B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

For discussion of other cellular automata.
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B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by Apple Bottom » July 30th, 2017, 7:47 am

toroidalet suggested that this rule should get its own thread.

This rule, first proposed by Aidan F. Pierce (A for awesome), has a very cool family of c/(2n+1) spaceships, related to and complementing the c/2n ships that AbhpzTa previously reported in B2c3ae4ai56c/S2-kn3-enq4:
A for awesome wrote:All speeds of the form c/(2n+1), n > 3:

Code: Select all

x = 9, y = 31, rule = B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67
o3bo$4o$o3bo5$o4bo$5o$o4bo5$o5bo$6o$o5bo5$o6bo$7o$o6bo5$o7bo$8o$o7bo!
Now every c/n orthogonal speed is known to exist at the minimal period in a 2-state isotropic rule in the range-1 Moore neighborhood.
So far, all the ships from this up to period 31 have shown up on Catagolue, as well as the period-59 ship -- a remarkable outlier. muzikbike has searched C1, while I have focussed on D2_+1.

There's more interesting stuff on Catagolue beyond the ships, too.
If you speak, your speech must be better than your silence would have been. — Arabian proverb

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » July 30th, 2017, 8:14 am

Don't forget the systematic c/5:

Code: Select all

x = 7, y = 17, rule = B2c3aj4nrt5i6c78_S1c23enr4aet5-iq67
ob2o$2o2bo$ob2o5$o2b2o$3o2bo$o2b2o5$o3b2o$4o2bo$o3b2o!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by Saka » July 30th, 2017, 8:21 am

Why is this even in PATHOLOGICAL

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
boboboooobobobbo$
obbbobobbobboooo$
obbobobobbooobbo$
bbbbbbbobooboboo$
bbbbooooobbboobo$
obbobbobbooboobb$
boobbobobbbooobb$
oobooobobbbobooo$
oboooboboooooobo$
oobbboooobbobbob$
boooboobbbobboob$
bobbobobbbbboobb$
obbobbboboboooob$
boobboboobobobbb$
bobooobbooboobbo$
ooooooobbbboobbo$
bobooobbooboobbo$
boobboboobobobbb$
obbobbboboboooob$
bobbobobbbbboobb$
boooboobbbobboob$
oobbboooobbobbob$
oboooboboooooobo$
oobooobobbbobooo$
boobbobobbbooobb$
obbobbobbooboobb$
bbbbooooobbboobo$
bbbbbbbobooboboo$
obbobobobbooobbo$
obbbobobbobboooo$
boboboooobobobbo!
Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » July 30th, 2017, 9:30 am

Presumably having difficulty separating oscillators, there was a ridiculous pathological in the even speeds rule as well.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by A for awesome » July 30th, 2017, 10:11 am

Code: Select all

x = 7, y = 9, rule = B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67
3bo$2bo2$bobo2bo$o2b3o$bobo2bo2$2bo$3bo!
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

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » July 30th, 2017, 10:15 am

What type of growth is that, exactly? catagolue lists it as a replicator but I'm ever so slightly doubtful of it being one.

I think I recall it being sqrt(t) growth, but might be wrong.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by A for awesome » July 30th, 2017, 10:28 am

muzik wrote:I think I recall it being sqrt(t) growth
I believe it is.
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

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » July 30th, 2017, 11:09 am

p25:

Code: Select all

x = 17, y = 9, rule = B2c3aj4nrt5i6c78_S1c23enr4aet5-iq67
5bo$4bo$2bo$bobobo2b2o5bo$o4b3o2bo3bobo$bobobo2b2o5bo$2bo$4bo$5bo!
Does not seem to be extendable for arbitrary higher periods, unfortunately.

Reduced:

Code: Select all

x = 15, y = 9, rule = B2c3aj4nrt5i6c78_S1c23enr4aet5-iq67
3bo$2bo2$bobo4bo4bo$o2b5o4bobo$bobo4bo4bo2$2bo$3bo!
Actually, I'm an idiot:

Code: Select all

x = 19, y = 31, rule = B2c3aj4nrt5i6c78_S1c23enr4aet5-iq67
3bo$2bo2$bobo4bo4bo$o2b5o4bobo$bobo4bo4bo2$2bo$3bo3$3bo$2bo2$bobo4bo6b
o$o2b5o6bobo$bobo4bo6bo2$2bo$3bo3$3bo$2bo2$bobo4bo8bo$o2b5o8bobo$bobo
4bo8bo2$2bo$3bo!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by BlinkerSpawn » July 30th, 2017, 3:31 pm

A for awesome wrote:
muzik wrote:I think I recall it being sqrt(t) growth
I believe it is.
Let L be the length of the stretcher.
The stretcher only grows once the signal travels its entire length.
Since the signal travels at constant speed, the rate at which the stretcher grows is proportional to 1/L.
dL/dt = k/L
L dL = k dt
(1/2)L^2 = k t
L = sqrt(2k t)
Q.E.D
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » July 30th, 2017, 4:52 pm

All speeds known from soups:

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bbbbbooboboooooo$
obbbobbobboboboo$
booobobooobbobbo$
boooobbbbboobobb$
obbobobobobooooo$
boobbobobobbobbo$
oobbboooobobbooo$
bbbobobbbboooooo$
obbbbbboboobbbob$
bbboobbbobbobobo$
bobbbbbbooooobbo$
oooboobbbboobboo$
oobboboobbobbobb$
bbbooboboooooobb$
bbbobbbbbobbbboo$
booobbobbooooooo$
bbbobbbbbobbbboo$
bbbooboboooooobb$
oobboboobbobbobb$
oooboobbbboobboo$
bobbbbbbooooobbo$
bbboobbbobbobobo$
obbbbbboboobbbob$
bbbobobbbboooooo$
oobbboooobobbooo$
boobbobobobbobbo$
obbobobobobooooo$
boooobbbbboobobb$
booobobooobbobbo$
obbbobbobboboboo$
bbbbbooboboooooo!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bboboooboobbbbob$
bobooobbboobobbb$
obbbobbbbobbooob$
bboobobobboobboo$
obbbbobbbbbboobo$
bbbbobbboboboboo$
ooboobbboboooboo$
bbooobboboboobbb$
bbbbobboobooobbo$
booobooooooooobb$
bbbbobbbooooobbo$
obobbbbbbbbbbbob$
bobbobbbbooboboo$
oooboboooboobbbo$
obooobboobboobob$
boobboboobbobobb$
obooobboobboobob$
oooboboooboobbbo$
bobbobbbbooboboo$
obobbbbbbbbbbbob$
bbbbobbbooooobbo$
booobooooooooobb$
bbbbobboobooobbo$
bbooobboboboobbb$
ooboobbboboooboo$
bbbbobbboboboboo$
obbbbobbbbbboobo$
bboobobobboobboo$
obbbobbbbobbooob$
bobooobbboobobbb$
bboboooboobbbbob!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
boobobooobooooob$
boobboboobbobbob$
bboooboobbbobobo$
bboooobbbbbboobo$
oobobboboooboobo$
oooobobobbbbobbb$
oboooobbooobobbo$
bbooobooobobbboo$
booooobobbbobbbb$
boobbbobboobbboo$
ooooboobbbbbooob$
obbboooooboboooo$
booooobbbooobooo$
bbbboobbboboooob$
bbbobooooobbbooo$
bbbobobobobboobb$
bbbobooooobbbooo$
bbbboobbboboooob$
booooobbbooobooo$
obbboooooboboooo$
ooooboobbbbbooob$
boobbbobboobbboo$
booooobobbbobbbb$
bbooobooobobbboo$
oboooobbooobobbo$
oooobobobbbbobbb$
oobobboboooboobo$
bboooobbbbbboobo$
bboooboobbbobobo$
boobboboobbobbob$
boobobooobooooob!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bbbbboobbooboboo$
bbobobbbbboboooo$
oboooooobobbobbo$
booooboobbbobobb$
oooooboobobbbobb$
oobbbobbboobbooo$
bbooobbobooboobb$
obbobbbbobbbobob$
ooobooobbbbboobb$
obobbbboooobooob$
oboooobobboobobb$
bobobboobbobobob$
bbboobbbbobbobob$
obboooobboooobbo$
obbbboobobooobbb$
bobooboboobboboo$
obbbboobobooobbb$
obboooobboooobbo$
bbboobbbbobbobob$
bobobboobbobobob$
oboooobobboobobb$
obobbbboooobooob$
ooobooobbbbboobb$
obbobbbbobbbobob$
bbooobbobooboobb$
oobbbobbboobbooo$
oooooboobobbbobb$
booooboobbbobobb$
oboooooobobbobbo$
bbobobbbbboboooo$
bbbbboobbooboboo!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bobbobbobboooobb$
ooboobbooooobbbb$
boobooooooobobbb$
bbobbobbbooobbbb$
bobobbbbbbboooob$
oooobbbbbbobboob$
ooobobooooooobbo$
obooooobboboobbo$
oobbbbbooooobobb$
obbbbbbobbbobboo$
obboobbooooobooo$
oobobboboboobooo$
oobooobobboobooo$
obboobbbobbooobb$
bbboooobboobobbo$
boobobbobboooboo$
bbboooobboobobbo$
obboobbbobbooobb$
oobooobobboobooo$
oobobboboboobooo$
obboobbooooobooo$
obbbbbbobbbobboo$
oobbbbbooooobobb$
obooooobboboobbo$
ooobobooooooobbo$
oooobbbbbbobboob$
bobobbbbbbboooob$
bbobbobbbooobbbb$
boobooooooobobbb$
ooboobbooooobbbb$
bobbobbobboooobb!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
boobbbooooobbobb$
oobbboobbbbbobob$
boobbboobooboobb$
oooooobooboobobo$
bbbbbboobooooooo$
oooooboboooooobb$
ooobbobbbbobbobo$
bobooobbboboobbo$
bobbobobboobbbbb$
booobooobbooobbo$
obbbbobbbbbobbbo$
boboobobobbobbbb$
bobbooobbooboobb$
booooooboobooobb$
obbbooobbobooooo$
oobbbobbooboobob$
obbbooobbobooooo$
booooooboobooobb$
bobbooobbooboobb$
boboobobobbobbbb$
obbbbobbbbbobbbo$
booobooobbooobbo$
bobbobobboobbbbb$
bobooobbboboobbo$
ooobbobbbbobbobo$
oooooboboooooobb$
bbbbbboobooooooo$
oooooobooboobobo$
boobbboobooboobb$
oobbboobbbbbobob$
boobbbooooobbobb!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
oobobbobbbboooob$
bbobbooobbobboob$
oooobbbbbbbobobb$
obbooobobbbbbooo$
oboooobooobbbooo$
bbboooobobbobbbo$
bbobbbobbboboboo$
ooobbbbbobbobobb$
boooobobbboobbob$
bbobbbbbbooobbbo$
obbooboooboobbbo$
ooobbbbobboboobo$
oboboobbooobbbbo$
ooobobbooobooobo$
bboobbobboooooob$
obbbobbobbbobooo$
bboobbobboooooob$
ooobobbooobooobo$
oboboobbooobbbbo$
ooobbbbobboboobo$
obbooboooboobbbo$
bbobbbbbbooobbbo$
boooobobbboobbob$
ooobbbbbobbobobb$
bbobbbobbboboboo$
bbboooobobbobbbo$
oboooobooobbbooo$
obbooobobbbbbooo$
oooobbbbbbbobobb$
bbobbooobbobboob$
oobobbobbbboooob!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bbbbbbbobobbooob$
oobboooooboooobb$
obboobbboboboooo$
bobobbbboobobooo$
bobooooboboobbob$
bobbbobobbobobob$
oobbbooboobbboob$
bbboobbbbobooboo$
obboobbobobbobbo$
booooobbobooobob$
obobbooobbbooobb$
bbbbobbobobooobo$
booobbooboobbboo$
oboooboobbobboob$
bbboboobbbbobbbb$
obbbbboboooboboo$
bbboboobbbbobbbb$
oboooboobbobboob$
booobbooboobbboo$
bbbbobbobobooobo$
obobbooobbbooobb$
booooobbobooobob$
obboobbobobbobbo$
bbboobbbbobooboo$
oobbbooboobbboob$
bobbbobobbobobob$
bobooooboboobbob$
bobobbbboobobooo$
obboobbboboboooo$
oobboooooboooobb$
bbbbbbbobobbooob!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
boboobbbbbobbbbo$
oooooobbbooboobb$
ooboooooobbbooob$
bbobobbobbobobbo$
bbbbbbooooooobbb$
obbbbbobboboobbb$
bobobbobooobobbb$
bobobobboobbooob$
oobbbbooobbboboo$
obobobobooooobob$
bobbboooobbbobbb$
bbbobbbobobbbbbb$
bobbooobbooobbbo$
obboboooooobooob$
oboooobobobbbooo$
bboobobboooboobb$
oboooobobobbbooo$
obboboooooobooob$
bobbooobbooobbbo$
bbbobbbobobbbbbb$
bobbboooobbbobbb$
obobobobooooobob$
oobbbbooobbboboo$
bobobobboobbooob$
bobobbobooobobbb$
obbbbbobboboobbb$
bbbbbbooooooobbb$
bbobobbobbobobbo$
ooboooooobbbooob$
oooooobbbooboobb$
boboobbbbbobbbbo!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
obobbboboboooobb$
oooboobobboobobb$
obobbbbboobbboob$
bbooobbobooboooo$
oooboobbbobbbbbb$
obbooboobbooooob$
bobbobooboboobbb$
bbooobobbooobbbo$
bbobbbobbbboooob$
oooooboooboobbbo$
bbobobobboooooob$
boobboobbobbobbb$
bobboobooobobooo$
oobbboboobboobbb$
obbobboobboooooo$
boboobooooobbboo$
obbobboobboooooo$
oobbboboobboobbb$
bobboobooobobooo$
boobboobbobbobbb$
bbobobobboooooob$
oooooboooboobbbo$
bbobbbobbbboooob$
bbooobobbooobbbo$
bobbobooboboobbb$
obbooboobbooooob$
oooboobbbobbbbbb$
bbooobbobooboooo$
obobbbbboobbboob$
oooboobobboobobb$
obobbboboboooobb!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
obobooobobbooobb$
bobboboooooboobb$
bobbboboobobbooo$
bbobbbbooooboboo$
bbobbbbbbooooobb$
oooooboobboboobb$
obbbobooobbbbbbo$
obooobobbbboobbb$
obooboboooboobbo$
bbbooboobobbbbbb$
ooobbobbobbboobb$
oobbbbobooobboob$
oooboobboboobobb$
bobbbobobobbbbob$
obbbobbooooooobb$
booooooobboobbob$
obbbobbooooooobb$
bobbbobobobbbbob$
oooboobboboobobb$
oobbbbobooobboob$
ooobbobbobbboobb$
bbbooboobobbbbbb$
obooboboooboobbo$
obooobobbbboobbb$
obbbobooobbbbbbo$
oooooboobboboobb$
bbobbbbbbooooobb$
bbobbbbooooboboo$
bobbboboobobbooo$
bobboboooooboobb$
obobooobobbooobb!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bobbobbobobooooo$
bbboobooobboobbo$
booooobbobooobbb$
bbooooooobbooooo$
bbbboobooboobobo$
boooooboboooboob$
oobbbboooobobobo$
boobbbbbobbboooo$
bbooobboobooboob$
oboobbboobobboob$
bbbbobooobooobbo$
obooobbbbboobooo$
bboobbbbobbbbooo$
bbbboobbooobobbo$
bbbobbobbobooooo$
boobbbbobobboobo$
bbbobbobbobooooo$
bbbboobbooobobbo$
bboobbbbobbbbooo$
obooobbbbboobooo$
bbbbobooobooobbo$
oboobbboobobboob$
bbooobboobooboob$
boobbbbbobbboooo$
oobbbboooobobobo$
boooooboboooboob$
bbbboobooboobobo$
bbooooooobbooooo$
booooobbobooobbb$
bbboobooobboobbo$
bobbobbobobooooo!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bbooboobboboobbb$
bbbobbobbobbobbb$
obbobbboooobooob$
bobbbbbbobbbobob$
bbbboobboooooooo$
obobbbboobobbobo$
booooooooobobbob$
bbboobobboobbooo$
bbooboobbboobooo$
obobbooobbbbbboo$
bbboooobobboobbo$
booobbbbbbbbooob$
obbbbooobobbbbob$
bbobbooobooooobb$
boobbboboobobooo$
bboooooboooobobo$
boobbboboobobooo$
bbobbooobooooobb$
obbbbooobobbbbob$
booobbbbbbbbooob$
bbboooobobboobbo$
obobbooobbbbbboo$
bbooboobbboobooo$
bbboobobboobbooo$
booooooooobobbob$
obobbbboobobbobo$
bbbboobboooooooo$
bobbbbbbobbbobob$
obbobbboooobooob$
bbbobbobbobbobbb$
bbooboobboboobbb!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
obbobbbbbobbbbbo$
bbobbobobobbbobb$
oobobboooobbobbo$
obobooooboobobbb$
obbobbbooboboobb$
oobbbbooobobbobo$
booooooooboobbbo$
bbobbooooobobbob$
bboooboooobooooo$
bbooobobooboobob$
bboobboobobobbob$
bbooobbbobbobooo$
oooobobbbbbbbooo$
bbbbobobbbbbbbob$
bbooooobbbbobboo$
ooobobbobbboobbo$
bbooooobbbbobboo$
bbbbobobbbbbbbob$
oooobobbbbbbbooo$
bbooobbbobbobooo$
bboobboobobobbob$
bbooobobooboobob$
bboooboooobooooo$
bbobbooooobobbob$
booooooooboobbbo$
oobbbbooobobbobo$
obbobbbooboboobb$
obobooooboobobbb$
oobobboooobbobbo$
bbobbobobobbbobb$
obbobbbbbobbbbbo!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
boobboobbobobooo$
bobobbbobbbbobbo$
bbobbboobobbbbbb$
booobooboooooobb$
obobbobbbbbbbooo$
obobobbooobobobo$
bbbboboboobbbobo$
bbboobboooooooob$
oobbbbboboooboob$
booooobbobobobbo$
obobobooooooobbo$
oobbooobbbobbooo$
obobooooboobbbob$
obobbobbbobobbbb$
oooobboobobbbobo$
obbobooboooooooo$
oooobboobobbbobo$
obobbobbbobobbbb$
obobooooboobbbob$
oobbooobbbobbooo$
obobobooooooobbo$
booooobbobobobbo$
oobbbbboboooboob$
bbboobboooooooob$
bbbboboboobbbobo$
obobobbooobobobo$
obobbobbbbbbbooo$
booobooboooooobb$
bbobbboobobbbbbb$
bobobbbobbbbobbo$
boobboobbobobooo!

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
ooobobbobobbbbbb$
obobbobobbbobboo$
bbooooooobbbooob$
bobbooobbbbobobb$
oboooboooboboooo$
oobbbooobobboobo$
obobboobbbboobbb$
bbobooboboooobbo$
oooobobbbboooobb$
bobooobobboooobo$
obobbobboboboobb$
bbbobbbbbbobbbbo$
obbobobobboboobb$
booobboooobboboo$
bbbbbooooooboobo$
boobbbooobbboboo$
bbbbbooooooboobo$
booobboooobboboo$
obbobobobboboobb$
bbbobbbbbbobbbbo$
obobbobboboboobb$
bobooobobboooobo$
oooobobbbboooobb$
bbobooboboooobbo$
obobboobbbboobbb$
oobbbooobobboobo$
oboooboooboboooo$
bobbooobbbbobobb$
bbooooooobbbooob$
obobbobobbbobboo$
ooobobbobobbbbbb!
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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » July 30th, 2017, 8:28 pm

It appears that the extendable period thing gives the following periods:

25, 51, 85, 127, 177, 235, 301, 375, 457


Searching these on the OEIS brings up no results, so can anyone tell me what's going on exactly?
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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by toroidalet » July 30th, 2017, 8:55 pm

muzik wrote:It appears that the extendable period thing gives the following periods, [...] can anyone tell me what's going on exactly?
The oscillation consists of 2 parts. Part 1: The head goes forward as a sqrt(t) and after x^2 generations, where x is the gap between the head, it takes a linear function of x to move back. The resulting period is therefore quadratic. If you're not sure, here's a proof that the growth is quadratic (over this short span)
It is a theorem that when consecutive terms in a quadratic sequence are subtracted, the differences form an arithmetic sequence. The sequence of differences is:

Code: Select all

26, 34, 42, 50, 58, 66, 74
, and so on. This sequence is y=8x+26. That's why the period growth is quadratic
I'm pretty sure the formula is 3x^2+11x-9, starting with x=2 for the p25. The formula was derived algebraically from the data, after the period growth was determined.
(I would like a proof that it actually is quadratic, not just that the empirical data happens to suggest the quadratic result.)
(more specifically, x refers to the amount of extensions from this phase until it interacts with the tub).

Code: Select all

x = 15, y = 9, rule = B2c3aj4nrt5i6c78/S1c23enr4aet5-iq67
3bo$2bo2$bobo2b2o5bo$o2b3o2bo3bobo$bobo2b2o5bo2$2bo$3bo!
Also, you *really* didn't need to post soups for *all* the natural ship speeds.
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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » July 31st, 2017, 12:52 pm

New natural c/47:

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
obobobboobbboboo$
boobbbboooobbbbo$
bbbbbooboooboobo$
bboboooboboobobo$
oobooobbooobbobb$
obbooboobbbobobb$
booobobbboboobob$
booboooobbobbbbo$
ooobbbboooobbbbo$
oobobbobobbobbbo$
oobobobbobooobbo$
bobbbobooboobbob$
oboooobbobboboob$
ooooobbobbobbobo$
oboboobbbobboobo$
oobobbbbobbbboob$
oboboobbbobboobo$
ooooobbobbobbobo$
oboooobbobboboob$
bobbbobooboobbob$
oobobobbobooobbo$
oobobbobobbobbbo$
ooobbbboooobbbbo$
booboooobbobbbbo$
booobobbboboobob$
obbooboobbbobobb$
oobooobbooobbobb$
bboboooboboobobo$
bbbbbooboooboobo$
boobbbboooobbbbo$
obobobboobbboboo!
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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » July 31st, 2017, 3:56 pm

yl24:

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
obobbobboooobooo$
obobbooboooobobo$
bbbbbbbooboobbbo$
oooooobobobooobb$
obobbobboobbbbbb$
boooboobboobboob$
bboobbbbbobooobo$
oooooobooobbbbbo$
boobbooobbobboob$
oboboobbbobooobb$
bboboobobobbbboo$
booobobbbooobobo$
bobbbobbobbobboo$
oboobbbobbbbboob$
boooboobbooobbbo$
boboooobobooboob$
boooboobbooobbbo$
oboobbbobbbbboob$
bobbbobbobbobboo$
booobobbbooobobo$
bboboobobobbbboo$
oboboobbbobooobb$
boobbooobbobboob$
oooooobooobbbbbo$
bboobbbbbobooobo$
boooboobboobboob$
obobbobboobbbbbb$
oooooobobobooobb$
bbbbbbbooboobbbo$
obobbooboooobobo$
obobbobboooobooo!
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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by Apple Bottom » July 31st, 2017, 4:51 pm

muzik wrote:New natural c/47:
Not new as such, it's part of the same known family...
muzik wrote:yl24:
...and this is just a double-ended variant of the common yl8 where the middle part connecting the two halves is oscillating at period 12.
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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » August 1st, 2017, 10:44 am

c/41:

Code: Select all

x = 16, y = 31, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
bboobbbbbbobobbb$
oobbbbobobbobobo$
boooooboooobbbob$
obbbobbooobbobob$
ooobbbbobbobbbbb$
boboobobbbbobooo$
oobbbooboobbbbbo$
oboboobobooboobb$
obobobbbobbbbbbb$
booobobboboooobb$
bbbboooobbobbbbo$
oooobobooobboboo$
obbobboobboooboo$
oobooobbbbboooob$
bbobobooboobooob$
ooobbobbbooboobb$
bbobobooboobooob$
oobooobbbbboooob$
obbobboobboooboo$
oooobobooobboboo$
bbbboooobbobbbbo$
booobobboboooobb$
obobobbbobbbbbbb$
oboboobobooboobb$
oobbbooboobbbbbo$
boboobobbbbobooo$
ooobbbbobbobbbbb$
obbbobbooobbobob$
boooooboooobbbob$
oobbbbobobbobobo$
bboobbbbbbobobbb!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67

Post by muzik » August 1st, 2017, 12:16 pm

Another c/59 has appeared:

Code: Select all

x = 16, y = 67, rule = B2c3aj4nrt5i6c78/S1-e23enr4aet5-iq67
3obo2bobo$obo2bobo3bo2b2o$2b7o3b3o$bo2b3o4bobo$ob3ob3obob4o$2o3b3obo2b
2obo$obo2b2o4b2o$2bob2obob4o2bo$4obo4b4o$bob3obo2b4obo$obo2bo2bobob2o$
3bo6bo4bo$o2bobobo2bob2o$b3o2b4o2bob2o$5b6ob2obo$b2o3b3o3bob2o$5b6ob2o
bo$b3o2b4o2bob2o$o2bobobo2bob2o$3bo6bo4bo$obo2bo2bobob2o$bob3obo2b4obo
$4obo4b4o$2bob2obob4o2bo$obo2b2o4b2o$2o3b3obo2b2obo$ob3ob3obob4o$bo2b
3o4bobo$2b7o3b3o$obo2bobo3bo2b2o$3obo2bobo6$o4bobo2b2obo$o2bobo4bo4bo$
3obobo2b2o2bobo$bo2bo2bobo2b3o$6obobobo$4b6obob3o$o7b2ob3obo$ob5o2bob
5o$2ob5obo3b3o$3bo3bobob3o$2bobob2obob3obo$b3o3b3o2b3o$2obo2b2ob2obo$
2b6o2bo2b3o$2o2b2o2bo2b4o$ob5o2bo2b2obo$2o2b2o2bo2b4o$2b6o2bo2b3o$2obo
2b2ob2obo$b3o3b3o2b3o$2bobob2obob3obo$3bo3bobob3o$2ob5obo3b3o$ob5o2bob
5o$o7b2ob3obo$4b6obob3o$6obobobo$bo2bo2bobo2b3o$3obobo2b2o2bobo$o2bobo
4bo4bo$o4bobo2b2obo!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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