3D, 4D or arbitrary multiD gliders guns

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3D, 4D or arbitrary multiD gliders guns
Has anybody found such things? Has Professor Carter Bays discovered 3D guns? I'd like to know if high dimensional Lifes DID/DO turn out to be UTMs or not.
Re: 3D, 4D or arbitrary multiD gliders guns
Hi,Koiti Kimura wrote:Has anybody found such things? Has Professor Carter Bays discovered 3D guns? I'd like to know if high dimensional Lifes DID/DO turn out to be UTMs or not.
No need for "artillery". All elementary onedimensional cellular automata could be emulated on a sixdimensional euclydean grid using Neumannneighbourhood and only 3 states. I constucted a subgridfinder mixed integer linear programming model and solved with several opensource LP solvers. So there are simple rules in higher dimensions that support arbitrary computations due to Wolfram110.
 A for awesome
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Re: 3D, 4D or arbitrary multiD gliders guns
While you're allowing nonempty backgrounds, B6/S5678 in a cubical 3D Moore neighborhood can emulate CGOL in a twocellwide layer sandwiched (with a layer of empty space on each side) between onecellwide solid planes, and thus can do anything that Life can.Naszvadi wrote:So there are simple rules in higher dimensions that support arbitrary computations due to Wolfram110.
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
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
Re: 3D, 4D or arbitrary multiD gliders guns
Interesting  I hadn't run into that additional "8" before. The old "Life 5766" that Carter Bays investigated seems to have been just B6/S567, and it also allows a sixcellthick sandwich to emulate Conway's Life in the middle two layers.A for awesome wrote:While you're allowing nonempty backgrounds, B6/S5678 in a cubical 3D Moore neighborhood can emulate CGOL in a twocellwide layer sandwiched (with a layer of empty space on each side) between onecellwide solid planes, and thus can do anything that Life can.Naszvadi wrote:So there are simple rules in higher dimensions that support arbitrary computations due to Wolfram110.
If you hunt around, you can find papers from the 1990s about other gliders. Haven't noticed any 3D alien guns yet, though, except for the various trivial cases where a 3D rule emulates a 2D rule that has guns.
 Those two links sure give a sense of the distance between 1990 computing technology and what's available today!
Re: 3D, 4D or arbitrary multiD gliders guns
I thought about similar things about 8 years ago, and realised that it's possible to make the 'bread' of the sandwich finitelysupported. In particular, take the rule:A for awesome wrote:While you're allowing nonempty backgrounds, B6/S5678 in a cubical 3D Moore neighborhood can emulate CGOL in a twocellwide layer sandwiched (with a layer of empty space on each side) between onecellwide solid planes, and thus can do anything that Life can.Naszvadi wrote:So there are simple rules in higher dimensions that support arbitrary computations due to Wolfram110.
B6/S45678
and sandwich a doublethick pattern between two blank layers and two layers of 'bread' resembling this:
Code: Select all
x = 8, y = 12, rule = B6/S4678
b2o2b2o$8o$8o$b6o$b6o$8o$8o$b6o$b6o$8o$8o$b2o2b2o!
We can emulate sixcellthick bilaterallysymmetric B6/S45678 patterns by means of an 8state rule in the obvious way, and therefore run them in Golly.
What do you do with ill crystallographers? Take them to the monoclinic!
Re: 3D, 4D or arbitrary multiD gliders guns
What we would really want is some way to grow the bread at the edges, so that we can implement the unbounded Turing machine, and extend the universality of life to the new rule.

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 Location: Milky Way Galaxy: Planet Earth
Re: 3D, 4D or arbitrary multiD gliders guns
For twolayer CGOL, you only need B6/S57.
Code: Select all
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
Re: 3D, 4D or arbitrary multiD gliders guns
No, because then some live cells will appear outside your two layers and mess everything up.Gamedziner wrote:For twolayer CGOL, you only need B6/S57.

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Re: 3D, 4D or arbitrary multiD gliders guns
Good point. The glider still works, though.Macbi wrote:No, because then some live cells will appear outside your two layers and mess everything up.Gamedziner wrote:For twolayer CGOL, you only need B6/S57.
Code: Select all
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!

 Posts: 24
 Joined: October 13th, 2017, 2:14 am
Re: 3D, 4D or arbitrary multiD gliders guns
How can you give a CA the three kinds of logic gates without guns, I wonder? Would anyone explain the principles outlines to me, a CAology beginner?