Rules in which every spaceship speed is possible

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Pteriforever
Posts: 37
Joined: April 10th, 2013, 9:43 pm

Rules in which every spaceship speed is possible

Post by Pteriforever » April 21st, 2013, 11:34 pm

I was wondering if this is a thing people do or not.

So, I put together this 4-state rule:

Code: Select all

n_states:4
neighborhood:Moore
symmetries:none
var a={1,2}
var ss={0,1,2,3}
var tt={0,1,2,3}
var uu={0,1,2,3}
var vv={0,1,2,3}
var ww={0,1,2,3}
var xx={0,1,2,3}
var yy={0,1,2,3}
var zz={0,1,2,3}
0,ss,tt,uu,vv,1,2,ww,xx,2
0,ss,tt,uu,1,2,vv,ww,xx,1
a,ss,tt,uu,vv,ww,xx,yy,zz,0
0,ss,tt,1,uu,vv,ww,xx,yy,1
0,ss,tt,uu,vv,ww,xx,2,yy,2
0,ss,tt,uu,1,3,vv,ww,xx,3
0,ss,tt,uu,vv,3,2,ww,xx,3
0,ss,tt,uu,vv,1,3,ww,xx,2
0,ss,tt,uu,3,2,vv,ww,xx,1
0,ss,tt,uu,vv,3,1,ww,xx,3
0,ss,tt,uu,2,3,vv,ww,xx,3
3,ss,tt,a,uu,vv,ww,xx,yy,0
3,ss,tt,uu,vv,ww,xx,a,yy,0
In which spaceships are possible in every rational speed c ≥ s > 0. I've put together a set of examples here to illustrate how the rule works:

Code: Select all

#CXRLE Pos=-11,-10
x = 215, y = 1, rule = pteriforeverspaceships
CABABAB.C6.CBABAB.C10.CABAB.C9.CBAB.C7.CBABAB2.C7.CAB.C5.CBAB2.C5.CAB
AB3.C4.CB.C7.CBAB4.C4.CAB3.C6.CB2.C4.CAB5.C4.CB3.C3.CB4.C5.CB5.C5.CB
6.C!
So, I'm curious as to if this is something which has been tried before and what results have been achieved?

EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Re: Rules in which every spaceship speed is possible

Post by EricG » April 22nd, 2013, 1:06 pm

This is great! Nice job! I like that a randomly filled in field results in spaceships of various speeds. For anyone just casually reading, the idea here is that a reflector advances one cell along with the reflected ship -- two such reflectors make a shuttle which is also a spaceship. (Edit: And colliding ships can reflect and advance as well!)

It would be interesting to see a fleshed out version of this rule in which the spaceships can travel in all four (or eight) directions (in other words, an isotropic version of the rule).

Leaving aside the "every possible speed" attribute, I've seen rules in which commonly occurring sparky oscillators reflect a ship and also move over, but I haven't found one in which everything worked out to make a traveling shuttle. Does anyone know of examples of this?

One place to look: in the "9:43 at Knight" rule and its related rules (viewtopic.php?f=11&t=861), there are seemingly thousands of potentially useful collisions between spaceships and the ubiquitous spinner oscillator. Some of the collisions result in a reflected spaceship and a spinner which moves over.

Hmmm, this was in my notes as a candidate:
x = 62, y = 75, rule = 237/34578/4
9$29.B$28.C.C$26.C5.C$24.2A2.BCB2.2A$24.AB.B3CB.BA$24.A4BA4BA$25.A2B.
B.2BA$26.A2B.2BA$27.2AB2A$29.A31$21.C$17.C2A$17.A2B2.C$18.A2BA$19.3A!

Sorry for the diversion if your focus was "every possible speed". Again, nice rule.
Last edited by EricG on April 22nd, 2013, 2:18 pm, edited 1 time in total.

EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Re: Rules in which every spaceship speed is possible

Post by EricG » April 22nd, 2013, 1:33 pm

Oh, I see - the spinner in my example reverses direction, which complicates things! Anyone have a better example?

EricG
Posts: 199
Joined: August 19th, 2011, 5:41 pm
Location: Chicago-area, USA

Re: Rules in which every spaceship speed is possible

Post by EricG » April 22nd, 2013, 2:55 pm

Pteriforever,

You might also like this thread:
"Weird speeds ships" by Wojowu
viewtopic.php?f=11&t=821

bprentice
Posts: 920
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

Re: Rules in which every spaceship speed is possible

Post by bprentice » April 22nd, 2013, 9:00 pm

Beautiful!

I used a similar approach for Knight Ships. Patterns are included in Rule 015 of my Knight Ship Guns collection posted here:

viewtopic.php?f=11&t=1003

Brian Prentice

Pteriforever
Posts: 37
Joined: April 10th, 2013, 9:43 pm

Re: Rules in which every spaceship speed is possible

Post by Pteriforever » April 22nd, 2013, 10:31 pm

EricG wrote:Pteriforever,

You might also like this thread:
"Weird speeds ships" by Wojowu
viewtopic.php?f=11&t=821
That's really cool. I like their structure, and how their speed is influenced by their size like that.

There's probably some reaction out there which could both shift something and reflect a spaceship in a useful manner...

Not really sure how I'd go about extending it to multiple directions, other than the obvious solution of adding six more states for extra spaceships.

Sphenocorona
Posts: 549
Joined: April 9th, 2013, 11:03 pm

Re: Rules in which every spaceship speed is possible

Post by Sphenocorona » April 22nd, 2013, 11:09 pm

I've thought of something really similar to this before but had no idea how it might be achieved. Now that part of it has been, I'd like to post the other part that wasn't covered here: what about rules where every spaceship direction is possible? (ingoring universal constructor ships like Gemini in standard life where it's trivial to prove that such is possible, but not to provide an example)
What I mean is that there is either enough spaceship slopes to combine them into new ones or some simple example like the speed one here. Obviously they must be rational slopes.

bprentice
Posts: 920
Joined: September 10th, 2009, 6:20 pm
Location: Coos Bay, Oregon

Re: Rules in which every spaceship speed is possible

Post by bprentice » April 23rd, 2013, 1:12 am

Rule 018 in my Knight Ship Guns collection mentioned above supports ships that move in 24 different directions, has guns for each of them and uses only 3 states.

Brian Prentice

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gameoflifemaniac
Posts: 1242
Joined: January 22nd, 2017, 11:17 am
Location: There too

Re: Rules in which every spaceship speed is possible

Post by gameoflifemaniac » June 28th, 2017, 1:16 pm

Here are all a/b speed spaceships in this rule with a≤b≤32. Some speeds might repeat.

Code: Select all

x = 1088, y = 63, rule = pteriforeverspaceships
CBC31.CABC30.CBABC29.CABABC28.CBABABC27.CABABABC26.CBABABABC25.CABABA
BABC24.CBABABABABC23.CABABABABABC22.CBABABABABABC21.CABABABABABABC20.
CBABABABABABABC19.CABABABABABABABC18.CBABABABABABABABC17.CABABABABABA
BABABC16.CBABABABABABABABABC15.CABABABABABABABABABC14.CBABABABABABABA
BABABC13.CABABABABABABABABABABC12.CBABABABABABABABABABABC11.CABABABAB
ABABABABABABABC10.CBABABABABABABABABABABABC9.CABABABABABABABABABABABA
BC8.CBABABABABABABABABABABABABC7.CABABABABABABABABABABABABABC6.CBABAB
ABABABABABABABABABABABC5.CABABABABABABABABABABABABABABC4.CBABABABABAB
ABABABABABABABABABC3.CABABABABABABABABABABABABABABABC2.CBABABABABABAB
ABABABABABABABABABC.CABABABABABABABABABABABABABABABABC2$CB.C30.CAB.C
29.CBAB.C28.CABAB.C27.CBABAB.C26.CABABAB.C25.CBABABAB.C24.CABABABAB.C
23.CBABABABAB.C22.CABABABABAB.C21.CBABABABABAB.C20.CABABABABABAB.C19.
CBABABABABABAB.C18.CABABABABABABAB.C17.CBABABABABABABAB.C16.CABABABAB
ABABABAB.C15.CBABABABABABABABAB.C14.CABABABABABABABABAB.C13.CBABABABA
BABABABABAB.C12.CABABABABABABABABABAB.C11.CBABABABABABABABABABAB.C10.
CABABABABABABABABABABAB.C9.CBABABABABABABABABABABAB.C8.CABABABABABABA
BABABABABAB.C7.CBABABABABABABABABABABABAB.C6.CABABABABABABABABABABABA
BAB.C5.CBABABABABABABABABABABABABAB.C4.CABABABABABABABABABABABABABAB.
C3.CBABABABABABABABABABABABABABAB.C2.CABABABABABABABABABABABABABABAB.
C.CBABABABABABABABABABABABABABABAB.C2$CB2.C29.CAB2.C28.CBAB2.C27.CABA
B2.C26.CBABAB2.C25.CABABAB2.C24.CBABABAB2.C23.CABABABAB2.C22.CBABABAB
AB2.C21.CABABABABAB2.C20.CBABABABABAB2.C19.CABABABABABAB2.C18.CBABABA
BABABAB2.C17.CABABABABABABAB2.C16.CBABABABABABABAB2.C15.CABABABABABAB
ABAB2.C14.CBABABABABABABABAB2.C13.CABABABABABABABABAB2.C12.CBABABABAB
ABABABABAB2.C11.CABABABABABABABABABAB2.C10.CBABABABABABABABABABAB2.C
9.CABABABABABABABABABABAB2.C8.CBABABABABABABABABABABAB2.C7.CABABABABA
BABABABABABABAB2.C6.CBABABABABABABABABABABABAB2.C5.CABABABABABABABABA
BABABABAB2.C4.CBABABABABABABABABABABABABAB2.C3.CABABABABABABABABABABA
BABABAB2.C2.CBABABABABABABABABABABABABABAB2.C.CABABABABABABABABABABAB
ABABABAB2.C2$CB3.C28.CAB3.C27.CBAB3.C26.CABAB3.C25.CBABAB3.C24.CABABA
B3.C23.CBABABAB3.C22.CABABABAB3.C21.CBABABABAB3.C20.CABABABABAB3.C19.
CBABABABABAB3.C18.CABABABABABAB3.C17.CBABABABABABAB3.C16.CABABABABABA
BAB3.C15.CBABABABABABABAB3.C14.CABABABABABABABAB3.C13.CBABABABABABABA
BAB3.C12.CABABABABABABABABAB3.C11.CBABABABABABABABABAB3.C10.CABABABAB
ABABABABABAB3.C9.CBABABABABABABABABABAB3.C8.CABABABABABABABABABABAB3.
C7.CBABABABABABABABABABABAB3.C6.CABABABABABABABABABABABAB3.C5.CBABABA
BABABABABABABABABAB3.C4.CABABABABABABABABABABABABAB3.C3.CBABABABABABA
BABABABABABABAB3.C2.CABABABABABABABABABABABABABAB3.C.CBABABABABABABAB
ABABABABABABAB3.C2$CB4.C27.CAB4.C26.CBAB4.C25.CABAB4.C24.CBABAB4.C23.
CABABAB4.C22.CBABABAB4.C21.CABABABAB4.C20.CBABABABAB4.C19.CABABABABAB
4.C18.CBABABABABAB4.C17.CABABABABABAB4.C16.CBABABABABABAB4.C15.CABABA
BABABABAB4.C14.CBABABABABABABAB4.C13.CABABABABABABABAB4.C12.CBABABABA
BABABABAB4.C11.CABABABABABABABABAB4.C10.CBABABABABABABABABAB4.C9.CABA
BABABABABABABABAB4.C8.CBABABABABABABABABABAB4.C7.CABABABABABABABABABA
BAB4.C6.CBABABABABABABABABABABAB4.C5.CABABABABABABABABABABABAB4.C4.CB
ABABABABABABABABABABABAB4.C3.CABABABABABABABABABABABABAB4.C2.CBABABAB
ABABABABABABABABABAB4.C.CABABABABABABABABABABABABABAB4.C2$CB5.C26.CAB
5.C25.CBAB5.C24.CABAB5.C23.CBABAB5.C22.CABABAB5.C21.CBABABAB5.C20.CAB
ABABAB5.C19.CBABABABAB5.C18.CABABABABAB5.C17.CBABABABABAB5.C16.CABABA
BABABAB5.C15.CBABABABABABAB5.C14.CABABABABABABAB5.C13.CBABABABABABABA
B5.C12.CABABABABABABABAB5.C11.CBABABABABABABABAB5.C10.CABABABABABABAB
ABAB5.C9.CBABABABABABABABABAB5.C8.CABABABABABABABABABAB5.C7.CBABABABA
BABABABABABAB5.C6.CABABABABABABABABABABAB5.C5.CBABABABABABABABABABABA
B5.C4.CABABABABABABABABABABABAB5.C3.CBABABABABABABABABABABABAB5.C2.CA
BABABABABABABABABABABABAB5.C.CBABABABABABABABABABABABABAB5.C2$CB6.C
25.CAB6.C24.CBAB6.C23.CABAB6.C22.CBABAB6.C21.CABABAB6.C20.CBABABAB6.C
19.CABABABAB6.C18.CBABABABAB6.C17.CABABABABAB6.C16.CBABABABABAB6.C15.
CABABABABABAB6.C14.CBABABABABABAB6.C13.CABABABABABABAB6.C12.CBABABABA
BABABAB6.C11.CABABABABABABABAB6.C10.CBABABABABABABABAB6.C9.CABABABABA
BABABABAB6.C8.CBABABABABABABABABAB6.C7.CABABABABABABABABABAB6.C6.CBAB
ABABABABABABABABAB6.C5.CABABABABABABABABABABAB6.C4.CBABABABABABABABAB
ABABAB6.C3.CABABABABABABABABABABABAB6.C2.CBABABABABABABABABABABABAB6.
C.CABABABABABABABABABABABABAB6.C2$CB7.C24.CAB7.C23.CBAB7.C22.CABAB7.C
21.CBABAB7.C20.CABABAB7.C19.CBABABAB7.C18.CABABABAB7.C17.CBABABABAB7.
C16.CABABABABAB7.C15.CBABABABABAB7.C14.CABABABABABAB7.C13.CBABABABABA
BAB7.C12.CABABABABABABAB7.C11.CBABABABABABABAB7.C10.CABABABABABABABAB
7.C9.CBABABABABABABABAB7.C8.CABABABABABABABABAB7.C7.CBABABABABABABABA
BAB7.C6.CABABABABABABABABABAB7.C5.CBABABABABABABABABABAB7.C4.CABABABA
BABABABABABABAB7.C3.CBABABABABABABABABABABAB7.C2.CABABABABABABABABABA
BABAB7.C.CBABABABABABABABABABABABAB7.C2$CB8.C23.CAB8.C22.CBAB8.C21.CA
BAB8.C20.CBABAB8.C19.CABABAB8.C18.CBABABAB8.C17.CABABABAB8.C16.CBABAB
ABAB8.C15.CABABABABAB8.C14.CBABABABABAB8.C13.CABABABABABAB8.C12.CBABA
BABABABAB8.C11.CABABABABABABAB8.C10.CBABABABABABABAB8.C9.CABABABABABA
BABAB8.C8.CBABABABABABABABAB8.C7.CABABABABABABABABAB8.C6.CBABABABABAB
ABABABAB8.C5.CABABABABABABABABABAB8.C4.CBABABABABABABABABABAB8.C3.CAB
ABABABABABABABABABAB8.C2.CBABABABABABABABABABABAB8.C.CABABABABABABABA
BABABABAB8.C2$CB9.C22.CAB9.C21.CBAB9.C20.CABAB9.C19.CBABAB9.C18.CABAB
AB9.C17.CBABABAB9.C16.CABABABAB9.C15.CBABABABAB9.C14.CABABABABAB9.C
13.CBABABABABAB9.C12.CABABABABABAB9.C11.CBABABABABABAB9.C10.CABABABAB
ABABAB9.C9.CBABABABABABABAB9.C8.CABABABABABABABAB9.C7.CBABABABABABABA
BAB9.C6.CABABABABABABABABAB9.C5.CBABABABABABABABABAB9.C4.CABABABABABA
BABABABAB9.C3.CBABABABABABABABABABAB9.C2.CABABABABABABABABABABAB9.C.C
BABABABABABABABABABABAB9.C2$CB10.C21.CAB10.C20.CBAB10.C19.CABAB10.C
18.CBABAB10.C17.CABABAB10.C16.CBABABAB10.C15.CABABABAB10.C14.CBABABAB
AB10.C13.CABABABABAB10.C12.CBABABABABAB10.C11.CABABABABABAB10.C10.CBA
BABABABABAB10.C9.CABABABABABABAB10.C8.CBABABABABABABAB10.C7.CABABABAB
ABABABAB10.C6.CBABABABABABABABAB10.C5.CABABABABABABABABAB10.C4.CBABAB
ABABABABABABAB10.C3.CABABABABABABABABABAB10.C2.CBABABABABABABABABABAB
10.C.CABABABABABABABABABABAB10.C2$CB11.C20.CAB11.C19.CBAB11.C18.CABAB
11.C17.CBABAB11.C16.CABABAB11.C15.CBABABAB11.C14.CABABABAB11.C13.CBAB
ABABAB11.C12.CABABABABAB11.C11.CBABABABABAB11.C10.CABABABABABAB11.C9.
CBABABABABABAB11.C8.CABABABABABABAB11.C7.CBABABABABABABAB11.C6.CABABA
BABABABABAB11.C5.CBABABABABABABABAB11.C4.CABABABABABABABABAB11.C3.CBA
BABABABABABABABAB11.C2.CABABABABABABABABABAB11.C.CBABABABABABABABABAB
AB11.C2$CB12.C19.CAB12.C18.CBAB12.C17.CABAB12.C16.CBABAB12.C15.CABABA
B12.C14.CBABABAB12.C13.CABABABAB12.C12.CBABABABAB12.C11.CABABABABAB
12.C10.CBABABABABAB12.C9.CABABABABABAB12.C8.CBABABABABABAB12.C7.CABAB
ABABABABAB12.C6.CBABABABABABABAB12.C5.CABABABABABABABAB12.C4.CBABABAB
ABABABABAB12.C3.CABABABABABABABABAB12.C2.CBABABABABABABABABAB12.C.CAB
ABABABABABABABABAB12.C2$CB13.C18.CAB13.C17.CBAB13.C16.CABAB13.C15.CBA
BAB13.C14.CABABAB13.C13.CBABABAB13.C12.CABABABAB13.C11.CBABABABAB13.C
10.CABABABABAB13.C9.CBABABABABAB13.C8.CABABABABABAB13.C7.CBABABABABAB
AB13.C6.CABABABABABABAB13.C5.CBABABABABABABAB13.C4.CABABABABABABABAB
13.C3.CBABABABABABABABAB13.C2.CABABABABABABABABAB13.C.CBABABABABABABA
BABAB13.C2$CB14.C17.CAB14.C16.CBAB14.C15.CABAB14.C14.CBABAB14.C13.CAB
ABAB14.C12.CBABABAB14.C11.CABABABAB14.C10.CBABABABAB14.C9.CABABABABAB
14.C8.CBABABABABAB14.C7.CABABABABABAB14.C6.CBABABABABABAB14.C5.CABABA
BABABABAB14.C4.CBABABABABABABAB14.C3.CABABABABABABABAB14.C2.CBABABABA
BABABABAB14.C.CABABABABABABABABAB14.C2$CB15.C16.CAB15.C15.CBAB15.C14.
CABAB15.C13.CBABAB15.C12.CABABAB15.C11.CBABABAB15.C10.CABABABAB15.C9.
CBABABABAB15.C8.CABABABABAB15.C7.CBABABABABAB15.C6.CABABABABABAB15.C
5.CBABABABABABAB15.C4.CABABABABABABAB15.C3.CBABABABABABABAB15.C2.CABA
BABABABABABAB15.C.CBABABABABABABABAB15.C2$CB16.C15.CAB16.C14.CBAB16.C
13.CABAB16.C12.CBABAB16.C11.CABABAB16.C10.CBABABAB16.C9.CABABABAB16.C
8.CBABABABAB16.C7.CABABABABAB16.C6.CBABABABABAB16.C5.CABABABABABAB16.
C4.CBABABABABABAB16.C3.CABABABABABABAB16.C2.CBABABABABABABAB16.C.CABA
BABABABABABAB16.C2$CB17.C14.CAB17.C13.CBAB17.C12.CABAB17.C11.CBABAB
17.C10.CABABAB17.C9.CBABABAB17.C8.CABABABAB17.C7.CBABABABAB17.C6.CABA
BABABAB17.C5.CBABABABABAB17.C4.CABABABABABAB17.C3.CBABABABABABAB17.C
2.CABABABABABABAB17.C.CBABABABABABABAB17.C2$CB18.C13.CAB18.C12.CBAB
18.C11.CABAB18.C10.CBABAB18.C9.CABABAB18.C8.CBABABAB18.C7.CABABABAB
18.C6.CBABABABAB18.C5.CABABABABAB18.C4.CBABABABABAB18.C3.CABABABABABA
B18.C2.CBABABABABABAB18.C.CABABABABABABAB18.C2$CB19.C12.CAB19.C11.CBA
B19.C10.CABAB19.C9.CBABAB19.C8.CABABAB19.C7.CBABABAB19.C6.CABABABAB
19.C5.CBABABABAB19.C4.CABABABABAB19.C3.CBABABABABAB19.C2.CABABABABABA
B19.C.CBABABABABABAB19.C2$CB20.C11.CAB20.C10.CBAB20.C9.CABAB20.C8.CBA
BAB20.C7.CABABAB20.C6.CBABABAB20.C5.CABABABAB20.C4.CBABABABAB20.C3.CA
BABABABAB20.C2.CBABABABABAB20.C.CABABABABABAB20.C2$CB21.C10.CAB21.C9.
CBAB21.C8.CABAB21.C7.CBABAB21.C6.CABABAB21.C5.CBABABAB21.C4.CABABABAB
21.C3.CBABABABAB21.C2.CABABABABAB21.C.CBABABABABAB21.C2$CB22.C9.CAB
22.C8.CBAB22.C7.CABAB22.C6.CBABAB22.C5.CABABAB22.C4.CBABABAB22.C3.CAB
ABABAB22.C2.CBABABABAB22.C.CABABABABAB22.C2$CB23.C8.CAB23.C7.CBAB23.C
6.CABAB23.C5.CBABAB23.C4.CABABAB23.C3.CBABABAB23.C2.CABABABAB23.C.CBA
BABABAB23.C2$CB24.C7.CAB24.C6.CBAB24.C5.CABAB24.C4.CBABAB24.C3.CABABA
B24.C2.CBABABAB24.C.CABABABAB24.C2$CB25.C6.CAB25.C5.CBAB25.C4.CABAB
25.C3.CBABAB25.C2.CABABAB25.C.CBABABAB25.C2$CB26.C5.CAB26.C4.CBAB26.C
3.CABAB26.C2.CBABAB26.C.CABABAB26.C2$CB27.C4.CAB27.C3.CBAB27.C2.CABAB
27.C.CBABAB27.C2$CB28.C3.CAB28.C2.CBAB28.C.CABAB28.C2$CB29.C2.CAB29.C
.CBAB29.C2$CB30.C.CAB30.C2$CB31.C!
When you want you can post the pattern without repeating speeds.
I was so socially awkward in the past and it will haunt me for the rest of my life.

Code: Select all

b4o25bo$o29bo$b3o3b3o2bob2o2bob2o2bo3bobo$4bobo3bob2o2bob2o2bobo3bobo$
4bobo3bobo5bo5bo3bobo$o3bobo3bobo5bo6b4o$b3o3b3o2bo5bo9bobo$24b4o!

AforAmpere
Posts: 1334
Joined: July 1st, 2016, 3:58 pm

Re: Rules in which every spaceship speed is possible

Post by AforAmpere » June 28th, 2017, 5:54 pm

You should check out the thread for All Directions and Infinite Speeds:
viewtopic.php?f=11&t=2916
It has ships for every slope, and works with similar functionality, and was based on this rule by pteriforever.
I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. I also wrote EPE, a tool for searching in the INT rulespace.

Things to work on:
- Find (7,1)c/8 and 9c/10 ships in non-B0 INT.
- EPE improvements.

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