Challenges

[confocaloid]

Challenge:
in a non-alternating, non-B0 rule, find a spaceship/oscillator that has at least 1 generation of no birth and no death AT THE SAME TIME.
(Hint:this must be a generations rule.)

I do not have a working example, but there might be a 3-state modification of Life where the pi-heptomino would be a spaceship with these three consecutive phases:

Code: Select all

x = 24, y = 5, rule = nameless_rule
2B8.2B8.2B$B.A7.B.B7.B.B$2.B9.B9.BA$B.A7.B.B7.B.B$2B8.2B8.2B!

@RULE nameless_rule
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute

[toroidalet]

You can find a few here and here. There's also one on the interesting replicators thread that I don't care to find.

[breaker's glider gun]

adjusted challenge: at DIFFERENT points!
| >;
v

[squareroot12621]

adjusted challenge: at DIFFERENT points!

B3/S23 beacon.
Generation 0 % 2: No birth.
Generation 1 % 2: No death.

Code: Select all

x = 4, y = 4, rule = B3/S23
2o$o$3bo$2b2o!

[toroidalet]

This one has no birth or death in 3 separate intervals:

Code: Select all

x = 6, y = 3, rule = 1c23-y4c5e6c/34e6in/15
.A.2A$A.AMLA$.A.2A!

5 times (EDIT: nope, only 3. If you increase the generations to 16, it has 4, and at 28 it has 5):

Code: Select all

x = 23, y = 16, rule = 1c23-ny5e6c/34e6i/15
2.A17.A$.ABA15.ABA$.ABA15.ABA$11.A$10.ABA$.A.A6.ABA6.A.A$2.A17.A2$10.
A.A$11.A2$.A.A15.A.A$A3.A13.A3.A2$10.A.A$9.A3.A!

Both of these rules are from here (The first one is from "Another related rule which isn't explosive"/"But what a disappointment when you find it is nonetheless explosive" and the second is corderized from "A related rule")

[Citation needed]

ColorfulGalaxy found that the nine distinct 3-cell Garden of Eden patterns (seen as 1-cell-high prisms) in Life without Death rule can fit into a 3x3x3 cube. (citation needed)

Code: Select all

x rule = LifeColorful
ADA$
BDC$
BDC$
$
E2F$
F2G$
EGE$
$
HAC$
BIH$
IHI$!

[GUYTU6J]

Here is a period-1022 Margolus oscillator rendered in state 9 of Super mode.

Code: Select all

x = 35, y = 35, rule = B2c/SSuper
17.J$16.J.J$15.J.J.J$14.J.J.J.J$13.J.J.J.J.J$12.J.J.J.J.J.J$11.J.J.J.
J.J.J.J$10.J.J.J.J.J.J.J.J$9.J.J.J.J.J.J.J.J.J$8.J.J.J.J.J.J.J.J.J.J$
7.J.J.J.J.J.J.J.J.J.J.J$6.J.J.J.J.J.J.J.J.J.J.J.J$5.J.J.J.J.J.J.J.J.J
.J.J.J.J$4.J.J.J.J.J.J.J.J.J.J.J.J.J.J$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$2.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J$.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I$.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J.J$2.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J
$4.J.J.J.J.J.J.J.J.J.J.J.J.J.J$5.J.J.J.J.J.J.J.J.J.J.J.J.J$6.J.J.J.J.
J.J.J.J.J.J.J.J$7.J.J.J.J.J.J.J.J.J.J.J$8.J.J.J.J.J.J.J.J.J.J$9.J.J.J
.J.J.J.J.J.J$10.J.J.J.J.J.J.J.J$11.J.J.J.J.J.J.J$12.J.J.J.J.J.J$13.J.
J.J.J.J$14.J.J.J.J$15.J.J.J$16.J.J$17.J!

Pick a phase of this oscillator, set generation to 0, and change one (1) state-9 cell to state 1. The challenge is to maximize time duration with both type of history/off-trail cells present. Consider extinction of state-2 cells and extinction of state-10 cells separately.

[confocaloid]

State 10 can disappear at T = 55:

Code: Select all

x = 35, y = 35, rule = B2c/SSuper
17.J$16.J.J$15.J.J.J$14.J.J.J.J$13.J.J.J.J.J$12.J.J.J.J.J.J$11.J.J.J.
J.J.J.J$10.J.J.J.J.J.J.J.J$9.J.J.J.J.J.J.J.J.J$8.J.J.J.J.J.J.J.J.J.J$
7.J.J.J.J.J.J.J.J.J.J.J$6.J.J.J.J.J.J.J.J.J.J.J.J$5.J.J.J.J.J.J.J.J.J
.J.J.J.J$4.J.J.J.J.J.J.J.J.J.J.J.J.J.J$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$2.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J$.A.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.
I$J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J$.I.I.I.I.I.I.I.I.I.I.I.I.I.I.I.
I.I$2.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J
$4.J.J.J.J.J.J.J.J.J.J.J.J.J.J$5.J.J.J.J.J.J.J.J.J.J.J.J.J$6.J.J.J.J.
J.J.J.J.J.J.J.J$7.J.J.J.J.J.J.J.J.J.J.J$8.J.J.J.J.J.J.J.J.J.J$9.J.J.J
.J.J.J.J.J.J$10.J.J.J.J.J.J.J.J$11.J.J.J.J.J.J.J$12.J.J.J.J.J.J$13.J.
J.J.J.J$14.J.J.J.J$15.J.J.J$16.J.J$17.J!

State 2 can disappear at T = 28:

Code: Select all

x = 35, y = 35, rule = B2c/SSuper
17.J$16.J.J$15.I.A.I$14.J.J.J.J$13.J.I.I.I.J$12.J.J.J.J.J.J$11.J.J.I.
I.I.J.J$10.J.J.J.J.J.J.J.J$9.J.J.J.I.I.I.J.J.J$8.J.J.J.J.J.J.J.J.J.J$
7.J.J.J.J.I.I.I.J.J.J.J$6.J.J.J.J.J.J.J.J.J.J.J.J$5.J.J.J.J.J.I.I.I.J
.J.J.J.J$4.J.J.J.J.J.J.J.J.J.J.J.J.J.J$3.J.J.J.J.J.J.I.I.I.J.J.J.J.J.
J$2.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J$.J.J.J.J.J.J.J.I.I.I.J.J.J.J.J.J.
J$J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J$.J.J.J.J.J.J.J.I.I.I.J.J.J.J.J.
J.J$2.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J$3.J.J.J.J.J.J.I.I.I.J.J.J.J.J.J
$4.J.J.J.J.J.J.J.J.J.J.J.J.J.J$5.J.J.J.J.J.I.I.I.J.J.J.J.J$6.J.J.J.J.
J.J.J.J.J.J.J.J$7.J.J.J.J.I.I.I.J.J.J.J$8.J.J.J.J.J.J.J.J.J.J$9.J.J.J
.I.I.I.J.J.J$10.J.J.J.J.J.J.J.J$11.J.J.I.I.I.J.J$12.J.J.J.J.J.J$13.J.
I.I.I.J$14.J.J.J.J$15.I.I.I$16.J.J$17.J!

[GUYTU6J]

State 10 disappears at generation 76:

Code: Select all

x = 35, y = 35, rule = B2c/SSuper
17.J$16.I.I$15.J.J.J$14.J.I.I.J$13.J.J.J.J.J$12.J.J.I.I.J.J$11.J.J.J.
J.J.J.J$10.J.J.J.I.I.J.J.J$9.J.J.J.J.J.J.J.J.J$8.I.I.I.I.J.J.I.I.I.I$
7.J.J.J.J.J.J.J.J.J.J.J$6.J.I.I.I.I.J.J.I.I.I.I.J$5.J.J.J.J.J.J.J.J.J
.J.J.J.J$4.J.J.I.I.I.I.J.J.I.I.I.I.J.J$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$2.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.I$.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$J.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.A.J$.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J.J$2.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.I$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J
$4.J.J.I.I.I.I.J.J.I.I.I.I.J.J$5.J.J.J.J.J.J.J.J.J.J.J.J.J$6.J.I.I.I.
I.J.J.I.I.I.I.J$7.J.J.J.J.J.J.J.J.J.J.J$8.I.I.I.I.J.J.I.I.I.I$9.J.J.J
.J.J.J.J.J.J$10.J.J.J.I.I.J.J.J$11.J.J.J.J.J.J.J$12.J.J.I.I.J.J$13.J.
J.J.J.J$14.J.I.I.J$15.J.J.J$16.I.I$17.J!

The pattern has a one-cell-thick phase at T=287.

[breaker's glider gun]

State 10 disappears at generation 76:

Code: Select all

x = 35, y = 35, rule = B2c/SSuper
17.J$16.I.I$15.J.J.J$14.J.I.I.J$13.J.J.J.J.J$12.J.J.I.I.J.J$11.J.J.J.
J.J.J.J$10.J.J.J.I.I.J.J.J$9.J.J.J.J.J.J.J.J.J$8.I.I.I.I.J.J.I.I.I.I$
7.J.J.J.J.J.J.J.J.J.J.J$6.J.I.I.I.I.J.J.I.I.I.I.J$5.J.J.J.J.J.J.J.J.J
.J.J.J.J$4.J.J.I.I.I.I.J.J.I.I.I.I.J.J$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$2.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.I$.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$J.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.A.J$.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J.J$2.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.I$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J
$4.J.J.I.I.I.I.J.J.I.I.I.I.J.J$5.J.J.J.J.J.J.J.J.J.J.J.J.J$6.J.I.I.I.
I.J.J.I.I.I.I.J$7.J.J.J.J.J.J.J.J.J.J.J$8.I.I.I.I.J.J.I.I.I.I$9.J.J.J
.J.J.J.J.J.J$10.J.J.J.I.I.J.J.J$11.J.J.J.J.J.J.J$12.J.J.I.I.J.J$13.J.
J.J.J.J$14.J.I.I.J$15.J.J.J$16.I.I$17.J!

Cool! state 9 dies at 67.
|
V

[toroidalet]

State 10 disappears at generation 76:

Code: Select all

x = 35, y = 35, rule = B2c/SSuper
17.J$16.I.I$15.J.J.J$14.J.I.I.J$13.J.J.J.J.J$12.J.J.I.I.J.J$11.J.J.J.
J.J.J.J$10.J.J.J.I.I.J.J.J$9.J.J.J.J.J.J.J.J.J$8.I.I.I.I.J.J.I.I.I.I$
7.J.J.J.J.J.J.J.J.J.J.J$6.J.I.I.I.I.J.J.I.I.I.I.J$5.J.J.J.J.J.J.J.J.J
.J.J.J.J$4.J.J.I.I.I.I.J.J.I.I.I.I.J.J$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$2.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.I$.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J$J.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.A.J$.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J.
J.J$2.I.I.I.J.J.J.J.I.I.J.J.J.J.I.I.I$3.J.J.J.J.J.J.J.J.J.J.J.J.J.J.J
$4.J.J.I.I.I.I.J.J.I.I.I.I.J.J$5.J.J.J.J.J.J.J.J.J.J.J.J.J$6.J.I.I.I.
I.J.J.I.I.I.I.J$7.J.J.J.J.J.J.J.J.J.J.J$8.I.I.I.I.J.J.I.I.I.I$9.J.J.J
.J.J.J.J.J.J$10.J.J.J.I.I.J.J.J$11.J.J.J.J.J.J.J$12.J.J.I.I.J.J$13.J.
J.J.J.J$14.J.I.I.J$15.J.J.J$16.I.I$17.J!

No, I think you flipped the number around. It's 67.

No, state 10 is the dead history cell. One survives at the far left corner until 74, and another just a bit to the right is extinguished in generation 76.

[pzq_alex]

Find a non-rock catalysis for this still life:

Code: Select all

x = 7, y = 8, rule = B3/S23
2b2o$bob3o$o5bo$2ob3o$bobo$bo2b2o$2b2o2bo$5b2o!

[hotcrystal0]

Related to self-describing pattern: make a self describing apgcode. "xp0_nogliders" works but its kind of cheating

Does xp0_blinker work?
I didn't find this, I remembered this from another thread, but I forgot where...

After xp0_blinker, there are no more apgcodes in which a stable object's name yields the original object, let alone yield it cleanly. I did this a while ago and got to xp0_cismirroredrbee before giving up.

how about xp0_justablock?

[toroidalet]

Related to self-describing pattern: make a self describing apgcode. "xp0_nogliders" works but its kind of cheating

Does xp0_blinker work?
I didn't find this, I remembered this from another thread, but I forgot where...

After xp0_blinker, there are no more apgcodes in which a stable object's name yields the original object, let alone yield it cleanly. I did this a while ago and got to xp0_cismirroredrbee before giving up.

You didn't look long enough. While this pattern does not evolve into the still life it describes, it should at least show that there is a still life which is produced by the apgcode of its English name and give you some idea of how to find one.

[Hdjensofjfnen]

You didn't look long enough. While this pattern does not evolve into the still life it describes, it should at least show that there is a still life which is produced by the apgcode of its English name and give you some idea of how to find one.

I was searching for trivial examples at the time. Rather than pulling up a three-year-old post to criticize my methodology, it might be more productive to try to construct such a still life yourself.

[toroidalet]

I'm sorry if I wasn't clear. I was trying to make a joke, that you could have found such a still life by looking "long enough", when just finding this pattern would require you to look through a number of still lifes with 8.2*10^51 digits.

[pipsqueek]

xp0_666 gives you a beehive
xp0_thedevil also evolves into.. a beehive
xp0_deathisnear gives you another beehive
xp0_devilkiller GIVES YOU A BEEHIVE

[pzq_alex]

It seems to be some sort of error-correcting code on 12 bits (a Hamming code?). The original message can be recovered if there are one or probably even 2 errors (EDIT: the Hamming distance between codewords is 8, so it can correct errors of up to 3 bits and detect 4-bit errors).

A linear code on 12 bits with minimum Hamming weight 8 -- sounds like the binary Golay code!

[pipsqueek]

here's a challenge, find an inflated still life that grows infinitely. inflated still life examples:

Code: Select all

x = 38, y = 16, rule = B3/S23
26b4o$26b4o$26b4o$26b4o$22b4o4b4o$22b4o4b4o$22b4o4b4o$10b6o6b4o4b4o$
10b6o6b4o8b4o$2b2o6b6o6b4o8b4o$2b2o6b3o3b3o3b4o8b4o$2o2b2o4b3o3b3o3b4o
8b4o$2o2b2o4b3o3b3o7b8o$2b2o9b3o10b8o$2b2o9b3o10b8o$13b3o10b8o!

(inflation may be any size as long as the uninflated pattern is stable)
EDIT: fun fact, a 3x3 inflated tub evolves into a tub

Code: Select all

x = 9, y = 9, rule = B3/S23
3b3o$3b3o$3b3o$3o3b3o$3o3b3o$3o3b3o$3b3o$3b3o$3b3o!

[hotcrystal0]

Snowflake evolves from the traffic light in B3-qy4e/S23-c4yz, and is reasonably common:

Code: Select all

x = 3, y = 2, rule = B3-qy4e/S023-c4yz
3o$bo!

Bakery also evolves into a nice p2:

Code: Select all

x = 5, y = 5, rule = B3-qy4e/S023-c4yz
2b3o$bo2bo$o3bo$bobo$2bo!

Unsurprisingly, weird still lives are more common, but otherwise it's not too interesting.

Taking off S3n makes it more common:

Code: Select all

 x = 77, y = 76, rule = B3-qy4e/S023-cn4yz
6bo4b3o3bob2ob2obob4o2b2obo3b2ob3o2b3o2bo2bob3o2bo2bob3o2b4o$2b3obo2b
o3bob4o2b2obob5obob3o2bo3b3obobobob3o3b2ob2o2b6o3b2o$2ob2o2bo2b5obobo
bob2o4bob2ob2obo2bo2bo3b4o4b2o4b2o2b3o2b2obo2bo$2o2b2o2b2obo3b2obo2bo
b4o2bob5obob4obobo5b2o2bobo2bo2bo2b2obo3b3o$b3o2bo5bo3b2o2bo2bo2bobo2b
obobob2o2b4o2bob3obo2b2ob4ob2o3b5o$5o3b2o6bo2bobo2b2ob6o2b3ob3o2b2o3b
obob2obobob5o2bo2bo4b2o$b2o3b5o2b3ob3o6b5o2bo2b2ob2o2bobo2b2o4bo7b2ob
o2b2ob4o$2b4obo2bobo5bo2b3obob3o2b2ob2ob5o4bo2bob2o2b3o3b3ob4o4bobo$b
obo3bobob2o3bo2b3obo2b5obo2b5o2b2ob2obo2b2o3bobo2b2obo4b2o2bo$o2bob3o
bo3bobob3obo2bobob2obo5bo2bob3o3bo2bo2b2o2bob3o2bo2bobo2bo2bo$2o2b3o3b
o3bob2o2b2o2b3ob2o2b3ob4obo5bob2obo3b2ob4ob2o6bobobo$2bob10ob2obo3b3o
3bob2o2b2obobo4b6o9b5o4b2ob2o$obobob2obob3ob3o4b4obo3bob2ob5ob2ob2o5b
4o6b3obo2bo2b2ob2o$2b4o3bobo3bob3obob2o2b2obo5bo3b7o2b3o3bo2bo3bob3o4b
obob2o$5bob2o2bo3bo2b3ob2ob2o5bo3b3o8b2o5b2obobob2o3bo3b2o2bobo$obo2b
o3b2o2bo4bo2bobob2ob2ob2ob2o2bo2bob3o2b7o3bobobo4b3obobobo$3b9ob2o2bo
bobob2obo6b3o2bo3bo9b9o3bobo3bo2bo2bo$4bob2o2b2obobobobo7bob2obo2b3ob
ob2o2b2o2b2obobobobo3bo3b4ob3ob2o$obob2o2bobo4bo4b3o2b3o2bobo2bo3b4o2b
o5bob3o3bo5b2ob2o4b2o$b2o2bo2b2o3bobo3bo2bo3bob2o2b3ob2ob4o5bob2ob7o4b
o2b3o2b4o$b3obob5o3b5o2bo2bobobobo3b2o3b4o3bo2b6ob6o3b2ob5o2bo$5b2obo
3b4o3b4o3b4ob2o4bo3bo2b4obo10bob3obo4b3o$obo3b4ob2obob2o4bo2b2o4b4o2b
6obob3ob2o2b2obob2o2bobob2obob2o2bo$3obobobob6o2b2o4bob2ob6o3bo3bo3bo
bobo4b3obobo2b3o3bo3bo$5b4o4bo2bo2bob3o4bobo2b2obo8b4o2bobo4b2ob2o3bo
b3o2bo$3o2bo3bob2o3b2ob3o2b2o3b2obobo2b3obo2bobob2o2b3o2bobo2b2o2bo3b
4ob2o$o4b3o6b2ob2obo2bob2obobob3o9b2o3bobob4obobob4ob3ob2o2bo$4bobo3b
5o2b3obo5bo2bo3b2ob2o2b3ob3o2bo2b2ob2ob3o2b2o2bobobob3o$bo2b2o2bo5b5o
3b2obobob2obo4bo2bobo9b2ob4o3bo2bob4o2b2obo$o2b2o2bo3b7obobob3o4bob4o
bo2b3obo3bo2b2o5bobobobo2bobo4b3o$b2obobobo3bob4o2bob2ob4o2b2o2bobob2o
b2o3b3obobob2o7b4ob3ob4o$b2obo2bo3b3o2bo2bo2bo2bo3b2ob4ob2ob3o2b5o2b2o
3b2ob3ob2obob3o3bo$obob4o6bo2b2o2bo4bob4o7b3o3b2o2b2o2bobo4bo2bo2bob3o
2bo2bo$5o3b2obob2obo2bo2b6obo4bobo2bobobobo2bobobob6ob2obob5obo3bo$bo
b4obob2o3b2o3bobobo2bo2b3o3b5o2bo2b2o5b4obo3bo5bob3obobo$6ob2o4bo3b2o
bobo4bobo2bobo2b2o2b4obobo3bo2b4o3b3obob4ob2obo$bo2bo2b2obob5ob3o2b3o
3bobo2bo2bobobob2ob3ob6o4b2o2b3o2b2o3b3o$5bo3b4obob3ob2o6b3ob2ob2obo2b
ob5ob2obo2bo4b2obo2b4o2b3obo$2b2obob2o3bob3ob3o4bo3bob3ob3o2bob3o3b3o
2b5o2b2ob7o5bo$ob2o5bo2bob2ob7obob3o2b3obob2o2bo7b4ob2o4b2o2bobob2obo
b3o$3o3bo4b2ob2obo4bobo2b2o3bobob2o2bo2bo2b3o3bo3b6o2b2ob4o2bo2bo$3o2b
o2bo2b2obo2b4o5bob4ob2o4b2o4bo2bo2b3ob7o3b2ob2obob2o$bo3bobo2bo4bobo5b
obob4ob2ob3o2b3obob4obobobo2bob4obob2o4b2obo$o2bobobo3bo2bobobo2b2obo
bobo2bo3b5o3bob2obobobob2obob2ob2o3bobob2o$b2ob2obob3o4bo2bob7obob3ob
2obob4obo2bo2bobo2b5o4b4ob2o2bobo$ob2o5bo3b2o4b3o3bob2ob4o2bob3o5b4o5b
o2b2o3b4o2bob4obo$3obo2bob3o2b2o3b11ob8o2bobobo3bob2ob5obob2o2bo2b2ob
3obo$bobobo4bob2o3bo2bob2obo4bob2obo3b4o2bo2b3ob2o2b2ob2o3b3o2b2obobo
$ob4ob2o2bob4o4bob2o3b3o2b3o3bo2bob2ob3obob5o2b3o2bobobob2obobo$2b3o4b
o5b6o2bo2bobo5b3o3bobo3b4ob2o2bo2bo2b2o3b3ob4ob2o$4o4bobo4b3o2bo2bo2b
ob2o2b2o2bob2ob5o5b2o6bobobob4ob4o2bo$b2o3bo4bobobo3b4obo2bob2o2bo2b6o
2b3o4bobob4obobo2bobobobobo$3obobob2ob5o3bo3bob2o3b2o3b2ob2ob3obob11o
4b3ob2obo$obo3bob2ob2ob2ob2ob2obob2o6bobobo6b2o5bobo2bobo4bo5b4ob2o$o
2bobo2b2o2b3ob3o3bob4o4b2obo2b4o2bo3bo2b4ob2o2bo6bob4ob3o$2o3bobo2b2o
b3obob3o4b2o2bob2o4b3o2b2o5b5obobobo3b8o3bo$3obo2b4ob5obo3b2o5b4o2bob
5obob3ob2o2bobo2b3ob6o3b2ob2o$5bo2bo3b2o5bo2bo2bobobob10obob2obob2ob2o
3bobobobo3bo2bob5o$2b2o5bo3bo2b2o2bob2ob2o5b3o2bob3o3b2obo3b2o2b7o2b2o
b2obo2bo$ob2o2b3o5b4o2bo2b2obobob2o2bo3bo2bobob5o2bobob2obob3o2bo9bo$
2bo2bo5bob3o2b7o3bob2o2bob2o2bob3o2bo6b2ob2o2bobob3o2b2ob3o$b2o3b2ob3o
2bo3b3obob5ob2o4bob2ob3obob3obo3b2o2b2obo3b2o3bobo$bob2obo6bo3bob4o2b
o7b2o2b2obo3b7ob2o3bo2bobo2bo2bobo2bobo$bo4bo2b9o3bobob2obo7b4o4bobo2b
3ob3o2b2obo3bo2b2ob3ob2o$b2ob2obo2b3obo3b4o2b2o4bo2bo4bo2b4o2b2obobo3b
6obo7bobo$b2ob3obo2bo3bo2b2ob2ob2obo4bobobo2b2o2bob2o3b2obob2o2bo3bob
ob3o2bo2b2o$2bo5bo2bo2b6o3b9obobo2bob5obob9o3b4obo4b2ob2o$2o2bobo2bob
obo2b3ob2o5bob4obo4bo3bo2bo2bo2b2ob3o2b3ob5o2bobob2o$b3o2b2obobobob5o
2bo3b6obob3o2bob2o2bo4bo4b2ob2ob2o3b4o4bo$ob7ob3obo3bo2bo3bo3b4ob3o2b
ob4obo3bo3b3ob2o3b3o6b2o2bo$3obo2bob2o2bobob4o4bo2bobo4b3obo4b4o4b2ob
3o3bob3o5b2o3bo$3bob4ob5ob3ob3o3b2obo3b3o4b2obo2b2ob2ob3o3b4o3b3obo4b
3o$ob3o3bo4b3o3b6obo2bobo2b3obo2bobobo3b2o2bo3bobobobobobo2b3obo$3obo
3bob2o2bob3ob3o4b2o5b3o4b8o6bo4bobob4o2b4obo$ob6o2b2obo2bo2bo2b5o5b3o
4bobo5b2ob4o4b5obo2bobobob3o$obob4obo2b4o2bo2b2ob3o2b8o2b2o5b3obo4bo2b
3obobob2obo2bob2o!

[iddi01]

Here's a challenge that i wanted to post a long time ago:

Make a multistate von Neumann neighborhood rule, which behaves identically to CGoL when step size is set to n.

This is my failed attempt with n = 3 (i stopped here due to landing on a rule with lots of types of oscillators):

Code: Select all

#C [[ STEP 3 ]]
x = 221, y = 48, rule = VNlife
9$216.A$216.A$216.A$216.A$199.A16.A$184.A14.A16.A$169.A14.A14.A16.A$
131.A23.A13.A14.A14.A16.A$131.A11.A11.A13.A14.A14.A16.A$6.A2.4A.A3.A
112.A11.A11.A13.A14.A14.A16.A$5.A.2A.A2.A3.A4.A2.4A.A3.A96.A11.A11.A
13.A14.A14.A16.A$7.A.A2.A.2A3.A.A.2A.A2.A3.A84.A12.A11.A11.A13.A14.A
14.A16.A$7.A2.A5.2A2.A2.A.A2.A.2A3.A60.A10.2A9.A12.A11.A11.A13.A14.A
14.A16.A$7.A.3A4.A.A4.A2.A5.2A2.A30.A7.2A9.A9.A9.A2.A9.2A22.A11.A13.A
14.A14.A16.A$8.A.A3.A.A.3A2.A.3A4.A.A32.A6.A.A7.5A7.2A8.A2.A33.A11.A
13.A14.A14.A16.A$6.3A3.A6.2A3.A.A3.A.A.3A14.2A14.A7.2A19.A10.2A$5.2A.
A.3A3.A.A3.3A3.A6.2A14.A5.3A7.A$6.A.2A.2A.A2.A3.2A.A.3A3.A.A$7.A2.A.A
7.A.A.2A.2A.A2.A$5.2A.A.4A.A.A.A3.A2.A.A7.A$6.3A2.A.3A.2A.3A.A.4A.A.A
.A$5.A.2A.A2.2A.5A.3A2.A.3A.2A.A$6.6A2.A2.A3.A.2A.A2.2A.5A25.2A79.5A$
5.4A2.2A2.3A2.A.6A2.A2.A29.2A78.3A.A$6.2A4.2A.A.A3.4A2.2A2.3A2.A43.3A
48.A.A9.2A.2A$22.2A4.2A.A.A46.A.A29.3A16.A.A9.A.3A$80.A.A29.A2.A15.3A
$80.2A31.2A3$97.A2.A64.3A$97.4A61.A.2A2.A$161.9A2$161.9A$164.A.A.A$
163.4A.A!

[confocaloid]

0: The number of False statements is prime
1: All of these statements are false
2: There is a composite number of false statements
3: The number of false statements before this one is prime
4: The number of true statements is prime

0: The number of False statements is prime - TRUE
1: All of these statements are false - FALSE
2: There is a composite number of false statements - FALSE
3: The number of false statements before this one is prime - TRUE
4: The number of true statements is prime - TRUE

Statement 1 cannot be true. If it were true, it would contradict itself. Thus, statement 1 is false, and at least one of 0, 2, 3, 4 must be true.
Now let us look at statement 3. Assume it is true. Then, to satisfy it, one or both of statements 0 and 2 are false. If both 0 and 2 are false, the number of false statements must be 0 or 1, which is a contradiction. Thus, exactly 1 of these two statements are true, and statement 3 is true.
We know now that one of statements 0, 2 is true, and statement 3 is also true. Thus, statement 4 is true, making the number of true statements 3.
Now, we can see easily that statement 2 is false, and statement 0 is thus true.

I think there is also an unique stable assignment if every statement is replaced by its negation:

• 0: the number of false statements is not prime
• 1: not all of these statements are false
• 2: there is a non-composite number of false statements
• 3: the number of false statements before this one is not prime
• 4: the number of true statements is not prime

I did not find any periodic assignments or any other stable assignments.

Code: Select all

answer below






















False, true, true, true, false.