HR1D (1-Dimension Rulespace)

[Ohhhhhhhhh]

Sorry but I can’t change the topic’s name, and this is definitely not new. Can any editors help?
————— ————— ————— ————— ————— ————— ————— —————
Here’s some explanations on this rulespace:
as most of you know, the Rule 110 is a 1D rule, but all 1D rules with range 1 will either explode or die out because of the required birth of the cells. So why not - or probably nobody - search about Higher-Ranged 1-Dimension rules? They certainly can be chaotic, and here’s my few chaotic ones:
“B23/S24/R2HR1D”:R2,C2,S14,24,B10,15:T1000,10
“B24/S2/R2HR1D”:R2,C2,S14,B10,20:T1000,10
“B24/S13/R2HR1D”:R2,C2,S9,19,B10,20:T1000,10
The rule’s name can’t be used currently, because I don’t know how to make a ruletable. So I used the HROT rulespace with teris instead, and they will work well unless you turn the length or height to any number lower than the range of the rule.
These rules have oscs and spaceships, and the second one has an infinite growth like this:
111011001011100000……
(Unfortunately I found that they don’t have any still lives because they’re impossible.)
We can certainly find more about them. Happy and Relaxed for 1 Day, today!
Well that’s a bad joke for the capitals.

[LaundryPizza03]

There's a standard notation for all one-dimensional rules with any neighborhood and number of states. Assuming k states numbered 0 to k-1 and a neighborhood with range r on either side of the central cell, the rule is assigned an integer R with k^(2r+1) digits. For 0 ≤ i < k^(2r+1), we assign the neighborhood configuration given by writing i in base k and zero-padding, with the ones digit at the right end, and the ith digit of R is the next state of the central cell. So, for example, rule 110 is defined as:

Code: Select all

x = 54, y = 11, rule = B/S012345678History
.3B5.A6.A5.3B5.A6.A6.A5.3B$B3.B3.2A5.2A4.B3.B3.2A5.2A5.2A4.B3.B$B2.2B
4.A6.A4.B2.2B4.A6.A6.A4.B2.2B$B.B.B4.A6.A4.B.B.B4.A6.A6.A4.B.B.B$2B2.
B4.A6.A4.2B2.B4.A6.A6.A4.2B2.B$B3.B4.A6.A4.B3.B4.A6.A6.A4.B3.B$.3B4.
3A4.3A4.3B4.3A4.3A4.3A4.3B3$.3A4.2AB4.ABA4.A2B4.B2A4.BAB4.2BA4.3B$2.B
6.A6.A6.B6.A6.A6.A6.B!

The rules you defined in the OP as B23/S24/R2HR1D and B24/S2/R2HR1D, which have k=2 and r=2 for 32 different neighborhood configurations, would be respectively denoted as rules 2540596872 and 426141320, which you can verify yourself by carefully inspecting the transition charts below:

Code: Select all

#C Transitions of B23/S24/R2HR1D
x = 54, y = 14, rule = B/S012345678History
5B2.4BA2.3BAB2.3B2A2.2BA2B2.2BABA2.2B2AB2.2B3A$2.B6.B6.B6.A6.B6.B6.B
6.A3$BA3B2.BA2BA2.BABAB2.BAB2A2.B2A2B2.B2ABA2.B3AB2.B4A$2.B6.A6.A6.A
6.B6.A6.A6.B3$A4B2.A3BA2.A2BAB2.A2B2A2.ABA2B2.ABABA2.AB2AB2.AB3A$2.B
6.A6.A6.A6.B6.A6.A6.B3$2A3B2.2A2BA2.2ABAB2.2AB2A2.3A2B2.3ABA2.4AB2.5A
$2.A6.A6.A6.B6.A6.B6.B6.A!

Code: Select all

#C Transitions of B24/S2/R2HR1D
x = 54, y = 14, rule = B/S012345678History
5B2.4BA2.3BAB2.3B2A2.2BA2B2.2BABA2.2B2AB2.2B3A$2.B6.B6.B6.A6.B6.B6.B
6.A3$BA3B2.BA2BA2.BABAB2.BAB2A2.B2A2B2.B2ABA2.B3AB2.B4A$2.B6.A6.A6.B
6.B6.A6.A6.B3$A4B2.A3BA2.A2BAB2.A2B2A2.ABA2B2.ABABA2.AB2AB2.AB3A$2.B
6.A6.A6.B6.B6.A6.A6.B3$2A3B2.2A2BA2.2ABAB2.2AB2A2.3A2B2.3ABA2.4AB2.5A
$2.A6.B6.B6.A6.A6.B6.B6.B!

I can see, however, why you are advancing a HROT-like notation.

[Ohhhhhhhhh]

There's a standard notation for all one-dimensional rules with any neighborhood and number of states. Assuming k states numbered 0 to k-1 and a neighborhood with range r on either side of the central cell, the rule is assigned an integer R with k^(2r+1) digits. For 0 ≤ i < k^(2r+1), we assign the neighborhood configuration given by writing i in base k and zero-padding, with the ones digit at the right end, and the ith digit of R is the next state of the central cell. So, for example, rule 110 is defined as:

Code: Select all

x = 54, y = 11, rule = B/S012345678History
.3B5.A6.A5.3B5.A6.A6.A5.3B$B3.B3.2A5.2A4.B3.B3.2A5.2A5.2A4.B3.B$B2.2B
4.A6.A4.B2.2B4.A6.A6.A4.B2.2B$B.B.B4.A6.A4.B.B.B4.A6.A6.A4.B.B.B$2B2.
B4.A6.A4.2B2.B4.A6.A6.A4.2B2.B$B3.B4.A6.A4.B3.B4.A6.A6.A4.B3.B$.3B4.
3A4.3A4.3B4.3A4.3A4.3A4.3B3$.3A4.2AB4.ABA4.A2B4.B2A4.BAB4.2BA4.3B$2.B
6.A6.A6.B6.A6.A6.A6.B!

The rules you defined in the OP as B23/S24/R2HR1D and B24/S2/R2HR1D, which have k=2 and r=2 for 32 different neighborhood configurations, would be respectively denoted as rules 2540596872 and 426141320, which you can verify yourself by carefully inspecting the transition charts below:

Code: Select all

#C Transitions of B23/S24/R2HR1D
x = 54, y = 14, rule = B/S012345678History
5B2.4BA2.3BAB2.3B2A2.2BA2B2.2BABA2.2B2AB2.2B3A$2.B6.B6.B6.A6.B6.B6.B
6.A3$BA3B2.BA2BA2.BABAB2.BAB2A2.B2A2B2.B2ABA2.B3AB2.B4A$2.B6.A6.A6.A
6.B6.A6.A6.B3$A4B2.A3BA2.A2BAB2.A2B2A2.ABA2B2.ABABA2.AB2AB2.AB3A$2.B
6.A6.A6.A6.B6.A6.A6.B3$2A3B2.2A2BA2.2ABAB2.2AB2A2.3A2B2.3ABA2.4AB2.5A
$2.A6.A6.A6.B6.A6.B6.B6.A!

Code: Select all

#C Transitions of B24/S2/R2HR1D
x = 54, y = 14, rule = B/S012345678History
5B2.4BA2.3BAB2.3B2A2.2BA2B2.2BABA2.2B2AB2.2B3A$2.B6.B6.B6.A6.B6.B6.B
6.A3$BA3B2.BA2BA2.BABAB2.BAB2A2.B2A2B2.B2ABA2.B3AB2.B4A$2.B6.A6.A6.B
6.B6.A6.A6.B3$A4B2.A3BA2.A2BAB2.A2B2A2.ABA2B2.ABABA2.AB2AB2.AB3A$2.B
6.A6.A6.B6.B6.A6.A6.B3$2A3B2.2A2BA2.2ABAB2.2AB2A2.3A2B2.3ABA2.4AB2.5A
$2.A6.B6.B6.A6.A6.B6.B6.B!

I can see, however, why you are advancing a HROT-like notation.

Thanks for you reply, and I'm really expecting if anyone posted in this thread about anything.
The spaceships in "B23/S24/R2HR1D" are these:
11101 c
11011001 c/3 00011011001000->00101010110000->00011111101000
10101011001 c/3 find the stages of it by yourself~

[erictom333]

I have an idea: Adding a new neighborhood, NO (one-dimensional), to the HROT algorithm (which still needs to be supported in Golly). Under standard HROT notation, your rules would be R2/B2,3/S2,4/NO and R2/B2,4/S2/NO.

[Ohhhhhhhhh]

I have an idea: Adding a new neighborhood, NO (one-dimensional), to the HROT algorithm (which still needs to be supported in Golly). Under standard HROT notation, your rules would be R2/B2,3/S2,4/NO and R2/B2,4/S2/NO.

Yeah that’s a brilliant one!
We can search the rule’s patterns first before making this ruletable, and there’s certainly a huge requirement of searching algorithms.

[muzik]

I have an idea: Adding a new neighborhood, NO (one-dimensional), to the HROT algorithm (which still needs to be supported in Golly). Under standard HROT notation, your rules would be R2/B2,3/S2,4/NO and R2/B2,4/S2/NO.

Wouldn't it be better to have a dedicated notation, especially if we're to cover what WolframAlpha provides?

[erictom333]

I have an idea: Adding a new neighborhood, NO (one-dimensional), to the HROT algorithm (which still needs to be supported in Golly). Under standard HROT notation, your rules would be R2/B2,3/S2,4/NO and R2/B2,4/S2/NO.

Wouldn't it be better to have a dedicated notation, especially if we're to cover what WolframAlpha provides?

This notation is more convenient.

[GUYTU6J]

I have an idea: Adding a new neighborhood, NO (one-dimensional), to the HROT algorithm (which still needs to be supported in Golly). Under standard HROT notation, your rules would be R2/B2,3/S2,4/NO and R2/B2,4/S2/NO.

Wouldn't it be better to have a dedicated notation, especially if we're to cover what WolframAlpha provides?

This notation is more convenient.

But hey, Wolfram's notation can describe anisotropic higher-range non-totalistic rules (just like MAP for 2-dimensional 2-state rules, or as in http://www.mirekw.com/ca/rullex_1dbi.html) but yours is only for isotropic and totalistic ones (just like HROT for 2-dimensional 2-state rules, or as in http://www.mirekw.com/ca/rullex_1dto.html)

Frankly, I was unhappy when I saw the thread was created without reviewing any previous works, including but not limited to Stephen Wolfram's or what are in Mirek's Cellebration. This is definitely not the appropriate attitude for (semi-) academic research.

[erictom333]

Wouldn't it be better to have a dedicated notation, especially if we're to cover what WolframAlpha provides?

This notation is more convenient.

But hey, Wolfram's notation can describe anisotropic higher-range non-totalistic rules (just like MAP for 2-dimensional 2-state rules, or as in http://www.mirekw.com/ca/rullex_1dbi.html) but yours is only for isotropic and totalistic ones (just like HROT for 2-dimensional 2-state rules, or as in http://www.mirekw.com/ca/rullex_1dto.html)

While there's nothing wrong with having both, my notation would be much easier to use. It's like how MAP rules technically obsolete all other 2-state non-totalistic rules, nobody uses MAP notation for those because it's easier to use Hensel notation.

[Ohhhhhhhhh]

Thanks for your posts, and I have a few ideas:
1.Why don’t Wolfram post these here? If he didn’t, then I believe it’s OK for having a thread about these. Also non of us have made a ruletable in Golly or in Lifeviewer, so it’s really important to have one such rulespace thread…
2.I don’t think it’s time for quarrel - we can make some algorithms, check the patterns or do some engineering. Just anything except arguing about this topic.
3.I’m going to test my Teris-based pesudo-HR1D patterns, to see if we can post like that.

[Ohhhhhhhhh]

Frankly, I was unhappy when I saw the thread was created without reviewing any previous works, including but not limited to Stephen Wolfram's or what are in Mirek's Cellebration. This is definitely not the appropriate attitude for (semi-) academic research.

Sorry for that, but I can’t see how you did these research. Can you tell me more in PM?

[Yoel]

So why not - or probably nobody - search about Higher-Ranged 1-Dimension rules?

Perhaps. someone already did:

https://www.conwaylife.com/forums/viewt ... 71#p111071

https://www.conwaylife.com/forums/viewt ... 79#p134179

I have an idea: Adding a new neighborhood, NO (one-dimensional), to the HROT algorithm (which still needs to be supported in Golly). Under standard HROT notation, your rules would be R2/B2,3/S2,4/NO and R2/B2,4/S2/NO.

It is sort of supported (emulated by custom neighborhoods) in Golly 4.0. Look above how I did it. Here are a couple of Lisp tools for producing generalized higher-range 1D rule strings:

https://github.com/yoelmatveyev/Fireworld

[muzik]

Thanks for your posts, and I have a few ideas:
1.Why don’t Wolfram post these here?

I'm not entirely sure what this point is supposed to mean. It'd certainly be interesting if he could get in on the action, given his substantial research into early 1D rules, but this question is basically asking why Eric Clapton doesn't give anybody anywhere who asks guitar lessons.

[yujh]

But hey, Wolfram's notation can describe anisotropic higher-range non-totalistic rules (just like MAP for 2-dimensional 2-state rules, or as in http://www.mirekw.com/ca/rullex_1dbi.html) but yours is only for isotropic and totalistic ones (just like HROT for 2-dimensional 2-state rules, or as in http://www.mirekw.com/ca/rullex_1dto.html)

Frankly, I was unhappy when I saw the thread was created without reviewing any previous works, including but not limited to Stephen Wolfram's or what are in Mirek's Cellebration. This is definitely not the appropriate attitude for (semi-) academic research.

VERY VERY VERY STRONGLY AGREE. Just don't think you are the smartest.

[Ohhhhhhhhh]

Certainly nobody’s interested in this.
I tried the third idea and it do works!
And I’m not sure if you appriciate the patterns - or if it’s just nothing to you - and if that’s true I’d better get rid of this.
BTW, I worked on the search but hasn’t completed the program.

[Ohhhhhhhhh]

I’m certainly new to the whole thing compared to you guys.
I’m still a primary school student, so I have little time to search all the lists you gave me.
But I believe my thread will be more generally agreed, acting as a composer to the previous works (Remember I never appriciated, and is a bit unsatisfied with most of the rulespace naming). We don’t need to make a large Wolfram number cause it’s more of a series of computer codes that are too complicated for us to understand or to quickly change, and my definition’s too simple that it can’t contain some of the rulespace.
So I’m more concerned to the PATTERNS, as I said before.
I hope you’ll all understand me.

[Ohhhhhhhhh]

c/2 Partial in R2 B24/S13:

Code: Select all

#CXRLE Pos=-17,-2
x = 18, y = 4, rule = R2,C0,S9,19,B10,20:T2048,4
ob3obobo3b6o$ob3obobo3b6o$ob3obobo3b6o$ob3obobo3b6o!

Anybody can help me finish this?
Also, it seems like such partials can be easily finished by hand, as I built this by hand.

Finally, c spaceship in R2 B24/S13:

Code: Select all

#CXRLE Pos=-6,-2
x = 10, y = 4, rule = R2,C0,S9,19,B10,20:T2048,4
o2b4ob2o$o2b4ob2o$o2b4ob2o$o2b4ob2o!

Edit 1:
I can’t believe I finished this in 2 minutes:

Code: Select all

#CXRLE Pos=-23,-2
x = 24, y = 4, rule = R2,C0,S9,19,B10,20:T2048,4
3o3bob3obobo3b6o$3o3bob3obobo3b6o$3o3bob3obobo3b6o$3o3bob3obobo3b6o!

[GUYTU6J]

I was advertised to go here, but I don't know how to find spaceships manually.
My typical crummy contribution:
(6,0,1)

Code: Select all

x = 140, y = 4, rule = R2,C0,S9,19,B10,20:T140,4
4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob
2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o$4bobob2ob2o2bob6o3b2o4bobob2ob2o
2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o
3b2o$4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4b
obob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o$4bobob2ob2o2bob6o3b2o4bobob2o
b2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob
6o3b2o!

(7,0,1)

Code: Select all

x = 245, y = 4, rule = R2,C0,S9,19,B10,20:T245,4
5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b
2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobo
b2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o$5bob
ob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo
2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o
2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o$5bobob
2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b
4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo
2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o$5bobob2obo
3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b
2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o
2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o!

[Ohhhhhhhhh]

I was advertised to go here, but I don't know how to find spaceships manually.
My typical crummy contribution:
(6,0,1)

Code: Select all

x = 140, y = 4, rule = R2,C0,S9,19,B10,20:T140,4
4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob
2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o$4bobob2ob2o2bob6o3b2o4bobob2ob2o
2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o
3b2o$4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4b
obob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o$4bobob2ob2o2bob6o3b2o4bobob2o
b2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob6o3b2o4bobob2ob2o2bob
6o3b2o!

(7,0,1)

Code: Select all

x = 245, y = 4, rule = R2,C0,S9,19,B10,20:T245,4
5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b
2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobo
b2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o$5bob
ob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo
2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o
2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o$5bobob
2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b
4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo
2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o$5bobob2obo
3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b
2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o
2b2obo2b4o4b2o5bobob2obo3bobobob2o2bo2b2o2b2obo2b4o4b2o!

You can just draw lines behind the spaceship partial (the head are much easier to be found), and see if it goes right. I used this technology to find the c and c/2 spaceship in R2-B24/S13.

[Ohhhhhhhhh]

2c/3 partial failed. The best is below:
......000..00.0.0.0..00.0.0......
Not sure if other heads are possible.
Still searching...

[Ohhhhhhhhh]

Thanks for your posts, and I have a few ideas:
1.Why don’t Wolfram post these here?

I'm not entirely sure what this point is supposed to mean. It'd certainly be interesting if he could get in on the action, given his substantial research into early 1D rules, but this question is basically asking why Eric Clapton doesn't give anybody anywhere who asks guitar lessons.

Well, these 2 questions are probably the same.
Whatever you say, but I’d rather ask you why do I need to search all the pizza places and see them all and do a survey about their costumers before choosing one of them. People can’t get their researches done without any problems.
Despite that, thanks for your reply, and I’ll try better next time.

[Wyirm]

Code: Select all

x = 10, y = 4, rule = R2,C0,S9,19,B10,20:T2048,4
2o4bob2o$2o4bob2o$2o4bob2o$2o4bob2o!

Tada, a probably already known c9! I cannot find mention of this so if there is just point it out.

[Ohhhhhhhhh]

Code: Select all

x = 10, y = 4, rule = R2,C0,S9,19,B10,20:T2048,4
2o4bob2o$2o4bob2o$2o4bob2o$2o4bob2o!

Tada, a probably already known c9! I cannot find mention of this so if there is just point it out.

Wow that's pretty impressive!
Did you found it in a soup?
It's small but high-period, and probably the most common one in this rule...
Whatever, thanks for your reply.

[breaker's glider gun]

tada, a p2!

Code: Select all

x = 8, y = 4, rule = R2,C2,S9,19,B10,20:T2048,4
o2bob3o$o2bob3o$o2bob3o$o2bob3o!

(only thing that didn't just die)

[Wyirm]

Code: Select all

x = 14, y = 4, rule = R2,C0,S9,19,B10,20:T2048,4
5o4b5o$5o4b5o$5o4b5o$5o4b5o!

Another probably already known p22!

Also, I found the c/9 the same way things were done during the creation of gcol. Mapping out random patterns and seeing their evolution. I just got lucky while searching for frontends.