={405,0,0}
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stack{96}={313,1,0}
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stack{127}={328,1,0}
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stack{134}={297,0,0}
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stack{138}={285,1,0}
stack{139}={273,0,0}
stack{140}={289,1,0}
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stack{142}={276,0,0}
stack{143}={277,0,0}
stack{144}={278,0,0}
stack{145}={287,0,0}
stack{146}={272,1,0}
stack{147}={271,1,0}
stack{148}={270,0,1}
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stack{151}={267,1,0}
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stack{225}={200,1,0}
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stack{227}={179,0,0}
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stack{230}={191,0,0}
stack{231}={192,1,0}
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stack{373}={49,1,0}
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stack{375}={54,0,0}
stack{376}={44,1,0}
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stack{378}={43,0,0}
stack{379}={42,0,0}
stack{380}={41,1,0}
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stack{382}={39,1,0}
stack{383}={29,1,0}
stack{384}={30,1,0}
stack{385}={38,0,0}
stack{386}={37,0,0}
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stack{388}={28,0,0}
stack{389}={36,1,0}
stack{390}={26,1,0}
stack{391}={19,0,0}
stack{392}={35,0,0}
stack{393}={25,1,0}
stack{394}={18,0,0}
stack{395}={34,1,0}
stack{396}={33,0,0}
stack{397}={32,0,0}
stack{398}={15,0,0}
stack{399}={31,1,0}
stack{400}={20,1,0}
stack{401}={16,0,0}
stack{402}={21,1,0}
stack{403}={17,0,0}
stack{404}={22,0,0}
stack{405}={23,0,0}
stack{406}={24,0,1}
stack{407}={14,0,1}
stack{408}={13,1,0}
stack{409}={12,1,0}
stack{410}={11,0,1}
stack{411}={10,0,0}
stack{412}={9,1,0}
stack{413}={8,0,0}
stack{414}={4,1,0}
stack{415}={7,1,0}
stack{416}={6,1,0}
stack{417}={5,0,0}
stack{418}={0,1,0}
toroidalet wrote:This might work better:

Code: Select all

x = 23, y = 15, rule = B3/S23
14bo2bo$14b4o$6bo2bobo8bo$6b4ob10o2$6b4ob2o2bob4o$6bo2bobo2bob2o3bo$bo
2bobobo4b2o4b3o$b4obob2obobo2b3o$6bo3b3o2b2o2b3o$b3obob2o10bo2bo$o2bob
3o$o11bo$o11bo$3o2b3o2b3o$2bo2bobo2bo$2b4ob4o!  I say it's two. The oscillators don't interact. "I'm sure we all agree that we ought to love one another, and I know there are people in the world who do not love their fellow human beings, and I hate people like that!" -Tom Lehrer Caenbe Posts: 51 Joined: September 20th, 2016, 4:24 pm Location: Nowhere Land, USA Re: Thread for basic questions toroidalet wrote: I say it's two. The oscillators don't interact. Suppose it turned up in apgsearch, and it was counted as two oscillators. How would anyone know the blinker was inside the cross? 0.1485̅ BlinkerSpawn Posts: 1977 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's Re: Thread for basic questions Caenbe wrote: toroidalet wrote: I say it's two. The oscillators don't interact. Suppose it turned up in apgsearch, and it was counted as two oscillators. How would anyone know the blinker was inside the cross? The rotors for the blinker and cross are known, so we can look at the rotor of the combination, compare it to the individual rotors, and conclude that the oscillators do not interact in any meaningful way. LifeWiki: Like Wikipedia but with more spaceships. [citation needed] Caenbe Posts: 51 Joined: September 20th, 2016, 4:24 pm Location: Nowhere Land, USA Re: Thread for basic questions BlinkerSpawn wrote: Caenbe wrote: toroidalet wrote: I say it's two. The oscillators don't interact. Suppose it turned up in apgsearch, and it was counted as two oscillators. How would anyone know the blinker was inside the cross? The rotors for the blinker and cross are known, so we can look at the rotor of the combination, compare it to the individual rotors, and conclude that the oscillators do not interact in any meaningful way. So I take it apgsearch would count it as one thing? I dunno. If this appeared in ash, I'd be more excited than if the cross and blinker appeared separately. EDIT: I get that the blinker and cross don't interact. In hindsight, I shouldn't have added the one-or-two question. I just want to know if it would be called "blinker in cross 2" or something like that. 0.1485̅ shouldsee Posts: 406 Joined: April 8th, 2016, 8:29 am Re: Thread for basic questions What's the highest still-life-tiling density in B3/S23? (Assume repeated as square) I know we can get 50%, can we get higher? Code: Select all x = 12, y = 12, rule = B3/S23:T12,12 12o2$12o2$12o2$12o2$12o2$12o!


Alexey_Nigin
Posts: 324
Joined: August 4th, 2014, 12:33 pm
Location: Ann Arbor, MI
Contact:

shouldsee wrote:What's the highest still-life-tiling density in B3/S23? (Assume repeated as square)

I know we can get 50%, can we get higher?

Code: Select all

x = 12, y = 12, rule = B3/S23:T12,12
12o2$12o2$12o2$12o2$12o2\$12o!

No.
There are 10 types of people in the world: those who understand binary and those who don't.

Caenbe
Posts: 51
Joined: September 20th, 2016, 4:24 pm
Location: Nowhere Land, USA

Ok, I'll just call it a blinkross.
Suppose I want to know if a blinkross has appeared naturally in apgsearch. Do I have to look through all 300 sample soups in Catagolue containing a cross 2, and check if they have a blinker inside them?
0.1485̅

wildmyron
Posts: 1465
Joined: August 9th, 2013, 12:45 am