For general discussion about Conway's Game of Life.

### Re: Thread for basic questions

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.

biggiemac

Posts: 503
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Location: California, USA

### Re: Thread for basic questions

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!
muzik

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Location: Scotland

### Re: Thread for basic questions

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!

calcyman

Posts: 1949
Joined: June 1st, 2009, 4:32 pm

### Re: Thread for basic questions

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

blah

Posts: 244
Joined: April 9th, 2016, 7:22 pm

### Re: Thread for basic questions

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:

x = 12, y = 6, rule = B3/S23o2bo4bo2bo$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:

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:

x = 8, y = 8, rule = LifeHistory2.2A$.D2C3D$.D4.CA$.D4.CA$AC4.D$AC4.D$.3D2CD$4.2A! So now we're up to 2.4 septillion 9x9 patterns, minus shortcuts. I think at that size it's safe enough to say this method is not going to produce a proof by exhaustive analysis, any time soon. dvgrn Moderator Posts: 5342 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Thread for basic questions I've noticed that this still life seems to be the rarest one inside its bounding box, having only five occurrences on Catagolue. It's possible some periodic arrangement of these could suffice: x = 6, y = 5, rule = B3/S232o2b2o$o2bobo$2b2o$obo2bo$2o2b2o! x = 11, y = 31, rule = B3/S233b2ob2o$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!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

A for awesome

Posts: 1731
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: Thread for basic questions

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:
x = 6, y = 5, rule = B3/S232o2b2o$o2bobo$2b2o$obo2bo$2o2b2o!
x = 11, y = 31, rule = B3/S233b2ob2o$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? x = 11, y = 32, rule = B3/S233b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$4b3o$3bo3bo$4bobo$4bobo! The predecessor is different at the bottom. x = 4, y = 2, rule = B3/S23ob2o$2obo!

(Check Gen 2)

toroidalet

Posts: 916
Joined: August 7th, 2016, 1:48 pm
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### Re: Thread for basic questions

x = 11, y = 32, rule = B3/S233b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$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:

x = 11, y = 19, rule = B3/S233b2ob2o$4b2obo$5b2o2$2o3b2o2b2o$o2bobo2bobo$2b2obob2o$obo4bo2bo$2o2b2o3b2o$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.

# 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=15rows=21generations=2periods={2,1,2,3,4,5,6}outer_space_unset=Nosymmetry=Nonetile_horizontal=Notile_horizontal_shift_down=0tile_horizontal_shift_future=0tile_vertical=Notile_vertical_shift_right=0tile_vertical_shift_future=0tile_temporal=Notile_temporal_shift_right=0tile_temporal_shift_down=0translation=Nonerule_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=Yessort_to_future=Yessort_start_column=0sort_start_row=0sort_type=Circlesort_reverse=Noprepare_in_background=Yesignore_subperiods=Noprune_with_combination=Nopause_each_iteration=Nopause_on_solution=Yessave_solutions=Nosave_solutions_file=save_solutions_spacing=20save_solutions_all_generations=Nosave_status=Nosave_status_file=save_status_period=60display_status=Yesdisplay_status_period=5limit_generation_0=Nolimit_generation_0_cells=1limit_generation_0_variables_only=Nolayers_live_constraint=Nolayers_live_cells=1layers_live_cells_variables_only=Nolayers_active_constraint=Nolayers_active_cells=1layers_active_cells_variables_only=Nolayers_from_sorting=Yeslayers_start_column=0layers_start_row=0layers_type=Circles[CellArray]read_only=Yescells{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=630search_mode=Yesvariable_count=161time_passed_ns=4413498iterations_done=1529solutions_found=3cells{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 variablerepresentative{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}

dvgrn
Moderator

Posts: 5342
Joined: May 17th, 2009, 11:00 pm

### 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:

x = 11, y = 19, rule = B3/S233b2ob2o$4b2obo$5b2o2$2o3b2o2b2o$o2bobo2bobo$2b2obob2o$obo4bo2bo$2o2b2o3b2o$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?:
x = 11, y = 43, rule = B3/S233b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$4b3o$3bo3bo$3b2ob2o! x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce A for awesome Posts: 1731 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Thread for basic questions 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: x = 11, y = 19, rule = B3/S233b2ob2o$4b2obo$5b2o2$2o3b2o2b2o$o2bobo2bobo$2b2obob2o$obo4bo2bo$2o2b2o3b2o$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?: x = 11, y = 43, rule = B3/S233b2ob2o$3bo3bo$4b3o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$2o2b3o2b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b3o2b2o2$4b3o$3bo3bo$3b2ob2o!

Still, the original goal was to find a still life that has predecessors other than itself...
x = 20, y = 44, rule = B3/S2312b2ob2o$12bo3bo$13b3o$5bobo$9b2o2b3o2b2o$5bobobo2bobo2bobo$5bobo3b2o3b2o$9bobo2bobo2bo$5bobob2o2b3o2b2o$5bobo$9b2o2b3o2b2o$5bobobo2bobo2bobo$5bobo3b2o3b2o$9bobo2bobo2bo$5bobob2o2b3o2b2o$5bobo$9b2o2b3o2b2o$5bobobo2bobobo2bo$5bobo3b2o3b2o$9bobo2bo2bobo$5bobob2o2b3o2b2o$5bobo$9b2o2b3o2b2o$5bobobo2bobo2bobo$5bobo3b2o3b2o$9bobo2bobo2bo$5bobob2o2b3o2b2o$5bobo$9b2o2b3o2b2o$5bobobo2bobobo2bo$5bobo3b2o3b2o$9bobo2bo2bobo$5bobob2o2b3o2b2o$5bobo$9b2o2b3o2b2o$o4bobobo2bobo2bobo$2b2o4bo2b2o3b2o$b9obo2bobo2bo$b7o2bo2b3o2b2o$2b2o$o4b2obo4b3o$12bo3bo$13bobo$13bobo! What about changing the outside instead? This might work better: x = 23, y = 15, rule = B3/S2314bo2bo$14b4o$6bo2bobo8bo$6b4ob10o2$6b4ob2o2bob4o$6bo2bobo2bob2o3bo$bo2bobobo4b2o4b3o$b4obob2obobo2b3o$6bo3b3o2b2o2b3o$b3obob2o10bo2bo$o2bobo2b9o4b2o$bobob2o9bo$2bo7b4o$10bo2bo!
x = 4, y = 2, rule = B3/S23ob2o$2obo! (Check Gen 2) toroidalet Posts: 916 Joined: August 7th, 2016, 1:48 pm Location: my computer ### Re: Thread for basic questions toroidalet wrote:This might work better: x = 23, y = 15, rule = B3/S2314bo2bo$14b4o$6bo2bobo8bo$6b4ob10o2$6b4ob2o2bob4o$6bo2bobo2bob2o3bo$bo2bobobo4b2o4b3o$b4obob2obobo2b3o$6bo3b3o2b2o2b3o$b3obob2o10bo2bo$o2bobo2b9o4b2o$bobob2o9bo$2bo7b4o$10bo2bo!

I doubt it:
x = 23, y = 15, rule = B3/S2315bo$14bo$7bo6b5o$6bo4bo8b2o$6b14o2$6b4ob2o2bob2obo$6bo2bobo2bob2obobo$bo2bobobo4b2o4b2obo$b4obob2obobo2b3o$6bo3b3o2b2o2b3o$b3obob2o10bo2bo$o2bobo2b9o4bo$bobob2o5bo3bo5bo$2bo7bo3bo$9bobobo$9bo$11bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

A for awesome

Posts: 1731
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: Thread for basic questions

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:

x = 11, y = 43, rule = B3/S233b2ob2o$4b2obo$5b2o2$2o3b2o2b2o$o2bobo2bobo$2b2obob2o$obo4bo2bo$2o2b2o3b2o$5bo$2o3b2o2b2o$o2bo4bobo$2b2obob2o$obo2bobo2bo$2o2b2o3b2o2$2o2b2o3b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b2o3b2o2$2o2b2o3b2o$o2bobobo2bo$2b2o3b2o$obo2bo2bobo$2o2b3o2b2o2$2o2b3o2b2o$o2bobo2bobo$2b2o3b2o$obo2bobo2bo$2o2b2o3b2o2$4b2o$3bob2o$3b2ob2o!

The following JDF file finds 20 solutions:

# 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 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{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 variablerepresentative{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}stack{17}={391,0,1}stack{18}={381,0,1}stack{19}={380,1,0}stack{20}={390,1,0}stack{21}={379,1,0}stack{22}={400,0,1}stack{23}={371,1,0}stack{24}={370,0,0}stack{25}={369,1,0}stack{26}={359,1,0}stack{27}={368,0,0}stack{28}={367,0,0}stack{29}={357,0,0}stack{30}={360,1,0}stack{31}={378,0,0}stack{32}={358,0,0}stack{33}={349,0,0}stack{34}={347,0,0}stack{35}={389,0,0}stack{36}={356,1,0}stack{37}={348,0,0}stack{38}={388,1,0}stack{39}={346,0,0}stack{40}={399,1,0}stack{41}={345,0,0}stack{42}={416,0,1}stack{43}={420,1,0}stack{44}={415,1,0}stack{45}={410,0,0}stack{46}={405,0,0}stack{47}={406,0,0}stack{48}={411,1,0}stack{49}={398,1,0}stack{50}={377,1,0}stack{51}={376,0,0}stack{52}={387,0,0}stack{53}={365,0,0}stack{54}={366,0,0}stack{55}={355,1,0}stack{56}={344,1,0}stack{57}={354,0,0}stack{58}={397,0,1}stack{59}={396,0,0}stack{60}={386,0,1}stack{61}={338,1,0}stack{62}={337,1,0}stack{63}={375,1,0}stack{64}={364,1,0}stack{65}={342,0,0}stack{66}={343,0,0}stack{67}={353,0,0}stack{68}={385,1,0}stack{69}={374,1,0}stack{70}={362,0,0}stack{71}={363,0,0}stack{72}={373,0,0}stack{73}={384,0,0}stack{74}={394,1,0}stack{75}={383,1,0}stack{76}={395,1,0}stack{77}={372,0,0}stack{78}={361,1,0}stack{79}={350,1,0}stack{80}={351,1,0}stack{81}={339,0,0}stack{82}={336,0,1}stack{83}={335,0,0}stack{84}={327,1,0}stack{85}={316,0,0}stack{86}={326,0,1}stack{87}={334,0,1}stack{88}={333,1,0}stack{89}={332,1,0}stack{90}={325,0,1}stack{91}={324,1,0}stack{92}={322,0,0}stack{93}={323,0,0}stack{94}={315,0,1}stack{95}={314,1,0}stack{96}={313,1,0}stack{97}={352,0,1}stack{98}={305,1,0}stack{99}={304,0,0}stack{100}={303,1,0}stack{101}={293,1,0}stack{102}={302,0,0}stack{103}={301,0,0}stack{104}={291,0,0}stack{105}={294,1,0}stack{106}={312,0,0}stack{107}={292,0,0}stack{108}={283,0,0}stack{109}={281,0,0}stack{110}={311,1,0}stack{111}={290,1,0}stack{112}={282,0,0}stack{113}={310,0,0}stack{114}={300,1,0}stack{115}={280,0,0}stack{116}={321,0,0}stack{117}={299,0,0}stack{118}={279,0,0}stack{119}={341,0,1}stack{120}={340,0,0}stack{121}={331,0,1}stack{122}={330,0,1}stack{123}={320,0,1}stack{124}={309,1,0}stack{125}={298,1,0}stack{126}={329,1,0}stack{127}={328,1,0}stack{128}={319,1,0}stack{129}={318,0,0}stack{130}={308,1,0}stack{131}={296,0,0}stack{132}={317,1,0}stack{133}={307,0,0}stack{134}={297,0,0}stack{135}={306,0,0}stack{136}={295,1,0}stack{137}={284,1,0}stack{138}={285,1,0}stack{139}={273,0,0}stack{140}={289,1,0}stack{141}={288,0,0}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}stack{149}={269,0,0}stack{150}={268,1,0}stack{151}={267,1,0}stack{152}={286,0,1}stack{153}={261,1,0}stack{154}={250,0,0}stack{155}={260,0,1}stack{156}={259,0,1}stack{157}={258,1,0}stack{158}={257,0,0}stack{159}={266,0,1}stack{160}={265,0,0}stack{161}={275,0,1}stack{162}={274,0,0}stack{163}={249,0,1}stack{164}={248,1,0}stack{165}={247,1,0}stack{166}={246,0,0}stack{167}={256,1,0}stack{168}={255,0,1}stack{169}={254,1,0}stack{170}={264,0,1}stack{171}={239,1,0}stack{172}={238,0,0}stack{173}={237,1,0}stack{174}={227,1,0}stack{175}={236,0,0}stack{176}={235,0,0}stack{177}={225,0,0}stack{178}={228,1,0}stack{179}={226,0,0}stack{180}={217,0,0}stack{181}={215,0,0}stack{182}={224,1,0}stack{183}={216,0,0}stack{184}={214,0,0}stack{185}={213,0,0}stack{186}={245,0,1}stack{187}={234,1,0}stack{188}={223,1,0}stack{189}={263,1,0}stack{190}={262,1,0}stack{191}={253,0,1}stack{192}={252,0,0}stack{193}={251,1,0}stack{194}={240,0,0}stack{195}={244,0,1}stack{196}={243,1,0}stack{197}={242,1,0}stack{198}={233,0,0}stack{199}={232,0,1}stack{200}={241,0,1}stack{201}={231,1,0}stack{202}={230,0,0}stack{203}={229,1,0}stack{204}={218,1,0}stack{205}={219,1,0}stack{206}={207,0,0}stack{207}={220,0,0}stack{208}={208,0,0}stack{209}={221,0,0}stack{210}={209,0,0}stack{211}={222,1,0}stack{212}={210,0,0}stack{213}={211,0,0}stack{214}={212,0,0}stack{215}={206,1,0}stack{216}={205,1,0}stack{217}={204,0,1}stack{218}={203,0,0}stack{219}={202,1,0}stack{220}={201,1,0}stack{221}={195,1,0}stack{222}={184,0,0}stack{223}={194,0,1}stack{224}={193,0,1}stack{225}={200,1,0}stack{226}={178,0,0}stack{227}={179,0,0}stack{228}={180,0,0}stack{229}={189,0,0}stack{230}={191,0,0}stack{231}={192,1,0}stack{232}={199,0,1}stack{233}={198,0,0}stack{234}={190,1,0}stack{235}={183,0,1}stack{236}={182,1,0}stack{237}={181,1,0}stack{238}={197,1,0}stack{239}={196,1,0}stack{240}={188,0,1}stack{241}={177,1,0}stack{242}={187,1,0}stack{243}={186,0,0}stack{244}={176,1,0}stack{245}={185,1,0}stack{246}={175,0,0}stack{247}={174,0,0}stack{248}={173,1,0}stack{249}={172,0,0}stack{250}={171,1,0}stack{251}={161,1,0}stack{252}={170,0,0}stack{253}={169,0,0}stack{254}={159,0,0}stack{255}={162,1,0}stack{256}={168,1,0}stack{257}={160,0,0}stack{258}={151,0,0}stack{259}={149,0,0}stack{260}={167,0,0}stack{261}={158,1,0}stack{262}={150,0,0}stack{263}={166,1,0}stack{264}={157,1,0}stack{265}={148,0,0}stack{266}={165,0,0}stack{267}={164,0,0}stack{268}={144,0,0}stack{269}={147,0,0}stack{270}={163,1,0}stack{271}={145,0,0}stack{272}={152,1,0}stack{273}={146,0,0}stack{274}={153,1,0}stack{275}={141,0,0}stack{276}={155,0,0}stack{277}={156,0,1}stack{278}={154,0,1}stack{279}={140,1,0}stack{280}={139,1,0}stack{281}={138,0,1}stack{282}={137,0,0}stack{283}={136,1,0}stack{284}={135,1,0}stack{285}={143,0,1}stack{286}={142,0,0}stack{287}={129,1,0}stack{288}={118,0,0}stack{289}={134,0,1}stack{290}={133,0,0}stack{291}={128,0,1}stack{292}={127,0,1}stack{293}={126,1,0}stack{294}={125,0,0}stack{295}={132,0,1}stack{296}={124,1,0}stack{297}={131,1,0}stack{298}={130,1,0}stack{299}={123,0,1}stack{300}={122,1,0}stack{301}={117,0,1}stack{302}={116,1,0}stack{303}={115,1,0}stack{304}={114,0,0}stack{305}={121,0,1}stack{306}={120,0,0}stack{307}={119,1,0}stack{308}={108,0,0}stack{309}={113,0,1}stack{310}={112,0,1}stack{311}={111,1,0}stack{312}={110,1,0}stack{313}={107,1,0}stack{314}={106,0,0}stack{315}={105,1,0}stack{316}={95,1,0}stack{317}={104,0,0}stack{318}={103,0,0}stack{319}={93,0,0}stack{320}={96,1,0}stack{321}={102,1,0}stack{322}={94,0,0}stack{323}={85,0,0}stack{324}={83,0,0}stack{325}={101,0,0}stack{326}={92,1,0}stack{327}={84,0,0}stack{328}={91,1,0}stack{329}={82,0,0}stack{330}={81,0,0}stack{331}={109,0,1}stack{332}={100,0,1}stack{333}={99,1,0}stack{334}={98,0,0}stack{335}={97,1,0}stack{336}={86,1,0}stack{337}={87,1,0}stack{338}={75,0,0}stack{339}={88,0,0}stack{340}={76,0,0}stack{341}={89,0,0}stack{342}={77,0,0}stack{343}={90,1,0}stack{344}={78,0,0}stack{345}={79,0,0}stack{346}={80,0,0}stack{347}={74,1,0}stack{348}={73,1,0}stack{349}={72,0,1}stack{350}={71,0,0}stack{351}={70,1,0}stack{352}={69,1,0}stack{353}={68,1,0}stack{354}={46,0,0}stack{355}={47,0,0}stack{356}={48,0,0}stack{357}={57,0,0}stack{358}={59,0,0}stack{359}={63,1,0}stack{360}={52,0,0}stack{361}={62,0,1}stack{362}={67,0,1}stack{363}={66,0,0}stack{364}={61,0,1}stack{365}={60,1,0}stack{366}={58,1,0}stack{367}={65,1,0}stack{368}={64,1,0}stack{369}={56,0,1}stack{370}={45,1,0}stack{371}={51,0,1}stack{372}={50,1,0}stack{373}={49,1,0}stack{374}={55,1,0}stack{375}={54,0,0}stack{376}={44,1,0}stack{377}={53,1,0}stack{378}={43,0,0}stack{379}={42,0,0}stack{380}={41,1,0}stack{381}={40,0,0}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}stack{387}={27,0,0}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:
x = 23, y = 15, rule = B3/S2314bo2bo$14b4o$6bo2bobo8bo$6b4ob10o2$6b4ob2o2bob4o$6bo2bobo2bob2o3bo$bo2bobobo4b2o4b3o$b4obob2obobo2b3o$6bo3b3o2b2o2b3o$b3obob2o10bo2bo$o2bobo2b9o4b2o$bobob2o9bo$2bo7b4o$10bo2bo! 60 solutions with JavaLifeSearch, without going outside the boundaries of the still life. Doesn't seem like an improvement -- I think the still life is going to have to be bigger: x = 27, y = 19, rule = B3/S23$$16bobbo16b4o8bobbobo8bo8b4ob10o12bo8booboboobbob4o8bobbobobboboo3bo3bobbobobobboboo5boo3b5obboo3bobb4o8bo3boo3boobb3o3b3oboboo3bo9bobbobbobobb9obboboo3boboboo9bo4bo7b4o12bobbo! # 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=27rows=19generations=2periods={2,1,2,3,4,5,6}outer_space_unset=Nosymmetry=Nonetile_horizontal=Notile_horizontal_shift_down=0tile_horizontal_shift_future=0tile_vertical=Notile_vertical_shift_right=0tile_vertical_shift_future=0tile_temporal=Notile_temporal_shift_right=0tile_temporal_shift_down=0translation=Nonerule_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=Yessort_to_future=Yessort_start_column=0sort_start_row=0sort_type=Circlesort_reverse=Noprepare_in_background=Yesignore_subperiods=Noprune_with_combination=Nopause_each_iteration=Nopause_on_solution=Yessave_solutions=Nosave_solutions_file=save_solutions_spacing=20save_solutions_all_generations=Nosave_status=Nosave_status_file=save_status_period=60display_status=Yesdisplay_status_period=5limit_generation_0=Nolimit_generation_0_cells=1limit_generation_0_variables_only=Nolayers_live_constraint=Nolayers_live_cells=1layers_live_cells_variables_only=Nolayers_active_constraint=Nolayers_active_cells=1layers_active_cells_variables_only=Nolayers_from_sorting=Yeslayers_start_column=0layers_start_row=0layers_type=Circles[CellArray]read_only=Nocells{0,0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}cells{0,1}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}cells{0,2}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,0,0,0,0,0,0,0}cells{0,3}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,0,0,0,0,0,0,0}cells{0,4}={0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0}cells{0,5}={0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0}cells{0,6}={0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0}cells{0,7}={0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0}cells{0,8}={0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0}cells{0,9}={0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0}cells{0,10}={0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0}cells{0,11}={0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0}cells{0,12}={0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0}cells{0,13}={0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0}cells{0,14}={0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0}cells{0,15}={0,0,0,0,2,0,0,0,0,0,0,0,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0}cells{0,16}={0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,2,0,0,0,0,0,0,0,0,0,0,0}cells{0,17}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}cells{0,18}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}cells{1,0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}cells{1,1}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}cells{1,2}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0}cells{1,3}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0}cells{1,4}={0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0}cells{1,5}={0,0,0,0,0,0,0,0,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0}cells{1,6}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}cells{1,7}={0,0,0,0,0,0,0,0,1,1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0}cells{1,8}={0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0}cells{1,9}={0,0,0,1,0,0,1,0,1,0,1,0,0,0,0,1,1,0,0,0,0,1,1,1,0,0,0}cells{1,10}={0,0,0,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0,0}cells{1,11}={0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,0}cells{1,12}={0,0,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0}cells{1,13}={0,0,1,0,0,1,0,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0}cells{1,14}={0,0,0,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0}cells{1,15}={0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0}cells{1,16}={0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0}cells{1,17}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}cells{1,18}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}stacks{0}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}stacks{1}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}stacks{2}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,16,16,16,0,0,0,0,0,0,0}stacks{3}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,16,16,16,0,0,0,0,0,0,0}stacks{4}={0,0,0,0,0,0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0,0}stacks{5}={0,0,0,0,0,0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0,0}stacks{6}={0,0,0,0,0,0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0,0}stacks{7}={0,0,0,0,0,0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0,0}stacks{8}={0,0,0,0,0,0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0}stacks{9}={0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0}stacks{10}={0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0}stacks{11}={0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0}stacks{12}={0,0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0}stacks{13}={0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0}stacks{14}={0,0,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,0,0,0,0,0,0,0,0}stacks{15}={0,0,0,0,16,0,0,0,0,0,0,0,16,16,16,16,0,0,0,0,0,0,0,0,0,0,0}stacks{16}={0,0,0,0,0,0,0,0,0,0,0,0,16,16,16,16,0,0,0,0,0,0,0,0,0,0,0}stacks{17}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}stacks{18}={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} dvgrn Moderator Posts: 5342 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Thread for basic questions Are there any 2-state inner-totalistic rules with still lives, oscillators, and spaceships? 0.1485̅ Caenbe Posts: 51 Joined: September 20th, 2016, 4:24 pm Location: Nowhere Land, USA ### Re: Thread for basic questions Plenty... more than plenty, actually. Just take a look through the Other Cellular Automata forum. - B3/S2-i34q (my own) - B3-ckq/S2-c34ci - B35y/S236c - nearly everything from page 13 onwards in the non-CGoL accidental discoveries thread gamer54657 wrote:God save us all. God save humanity. hgkhjfgh nutshelltlifeDiscord 'Conwaylife Lounge' M. I. Wright Posts: 371 Joined: June 13th, 2015, 12:04 pm ### Re: Thread for basic questions @M. I. Wright: I believe you misunderstood the question. Caenbe wrote:Are there any 2-state inner-totalistic rules with still lives, oscillators, and spaceships? By inner-totalistic I assume you mean the state of a cell at time t depends only on the total of On cells in the neighbourhood of the cell at time t-1, including the cell itself in the total. For the Moore neighbourhood, the only example I can find with spaceships is B03/S2. It has oscillators but I don't know if still life is well defined in this case. Excluding B0, the potential candidates are B3/S2 and B2/S1, neither of which have known spaceships that I can find. Edit: Considering the rules related to the two candidates above, here's another which satisfies your request: x = 14, y = 18, rule = B35/S24boobo6b3obo8obobo4bobobobo2bo4bo2bobobo6bobob2obo4bob2o2b2obo2bob2ob2o8b2o3bobo2bobo5b4o! c/2 glider from http://fano.ics.uci.edu/ca/rules/b35s24/ wildmyron Posts: 1028 Joined: August 9th, 2013, 12:45 am ### Re: Thread for basic questions wildmyron wrote:Edit: Considering the rules related to the two candidates above, here's another which satisfies your request: x = 14, y = 18, rule = B35/S24boobo6b3obo8obobo4bobobobo2bo4bo2bobobo6bobob2obo4bob2o2b2obo2bob2ob2o8b2o3bobo2bobo5b4o! c/2 glider from http://fano.ics.uci.edu/ca/rules/b35s24/ One of my favorite rules is somewhat similar to this, B3578/S24678. It is by far the most complex inner-totalistic on/off-symmetric rule that exists, at least as far as I know. Your pattern also works in this rule: x = 14, y = 18, rule = B3578/S24678boobo6b3obo8obobo4bobobobo2bo4bo2bobobo6bobob2obo4bob2o2b2obo2bob2ob2o8b2o3bobo2bobo5b4o! x = 24, y = 28, rule = B3578/S2467824o24o24o24o24o6ob17o5obob6o3b7o6ob17o24o24o24o24o24o24o24o5obobob4obobob5o6ob2ob4ob2ob6o6obob6obob6o6o2bob4obo2b6o7o2bob2obo2b7o6o2b8o2b6o8obob2obob8o10o4b10o24o24o24o24o24o! x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)$$x_1=\eta xV^*_\eta=c^2\sqrt{\Lambda\eta}K=\frac{\Lambda u^2}2P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$http://conwaylife.com/wiki/A_for_all Aidan F. Pierce A for awesome Posts: 1731 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Thread for basic questions Thanks. Another question: how would this be classified? Is it one oscillator or two? x = 13, y = 13, rule = B3/S232b4ob4o$2bo2bobo2bo$3o2b3o2b3o$o11bo$o11bo$3o3bo3b3o$2bo3bo3bo$3o3bo3b3o$o11bo$o11bo$3o2b3o2b3o$2bo2bobo2bo$2b4ob4o! 0.1485̅ Caenbe Posts: 51 Joined: September 20th, 2016, 4:24 pm Location: Nowhere Land, USA ### Re: Thread for basic questions Caenbe wrote:Thanks. Another question: how would this be classified? Is it one oscillator or two? x = 13, y = 13, rule = B3/S232b4ob4o$2bo2bobo2bo$3o2b3o2b3o$o11bo$o11bo$3o3bo3b3o$2bo3bo3bo$3o3bo3b3o$o11bo$o11bo$3o2b3o2b3o$2bo2bobo2bo$2b4ob4o! I say it's two. The oscillators don't interact. x = 4, y = 2, rule = B3/S23ob2o$2obo!

(Check Gen 2)

toroidalet

Posts: 916
Joined: August 7th, 2016, 1:48 pm
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### 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
Caenbe

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

### 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]

Posts: 1836
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.

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
Caenbe

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

### 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?
x = 12, y = 12, rule = B3/S23:T12,1212o2$12o2$12o2$12o2$12o2$12o! shouldsee Posts: 406 Joined: April 8th, 2016, 8:29 am ### Re: Thread for basic questions 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? x = 12, y = 12, rule = B3/S23:T12,1212o2$12o2$12o2$12o2$12o2$12o!

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

Alexey_Nigin

Posts: 323
Joined: August 4th, 2014, 12:33 pm
Location: Ann Arbor, MI

### Re: Thread for basic questions

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
Caenbe

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

### Re: Thread for basic questions

Caenbe wrote: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?

Yes. In case it's not clear yet, Catagolue attempts to separate all non-interacting objects, including psuedo still life objects where possible, and the cross and blinker as you've noticed are not even close to interacting.
I would suggest you inspect the candidate soups programmatically rather than manually, but you can do it either way.
wildmyron

Posts: 1028
Joined: August 9th, 2013, 12:45 am

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