The Single Rotation Rule

[alexv]

For work with very big areas with sparse definition of cells instead of import0 function in archive
it is better to use modified version below. And yes, before running the script desired 5-state rule
should be already chosen

Code: Select all

from glife import rect
import golly as g

r = g.getselrect()
if len(r) == 0: 
  r = g.getrect()
  if len(r) == 0: g.exit("There is no selection and the pattern is empty.")

slist = g.getcells(r)
inc = 2
if len(slist) & 1 == 1: inc = 3

for i in xrange(0, len(slist)-1, inc):
        col = slist[i] 
        row = slist[i+1] 
        s = g.getcell(col,row)
        if (s > 0):
            g.setcell(col, row, 1 + (col%2) + 2*(row%2))

Alexander

[alexv]

The situation surrounding syntheses of still lifes is trivial: In reversible rules, a still life's only predecessor is itself, so it cannot have a group of gliders as a predecessor.

I suppose counterexample below is appropriate?: two gliders produces glider and still lifes

Code: Select all

x = 13, y = 3, rule = MargSingRot
CD9.DC2$CD9.DC!

[dvgrn]

The situation surrounding syntheses of still lifes is trivial: In reversible rules, a still life's only predecessor is itself, so it cannot have a group of gliders as a predecessor.

I suppose counterexample below is appropriate?: two gliders produces glider and still lifes...

Aren't those period-4 oscillators rather than still lifes, though?

Two gliders->glider+oscillator(s) must happen quite a lot. For example, crashing two gliders at an offset can convert one of them to a still life and send the other one/a new one of the same kind off at a 90-degree angle:

Code: Select all

x = 13, y = 7, rule = MargSingRot
CD2$CD2$11.DC2$11.DC!

Certainly doesn't seem like an easy system to build a universal constructor with, though! Maybe something could be arranged with just the right oscillators piled up in a long line, ready to be used; a UC could send a glider to collect the next oscillator in the line, whenever it needed more construction material... That's just handwaving, though -- leaves an awful pile of practical problems to be solved.

[alexv]

BTW, earlier I posted here links about "universal transformer" by Luke Schaeffer, I converted that in 5-state also:
https://cloud.mail.ru/public/9c2ba68898 ... PhysCA.zip

Alexander

[alexv]

The rule is defined via rotation and certainly should have right-left asymmetry (chirality). Sometimes it is
manifested in rather impressive way, e.g. in pattern below a glider makes round trip with four reflections
during 188 steps:

Code: Select all

x = 14, y = 14, rule = MargSingRot
BA10.BA$DC3.CD5.DC2$5.CD9$BA10.BA$DC10.DC!

but if to change direction of motion to opposite one then it restores initial position only after
12148 steps with transitions between two different kinds of gliders with orthogonal and diagonal
segments of trajectory:

Code: Select all

x = 14, y = 14, rule = MargSingRot
BA10.BA$DC4.DC4.DC2$6.DC9$BA10.BA$DC10.DC!

Alexander

[dmishin]

I tried to visualize this cellular automaton, painting cells with different colors according to their flashing rates. Constantly ON cells are red, flashing with period 2 are green and period 4 are blue.

The result is on youtube. Initial pattern is random block in the center and indestructible vertical bar at the right.

I especially like it, because different spaceships have different color. It is also possible to color Life in the same way, but result is less interesting.

[dmishin]

The rule is defined via rotation and certainly should have right-left asymmetry (chirality).

By the way, if you mirror some pattern (choosing mirror axis so that 2x2 block bounds are preserved), and then translate it by (1,1) , then you will obtain a pattern that have the same parameters as the original, but moves back in time. This is also true for many other rules.

[alexv]

By the way, if you mirror some pattern (choosing mirror axis so that 2x2 block bounds are preserved), and then translate it by (1,1) , then you will obtain a pattern that have the same parameters as the original, but moves back in time. This is also true for many other rules.

I don't think so, property you are talking about is true for Margolus rules with all squares of transformations are identity, but in your case only fourth degree are identity for rotation. To back in time you need not only reflect
pattern, but change time on one step - in such a case gliders on example are moving in the same direction as
in initial pattern. So in the example I failed to cause glider to move in opposite direction without radical change
of period and behavior.

PS. The situation may be described simpler - I have glider with clockwise motion - after reflection and change
of direction of time it is again clockwise motion. So I may not change direction of motion. For most other
known rules you do not need reflection and so after change of direction of time you produces glider with
opposite direction of motion.

[pi_guy314]

Here is a single cell reflector that doesn't change its position after reflecting a glider.

Code: Select all

[M2] (golly 2.6)
#R MargSingRot
1 0 0 0 4
2 0 0 1 0
3 0 0 2 0
1 1 0 0 0
1 1 0 3 0
2 4 5 0 0
3 6 0 0 0
4 0 3 0 7
2 0 1 0 4
2 0 0 5 0
3 9 10 0 0
1 0 2 0 0
2 0 0 12 0
3 13 0 0 0
4 11 0 0 14
5 8 0 0 15

Here is an unusual oscillator that can be extended.

Code: Select all

[M2] (golly 2.6)
#R MargSingRot
1 0 0 2 1
2 0 0 1 0
3 0 0 2 0
2 1 0 1 0
3 4 0 4 0
4 3 0 5 0
1 0 0 2 0
2 1 0 0 7
1 0 3 0 0
2 9 0 0 0
3 8 0 10 0
4 11 0 0 0
5 0 6 0 12

[dmishin]

To back in time you need not only reflect
pattern, but change time on one step - in such a case gliders on example are moving in the same direction as
in initial pattern.

Yes, exactly! And there is a very easy way to achieve this: by shifting pattern by 1 cell along each axis.

Here is an example, using the P11 diagonal spaceship. (Same in my simulator, I still find it more convenient sometimes)

Code: Select all

#CXRLE Pos=-9,-9 Gen=0
x = 6, y = 18, rule = MargSingRot
.C.C$.A.A$.CD5$B.B$D.D$BA6$3.A.A$3.C.C$4.BA!

Here, the bottom pattern is the original P11 spaceship, moving in the (1,1) direction.
The middle pattern is the same spaceship, but reflected left-right. It is not spaceship at all, it decomposes into an orthogonal spaceship and an oscillator.

And the the top one is the result of shifting the middle pattern by odd distance along each axis. It is a spaceship! Original spaceship moves in (1,1), the reflected one "should" move in the (-1,1), but since it moves back in time, it actually moves in the -1*(-1,1) = (1,-1) direction.

You can ensure that it is the real retrograde evolution: generation 1 of the top pattern looks like generation 10 (or -1, if you use my simulator and can go back in time) of the bottom one, but reflected.

Actually, many of the 205 spaceships I have found exist in 2 such forms. Without any better naming I called them "dual" spaceships, and counted such "dual" pair as one. Some of the spaceships coincide with their own duals ("dual" matches some intermediate generation of the original).
Somewhat resembles particles and anti-particles.

[dmishin]

The P11 spaceship above was not a very good example, because it is self-dual. In order to make a better example, I've checked several of the spaceships and unexpectedly discovered that most of them are self-dual, i.e. after several generations they are reflected and moved by an odd amount.

An automated search showed that only 7 of 205 discovered spaceships are not self-dual. All of them have 8 or 9 cells. Here are they, each paired by their dual.

Code: Select all

#CXRLE Pos=0,-29
x = 197, y = 23, rule = MargSingRot
71.D$71.B$71.D41.DC$2.A21.AB18.AB$C.C19.CD.D16.CD.D.D24.C$.B21.BA18.B
A69.A30.B.B32.A.A$26.C19.C67.C68.D$72.A74.B36.A$.D68.C.C73.C$A.A177.A
$2.C50.D59.D31.D35.D$31.B19.B20.A40.B66.A.A$33.DC18.DC58.D32.C$32.A.A
17.A.A$32.CD18.CD60.C$7.BA4.BA18.B19.B91.BA$9.D2.C$8.A4.B64.A2.BA2.B
108.A$87.DCD105.D$81.B37.B7.BA2.B58.A5.A$121.DCD7.D30.C.C26.D$154.A2.
B3.B28.A.A3.A$154.C4.D4.C!

It may seem that only #2 and #3 are true elementary patterns, while others are not a separate spaceships but composites of 2 4-cellers, but it not not true: the 4-cell components are interacting.

[dmishin]

Here is a single cell reflector that doesn't change its position after reflecting a glider.
...
Here is an unusual oscillator that can be extended.

Cool! I wanted to make a table of single cell collisions with the lightest spaceships, but haven't yet found the right way to write down relative position of a spaceship and a cell. I hoped that with such table it would be possible to build a "ping-pong spaceship" (2 reflectors, propelled by the collisions with a spaceship), or a "growing ping-pong" (one or 2 reflectors moving away from each other). It could also be interesting to explore, how type of the spaceship would change when it is traveling through a sparsely filled field of 1-cellers. It would be a kind of Markovian process.

Regarding the oscillator, it's also interesting. I saw such spaceships in the "Rotations" family of rules. Example.

And finally, I have some news! The idea to bruteforce spaceships appeared fruitful. I've updated my pattern analyzer tool (btw, it can be used for other rules too) to perform exhaustive search, starting from the most dense patterns and going to the more and more sparse ones. And after a weekend of computations, it discovered a bunch of 10-cellers, one 11-celler and 12-celler, and many new spaceships of 6 to 9 cells (no new 5-cellers so far). The updated library now contains 328 spaceships. Just a few excerpts from this list.

Largest period (p12206)

Code: Select all

#CXRLE Pos=-9,-10
x = 6, y = 5, rule = MargSingRot
5.A2$BAB2$2.BAB!

12-celler!

Code: Select all

#CXRLE Pos=0,-10
x = 6, y = 6, rule = MargSingRot
2.A2$2.AB$CDCDCD$2.A2.B$C!

11-celler (the only 11-cell spaceship I know)

Code: Select all

#CXRLE Pos=-10,-10
x = 4, y = 6, rule = MargSingRot
.BAB$2.C$3.B$.D$AB.B$CD!

Also, I have found 2 spaceships, that can be "chained" into the long linear spaceships with the same period and velocity. The faster one can be chained in zigzagged lines, and the slower one only allows straight chains. Formally, these long spaceships should be considered as a single pattern, because all cells in them interact: evolution of the sole "building block" is slightly different from the evolution of the chain block. However, these interactions cancel themselves out after a few steps. Anyways, they are interesting:

Code: Select all

#CXRLE Pos=1,-9
x = 234, y = 237, rule = MargSingRot
25.C2$28.D$32.B2.A$26.DC8.D4.C$34.B5.B4.A.A$41.C13.C$42.B5.B8.A4.B$
49.C6.D14.C$61.A.A$57.C7.C2.D2.C5.C$75.A$70.D8.C$79.A6.B$84.DC4.D4.C$
83.A7.AB6.AB$98.D8.CD$100.B3.B9.BA4.B$120.D$107.A2.B$112.D16.C$120.B
7.B6.A3.A$122.D7.D5.D6.C$129.A4.B10.A4.B6.A$140.D3.D5.D$151.A4.B6.A.A
$159.C7.C$150.B21.B$.C158.D10.C.C$166.B13.B$3.C171.C2.D$B178.A4.B2.A
5.A$3.C182.D$180.B7.B6.A3.A3.A$194.D13.D$195.A4.B9.B4.A$.C3.C197.C7.C
6.D4.C$.A216.B$210.D13.D$165.A.A50.B6.AB2.AB$4.D227.DC$152.B2.A4.BAB$
145.C.C2.D2.C12.DC$2.B2.A137.A12.B5.B$138.DC7.C4.D3.D$140.B9.B$6.D$4.
B135.B$139.C.C$137.A$5.C135.C$7.A$7.C$7.A$138.D.D2$140.D$138.B$6.D$6.
B128.A.A$8.DC$138.B$138.D3$136.BAB$6.DC$8.B129.B25.B$10.D151.D.D$135.
A.A25.A2$83.AB4.AB$11.C73.C2.D47.DC25.C$8.B75.B4.A72.B.B$164.D$10.B
125.B$134.D.D$10.B124.A$11.C150.D.D$161.A$135.C$130.B3.B.B26.A$10.DCD
115.D.D5.D25.D$129.A29.A$163.C$160.B$129.C$9.A2.B111.B3.B.B$12.D109.D
.D5.D29.DC$12.B51.B58.A37.A$62.D.D97.D$63.A$123.C$118.B3.B.B$63.C52.D
.D5.D35.DC$12.B49.B.B52.A40.B$12.D51.D$14.B144.A$16.D100.C44.D$112.B
3.B.B39.B$110.D.D5.D39.D$111.A48.B$17.C$157.A.A$16.D94.C$14.B91.B3.B.
B46.A$14.D89.D.D5.D46.C$105.A2$13.A$18.D86.C50.DC$17.A82.B3.B.B51.B$
16.D81.D.D5.D$99.A58.B$157.C.C$155.A$17.C.C79.C59.C$94.B3.B.B$19.C72.
D.D5.D$16.B76.A$156.D.D2$93.C64.D$19.A68.B3.B.B61.B$18.D67.D.D5.D$17.
A69.A65.A.A2$156.B$20.D66.C68.D$82.B3.B.B$21.C58.D.D5.D$19.A61.A72.BA
B2$17.AB137.B$73.C7.C$69.A6.B3.B.B70.A.A$76.D5.D$19.A36.B2.A4.BAB5.B
2.A$49.C.C2.D2.C12.DC82.DC$20.B26.A12.B5.B$42.DC7.C4.D3.D$21.AB21.B9.
B99.B$152.D.D$44.B108.A$43.C.C$41.A$45.C99.C7.C$22.BAB116.A6.B3.B.B$
148.D5.D$128.B2.A4.BAB5.B2.A$24.D17.D.D76.C.C2.D2.C12.DC$109.A.A7.A
12.B5.B$44.D69.DC7.C4.D3.D$23.A18.B61.B.B4.A4.B9.B$23.C3.C63.C2.DC4.D
C2.D6.C$23.A15.A.A45.A7.A2.B7.B9.B$79.C4.D.D4.C4.D4.C$42.B31.B3.B.B2.
A4.B$42.D29.D.D5.D$73.A10.B$27.C$22.B.B15.BAB2$26.B15.B2$39.A.A2$25.A
$40.DC$26.B$27.C$27.A3$27.C$27.A2$28.BA5$28.DCD2$31.C5$29.A$32.D$28.B
2$32.B3$33.C$29.A3$32.DC4$31.C.C2$35.C$32.B5$34.DC3$34.B$36.D4$34.DC
2.D3$36.B2$35.A2$37.A$40.D$37.A4$39.A$38.D2.C2$41.C!

[alexv]

The ping-pong idea recollected me one strange problem I encountered. Below is an example, how
spaceship moves "oscillating 2x2 block".

Code: Select all

#CXRLE Pos=-10,0
x = 12, y = 4, rule = MargSingRot
10.AB$CD8.CD2$CD!

I planned to move it further using other spaceships ... but failed. May be I missed something?

Alexander

[alexv]

Also, I have found 2 spaceships, that can be "chained" into the long linear spaceships with the same period and velocity. The faster one can be chained in zigzagged lines, and the slower one only allows straight chains. Formally, these long spaceships should be considered as a single pattern, because all cells in them interact: evolution of the sole "building block" is slightly different from the evolution of the chain block. However, these interactions cancel themselves out after a few steps. Anyways, they are interesting: ...

I tried the pattern, but it does not work as suggested. After couple tests with shifts and (re)imports I got
pattern looking more close to description. Hope, it's correct:

Code: Select all

#CXRLE Pos=0,-11
x = 234, y = 237, rule = MargSingRot
25.D2$28.C$32.A2.B$26.CD8.C4.D$34.A5.A4.B.B$41.D13.D$42.A5.A8.B4.A$
49.D6.C14.D$61.B.B$57.D7.D2.C2.D5.D$75.B$70.C8.D$79.B6.A$84.CD4.C4.D$
83.B7.BA6.BA$98.C8.DC$100.A3.A9.AB4.A$120.C$107.B2.A$112.C16.D$120.A
7.A6.B3.B$122.C7.C5.C6.D$129.B4.A10.B4.A6.B$140.C3.C5.C$151.B4.A6.B.B
$159.D7.D$150.A21.A$.D158.C10.D.D$166.A13.A$3.D171.D2.C$A178.B4.A2.B
5.B$3.D182.C$180.A7.A6.B3.B3.B$194.C13.C$195.B4.A9.A4.B$.D3.D197.D7.D
6.C4.D$.B216.A$210.C13.C$165.B.B50.A6.BA2.BA$4.C227.CD$152.A2.B4.ABA$
145.D.D2.C2.D12.CD$2.A2.B137.B12.A5.A$138.CD7.D4.C3.C$140.A9.A$6.C$4.
A135.A$139.D.D$137.B$5.D135.D$7.B$7.D$7.B$138.C.C2$140.C$138.A$6.C$6.
A128.B.B$8.CD$138.A$138.C3$136.ABA$6.CD$8.A129.A25.A$10.C151.C.C$135.
B.B25.B2$83.BA4.BA$11.D73.D2.C47.CD25.D$8.A75.A4.B72.A.A$164.C$10.A
125.A$134.C.C$10.A124.B$11.D150.C.C$161.B$135.D$130.A3.A.A26.B$10.CDC
115.C.C5.C25.C$129.B29.B$163.D$160.A$129.D$9.B2.A111.A3.A.A$12.C109.C
.C5.C29.CD$12.A51.A58.B37.B$62.C.C97.C$63.B$123.D$118.A3.A.A$63.D52.C
.C5.C35.CD$12.A49.A.A52.B40.A$12.C51.C$14.A144.B$16.C100.D44.C$112.A
3.A.A39.A$110.C.C5.C39.C$111.B48.A$17.D$157.B.B$16.C94.D$14.A91.A3.A.
A46.B$14.C89.C.C5.C46.D$105.B2$13.B$18.C86.D50.CD$17.B82.A3.A.A51.A$
16.C81.C.C5.C$99.B58.A$157.D.D$155.B$17.D.D79.D59.D$94.A3.A.A$19.D72.
C.C5.C$16.A76.B$156.C.C2$93.D64.C$19.B68.A3.A.A61.A$18.C67.C.C5.C$17.
B69.B65.B.B2$156.A$20.C66.D68.C$82.A3.A.A$21.D58.C.C5.C$19.B61.B72.AB
A2$17.BA137.A$73.D7.D$69.B6.A3.A.A70.B.B$76.C5.C$19.B36.A2.B4.ABA5.A
2.B$49.D.D2.C2.D12.CD82.CD$20.A26.B12.A5.A$42.CD7.D4.C3.C$21.BA21.A9.
A99.A$152.C.C$44.A108.B$43.D.D$41.B$45.D99.D7.D$22.ABA116.B6.A3.A.A$
148.C5.C$128.A2.B4.ABA5.A2.B$24.C17.C.C76.D.D2.C2.D12.CD$109.B.B7.B
12.A5.A$44.C69.CD7.D4.C3.C$23.B18.A61.A.A4.B4.A9.A$23.D3.D63.D2.CD4.C
D2.C6.D$23.B15.B.B45.B7.B2.A7.A9.A$79.D4.C.C4.D4.C4.D$42.A31.A3.A.A2.
B4.A$42.C29.C.C5.C$73.B10.A$27.D$22.A.A15.ABA2$26.A15.A2$39.B.B2$25.B
$40.CD$26.A$27.D$27.B3$27.D$27.B2$28.AB5$28.CDC2$31.D5$29.B$32.C$28.A
2$32.A3$33.D$29.B3$32.CD4$31.D.D2$35.D$32.A5$34.CD3$34.A$36.C4$34.CD
2.C3$36.A2$35.B2$37.B$40.C$37.B4$39.B$38.C2.D2$41.D!

[pi_guy314]

There can be no replicator in this rule, for example, without some mechanism for incorporating live cells from elsewhere.

I found a glider collision that moves a cell closer to the glider stream, similar to the sliding block memory in gol. This can be used for replicators while they're moving cells towards a certain location, though there has to be a collision for moving cells sideways and away from glider streams as well.

Code: Select all

[M2] (golly 2.6)
#R MargSingRot
1 0 0 1 0
2 0 0 0 1
3 0 2 0 0
1 3 0 1 0
1 0 4 0 0
2 0 4 0 5
2 1 0 0 0
3 6 7 0 0
4 3 0 8 0
2 0 0 4 1
2 5 0 0 0
3 10 0 11 0
4 0 12 0 0
5 0 9 13 0
3 0 0 0 6
3 0 0 7 0
4 15 16 0 0
5 0 17 0 0
6 0 14 18 0

[praosylen]

LifeViewer now supports Margolus rules!

Code: Select all

x = 4, y = 3, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
b3o2$2bo!

Code: Select all

x = 32, y = 21, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$3b2obob2o2bob9obob5o$obob2ob3obob4ob6o4b3o$3b2obo2b4o4bo5b3o2b4o$bo3b
3o2b3obo4bobob3o4b2o$2o2bobo6bob5obob4obob2o$4o5b10o3bob2o2b3o$b2ob3o
bob3ob3obob2o4bo4bo$2o3bo3bo2bob3ob2ob2o4b3obo$b2obo2b2ob2obobo2bo3b2o
bob4o$bobob2o3bo2bobo5b2o2b3o2bo$obobob3o4bob2o2bobo3b5o$3b4o3b3obo3b
2ob4o3b2o$obobobo3b3o2b3o4b2obobob2o$ob2o2b2ob4o3b3obob2o3bo$3b2ob2o3b
6obobo3bo2b2obo$5o3bo2b5o5bo2bo5bo$obo2bob3o2bob7ob2o3bobobo$7b3ob3ob
ob2obo3b2o$2obobo6bo3bobobob3o2b2obo$obo5bobob2o4bobo5b2ob2o!

[Macbi]

This variant was suggested in the comments to the original post:

Code: Select all

x = 16, y = 16, rule = M0,4,1,3,8,5,6,11,2,9,10,14,12,7,13,15
obobob2o2b2obobobo2b5o2bobo$b2ob4o4b3o2bobo4b2o2bobo$o2bo3b3ob2o2b3ob
4ob8o$3b6obobobo3b2o4b3ob3o$o7b2o2b3o4bobobo3bobo$2obo3b5o4b6o5b2o$o2b
obo2b2obobo4bo2bob2o3b2obo$3ob2obo3b3obo2b2obo4bob2obo$2b2ob6obobo7b3o
2b3obo$b6ob5obo2b2o5bo3b4o$2o2b2obo2b3ob3o2bo5bob4o$o3bo5bo5b3ob2obob
2o2bobo$bo3bobobobo3bo7bo2bo2bo$o7bobobobob4o2b2o$2bo2bobob2obo3b3o2bo
b4o2b3o$o2bob2o3bo2b2o2b2o2b4o3bo$obo2b3obobo8b3o5bo2bo$bo2b3o2b2o3b5o
bobob3ob3o$o2b5o3b2ob3o5b2o2b6o$b2obobo4bo2b2ob3ob2o2b4ob2o$bo6bo2bobo
5bo2b2o2b3ob2o$2b2o4bob2o2bo2bo2bo2b5o2b2o$2b2ob2o2bo4b2o3b2o7b2o$3bo
5b2o3bob2ob2o3bobo3b2o$ob3o3b5o3bo2b3o3bob3obo$6obo2bo2b2ob2o2bobo3b2o
$2obo2b3obob2o2bobo4b2o3b3o$bo2bo2b2o2bo3bo2b3obobobo2bo$b2o2bobo2b3ob
ob2o4b3ob3o2bo$8obo2b2o2bo2b4o2b4o2bo$6b4o3bo4bobo3bo3b2obo$b4o2b2obob
o4b3obo3b2o3bo!

Live cells are "clockwise", dead cells are "anticlockwise", and each 2×2 square rotates in a direction determined by majority vote.

[muzik]

Here is an example, using the P11 diagonal spaceship. (Same in my simulator, I still find it more convenient sometimes)

Code: Select all

#CXRLE Pos=-9,-9 Gen=0
x = 6, y = 18, rule = MargSingRot
.C.C$.A.A$.CD5$B.B$D.D$BA6$3.A.A$3.C.C$4.BA!

Here, the bottom pattern is the original P11 spaceship, moving in the (1,1) direction.
The middle pattern is the same spaceship, but reflected left-right. It is not spaceship at all, it decomposes into an orthogonal spaceship and an oscillator.

And the the top one is the result of shifting the middle pattern by odd distance along each axis. It is a spaceship! Original spaceship moves in (1,1), the reflected one "should" move in the (-1,1), but since it moves back in time, it actually moves in the -1*(-1,1) = (1,-1) direction.

I've decided to convert this pattern to a LifeViewer-readable format for testing purposes. I want to see if the same can be done for other patterns, but such a task would certainly not be trivial.

Code: Select all

x = 7, y = 19, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$2bobo$2bobo$2b2o5$bobo$bobo$b2o6$4bobo$4bobo$5b2o!
[[ GRID ]]

Another example:

Largest period (p12206)

Code: Select all

x = 7, y = 5, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
6bo2$b3o2$3b3o!

EDIT: Turns out there's an easier way to do it: just copy the pattern, use a text editor to change it to a Generations rule with the correct amount of states or more, then paste it into Golly, change the rule to 2-state, paste it into LifeViewer with the correct Margolus rulestring or alias and then nudge it until it works. Here's this big one:

Also, I have found 2 spaceships, that can be "chained" into the long linear spaceships with the same period and velocity. The faster one can be chained in zigzagged lines, and the slower one only allows straight chains. Formally, these long spaceships should be considered as a single pattern, because all cells in them interact: evolution of the sole "building block" is slightly different from the evolution of the chain block. However, these interactions cancel themselves out after a few steps. Anyways, they are interesting:

Code: Select all

x = 234, y = 238, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$25bo2$28bo$32bo2bo$26b2o8bo4bo$34bo5bo4bobo$41bo13bo$42bo5bo8bo4bo$49b
o6bo14bo$61bobo$57bo7bo2bo2bo5bo$75bo$70bo8bo$79bo6bo$84b2o4bo4bo$83b
o7b2o6b2o$98bo8b2o$100bo3bo9b2o4bo$120bo$107bo2bo$112bo16bo$120bo7bo6b
o3bo$122bo7bo5bo6bo$129bo4bo10bo4bo6bo$140bo3bo5bo$151bo4bo6bobo$159b
o7bo$150bo21bo$bo158bo10bobo$166bo13bo$3bo171bo2bo$o178bo4bo2bo5bo$3b
o182bo$180bo7bo6bo3bo3bo$194bo13bo$195bo4bo9bo4bo$bo3bo197bo7bo6bo4bo
$bo216bo$210bo13bo$165bobo50bo6b2o2b2o$4bo227b2o$152bo2bo4b3o$145bobo
2bo2bo12b2o$2bo2bo137bo12bo5bo$138b2o7bo4bo3bo$140bo9bo$6bo$4bo135bo$
139bobo$137bo$5bo135bo$7bo$7bo$7bo$138bobo2$140bo$138bo$6bo$6bo128bob
o$8b2o$138bo$138bo3$136b3o$6b2o$8bo129bo25bo$10bo151bobo$135bobo25bo2$
83b2o4b2o$11bo73bo2bo47b2o25bo$8bo75bo4bo72bobo$164bo$10bo125bo$134bo
bo$10bo124bo$11bo150bobo$161bo$135bo$130bo3bobo26bo$10b3o115bobo5bo25b
o$129bo29bo$163bo$160bo$129bo$9bo2bo111bo3bobo$12bo109bobo5bo29b2o$12b
o51bo58bo37bo$62bobo97bo$63bo$123bo$118bo3bobo$63bo52bobo5bo35b2o$12b
o49bobo52bo40bo$12bo51bo$14bo144bo$16bo100bo44bo$112bo3bobo39bo$110bo
bo5bo39bo$111bo48bo$17bo$157bobo$16bo94bo$14bo91bo3bobo46bo$14bo89bob
o5bo46bo$105bo2$13bo$18bo86bo50b2o$17bo82bo3bobo51bo$16bo81bobo5bo$99b
o58bo$157bobo$155bo$17bobo79bo59bo$94bo3bobo$19bo72bobo5bo$16bo76bo$156b
obo2$93bo64bo$19bo68bo3bobo61bo$18bo67bobo5bo$17bo69bo65bobo2$156bo$20b
o66bo68bo$82bo3bobo$21bo58bobo5bo$19bo61bo72b3o2$17b2o137bo$73bo7bo$69b
o6bo3bobo70bobo$76bo5bo$19bo36bo2bo4b3o5bo2bo$49bobo2bo2bo12b2o82b2o$
20bo26bo12bo5bo$42b2o7bo4bo3bo$21b2o21bo9bo99bo$152bobo$44bo108bo$43b
obo$41bo$45bo99bo7bo$22b3o116bo6bo3bobo$148bo5bo$128bo2bo4b3o5bo2bo$24b
o17bobo76bobo2bo2bo12b2o$109bobo7bo12bo5bo$44bo69b2o7bo4bo3bo$23bo18b
o61bobo4bo4bo9bo$23bo3bo63bo2b2o4b2o2bo6bo$23bo15bobo45bo7bo2bo7bo9bo
$79bo4bobo4bo4bo4bo$42bo31bo3bobo2bo4bo$42bo29bobo5bo$73bo10bo$27bo$22b
obo15b3o2$26bo15bo2$39bobo2$25bo$40b2o$26bo$27bo$27bo3$27bo$27bo2$28b
2o5$28b3o2$31bo5$29bo$32bo$28bo2$32bo3$33bo$29bo3$32b2o4$31bobo2$35bo
$32bo5$34b2o3$34bo$36bo4$34b2o2bo3$36bo2$35bo2$37bo$40bo$37bo4$39bo$38b
o2bo2$41bo!
[[ GRID ]]

----

The aftermath of a collision:

Code: Select all

x = 72, y = 72, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
3bo3$bo$bo2$3bo63$69bo$67bo3bo$69bo!

[pzq_alex]

Interesting -- signals can travel around a still life and interact with the surrounding:

Code: Select all

x = 40, y = 41, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$17bo3$23bo$bo16bo2$4bo10bo$12bo10bo2$8bo$7bo2b3o$bo7bob2o8b2o6bo$9b3o
bo4b2obobo6bo$12b9ob2o$13b5ob3obobo$3bo13b5obo$14bobo4bobo$5bo9bo6bob
o$11bo3bo7b2o$15bo7b2o$10b2o2bo2b3o3b2o13bo$10b4o4b2o19bo$5bo$27b2o$22b
2o$21bobo$21b2o$31bo7bo$30bo$10bo9bo$bo2$32bo$18bo13bo$16bo18bo4$31bo
$23bo4bo!

[masharpe]

In addition to the "Double Rotate" rule already discussed, there are two other similar variants. Like Double Rotate, they have the same pop-4 spaceships as Single Rotate, while avoiding indestructible structures.

1 clockwise; 3 half-turn
0,2,8,3,1,5,6,14,4,9,10,13,12,11,7,15
(The holes in a filled region move like billiard balls.)

Code: Select all

x = 12, y = 13, rule = M0,2,8,3,1,5,6,14,4,9,10,13,12,11,7,15:T256,256
$7ob4o$12o$12o$12o$12o$12o$12o$12o$12o$12o$12o$12o!

1 clockwise; 3 clockwise
0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
(This has complement symmetry instead of Double Rotate's mirror-complement symmetry.)

Code: Select all

x = 12, y = 13, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15:T256,256
$7ob4o$12o$12o$12o$12o$12o$12o$12o$12o$12o$12o$12o!

I'm puzzled why Tim Tyler's original Rotations series of rules didn't include any of these. Rotations IV is not far off: delete the one pop-2 rule and you get a mirrored version of 1cw1ht. But the pop-2 rule cuts the number of pop-4 spaceships from 6 (of SR and its variants) down to 1.

Edit:
1cw3ht has the funny property that you can bounce a hole around in a filled region for quite a while before it finally explodes.

Code: Select all

x = 12, y = 15, rule = M0,2,8,3,1,5,6,14,4,9,10,13,12,11,7,15:T256,256
$12o$12o$12o$12o$12o$12o$12o$12o$12o$12o$12o$12o$11o$12o!

[breaker's glider gun]

It's fun to make a predecessor of something:

Code: Select all

x = 11, y = 12, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
2bobo$4bo3bo4$4bo4bo$2bo2$6b2o2bo$bo2bo2bo$5bo$6b2o!

(run for 100 gens)
A 1100 gen partial synthesis:

Code: Select all

x = 251, y = 67, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
250bo$249b2o$248bo42$171bo3$170bobo$170bo8$188bo2$187bo3$178bo2$185bo
$o181bo$obo$o!

[NimbleRogue]

This oscillator is a riot

Code: Select all

x = 6, y = 6, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$bobobo2$bobobo$2b2o$bobobo!

It even works when fully surrounded, and never loses parity

Code: Select all

x = 10, y = 10, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$bobobobobo2$bobobobobo2$bobobobobo$4b2o$bobobobobo2$bobobobobo!
]

[masharpe]

It turns out that the Double Rotate rule has been studied recently by Kenichi Morita. (It is formulated as a partitioned CA, instead of using alternating neighborhoods.)

https://ir.lib.hiroshima-u.ac.jp/00052559
See section 4.3 on "ESPCA-01caef", which is its identifier in Morita's numbering. Figure 20 shows the rule.

http://bulletin.eatcs.org/index.php/bea ... e/view/760
Here, he uses it to construct a reversible Turing machine.

For Single Rotate, though, I didn't notice him studying it. It would be called ESPCA-01cadf or ESPCA-04cadf in his numbering, I believe.

A triangular counterpart of Single Rotate received some attention longer ago from Imai and Morita.
https://www.sciencedirect.com/science/a ... 7599000997
Figure 8 shows the rule: pop-1 rotates, other states don't. They show that it's computationally universal.

Tim Tyler had the same triangular-single-rotate on his site, but it's visualized differently.
https://cell-auto.com/neighbourhood/qbert/index.html

[XNTEABDSC]

Here are some rotation rules inspired by HPP.

HPPTL rules.zip

(5.94 KiB) Downloaded 6 times

I'll explain the rule HPPTL_R ( HPP turn left, reflect when colliding )

HPPTL_R rule.png (7.5 KiB) Viewed 216 times

Each cell may contains arrows to 4 direction.
Each generation, each arrow will move to the cell of its direction.
If not colliding ( only 1 arrow will enter the cell ) , the arrow will rotate anti-clockwisely (its left)
If colliding (more than 1 arrows will enter a cell), all arrow will rotate to its opposite direction.

The Single Rotate Rule and HPPTL_R are equivalent with relation shown below

relation (2).png (18.24 KiB) Viewed 216 times

It turns out that the Double Rotate rule has been studied recently by Kenichi Morita. (It is formulated as a partitioned CA, instead of using alternating neighborhoods.)

https://ir.lib.hiroshima-u.ac.jp/00052559

They are in the range of Kenichi Morita's study.

Sorry about last post which has some mistakes