New rule: Magnezones (B3/S123678)

[masonlgreen]

I just discovered a Life-like rule with very interesting behavior, which I haven't seen written about elsewhere. The rule is B3/S123678, and it can easily be simulated using Golly and similar programs.

The name I chose is an apt description of this rule's behavior, while also doubling as a subtle Pokemon reference. The rule's behavior may be a consequence of its bifurcated survival function (cells survive with 3 or fewer neighbors, die with 4 or 5, then survive again with 6 or more).

Magnezones exhibits features reminiscent of crystal growth and ferromagnetism. Most patterns keep expanding outward forever. The pattern initially consists mostly of a chaotic "liquid", which remains dominant on the boundary of the pattern as it grows. Over time, stable "crystals" form in the liquid, and these can have one of four different orientations: horizontal-odd, horizontal-even, vertical-odd, or vertical-even. Crystals are composed of alternating horizontal or vertical lines; "odd" crystals differ from "even" crystals only by being offset by one row or column (as the case may be). The crystals are somewhat similar to domains that form in ferromagnetic materials, hence the name Magnezones. Crystals are usually quite stable, but are not necessarily perfect (when they form, they usually have "vacancies" or individual missing cells in them, which do not disrupt their large-scale structure).

Where two crystals of different orientations intersect, they form a domain wall which is far less stable. Even after the center of the pattern has mostly crystallized, there will usually still be isolated bubbles of "liquid" which can travel along domain walls, eating away (or expanding) the adjacent crystals as they go. These bubbles are very persistent; sometimes they die out but other times they can expand or even split into two.

It is possible to design a pattern in Magnezones that does not expand forever; if the boundary of a pattern consists entirely of "saturated" domain walls, no further expansion will occur. A saturated domain wall is a wall with a critical density of vacancies. This happens when every third cell in the wall is missing; ON-ON-OFF-ON-ON-OFF, etc. Since no cells adjacent to this kind of wall have three neighbors, no further growth will occur.

It would be interesting to see what the size distribution of crystals is. It seems like it may follow some sort of power law, keeping in mind that the size of crystals can still vary over time due to the action of "bubbles" on their boundaries.
 
Magnezones is almost certainly Turing-complete; domain walls can be used to simulate Boolean circuits, and the "bubbles" that travel along them could then be used to simulate signals, as in WireWorld. It would be worthwhile to classify the different kinds of "bubbles" and their behavior to get a better understanding of how to build such circuits. Since there are four types of domain, this allows circuits/walls to branch.

Magnezones is also a good candidate for implementing variant colorings. We could color all "on" cells with one of four different colors depending on whether their (x,y) coordinates are even or odd. The four types of crystals will then be easily discernible, even when zoomed out very far, because each type will be built from a different combination of two of the colors. (This might also have the side effect of inducing a McCollough-style effect as well)...

There may be other rules which behave similarly to Magnezones. I wonder if analogous rules exist on the hexagonal grid as well (if so, there would be six possible crystal orientations instead of four).

[confocaloid]

A known spaceship from this post:

Code: Select all

#C https://conwaylife.com/forums/viewtopic.php?p=100479#p100479
x = 18, y = 29, rule = B3/S123678
2bo3b2o2b2o3bo$bo6b2o6bo$2bo2b2o4b2o2bo$2b2o4b2o4b2o$5b2o4b2o$8b2o2$3b
2ob6ob2o$3b2o8b2o$b2obo3b2o3bob2o$2bobo8bobo$2bobo3b2o3bobo$5bo6bo$4b
3o4b3o$3b3o6b3o$3b2o8b2o$2b5ob2ob5o$5bo6bo$5bo2b2o2bo$5b3o2b3o$3b2o8b
2o$3b2ob2o2b2ob2o$5bo6bo$5b3o2b3o$5b3o2b3o$o3b3o4b3o3bo$b2o2bo6bo2b2o$
2bo2bo6bo2bo$2b3o8b3o!

Edit: gliderdb-searcher gives one other spaceship:

Code: Select all

#C (0, 2)/4
#C Min Rule: B3/S1236
#C Max Rule: B3/S123678
x = 14, y = 19, rule = B3/S123678
2o2bo4bo2b2o$5o4b5o$6b2o$2b10o$4bob2obo$3b2o4b2o$bobo6bobo$bobo6bobo$2bo8bo$b3o6b3o$b3o6b3o$2bo8bo$b3
o6b3o$b3o6b3o$bo10bo$2o10b2o$b4o4b4o$2ob2o4b2ob2o$b3o6b3o!

One long-living "river of chaos" does not settle until generation 489,681:

Code: Select all

#CXRLE Pos=77,61
x = 19, y = 23, rule = B3/S123678:T256,256
2ob2obobo2bobo3b2o$2o2b3o6bo2bo$2b5o9b3o$obo5bo4bo2bobo$4b4o2b2o5b2o$b
2o4bo2b3ob2ob2o$2ob4ob2o2bo4b2o$bob2ob4obo2b2ob2o$obobo6bo3bobo$2bobob
2obo4bo2bo$3obo2bo3bo3bob2o$4bob3ob2obobobo$3o4bo2bo3b2o2bo$bo3b6ob3ob
o$o2bo3bob2o4bob2o$b2ob2o3bo3b4o$2b2ob3ob2o4bobo$5o6bo2b2obo$2bobobo5b
obobobo$o3bo2b2ob5o$bo2b3ob4ob2obobo$3ob6o3b3o2bo$3o2bo4bo4bobo!

It is possible to design a pattern in Magnezones that does not expand forever; if the boundary of a pattern consists entirely of "saturated" domain walls, no further expansion will occur. A saturated domain wall is a wall with a critical density of vacancies. This happens when every third cell in the wall is missing; ON-ON-OFF-ON-ON-OFF, etc. Since no cells adjacent to this kind of wall have three neighbors, no further growth will occur.

Is it possible to design a wall? This has "on-on-off-on-on-off" both on the inner and the outer side, yet easily destructible:

Code: Select all

x = 45, y = 42, rule = B3/S123678
2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$bo41bo$ob41obo$obo39bobo$
2bo2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2bo$obobo35bobobo$obobo35bobob
o$2bo39bo$obobo35bobobo$obobo35bobobo$2bo39bo$obobo35bobobo$obobo35bob
obo$2bo39bo$obobo35bobobo$obobo35bobobo$2bo39bo$obobo35bobobo$obobo35b
obobo$2bo39bo$obobo35bobobo$obobo20bo14bobobo$2bo21b3o15bo$obobo21bo
13bobobo$obobo35bobobo$2bo39bo$obobo35bobobo$obobo35bobobo$2bo39bo$obo
bo35bobobo$obobo35bobobo$2bo39bo$obobo35bobobo$obobo35bobobo$2bo39bo$o
bobo35bobobo$obobo35bobobo$2bo2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2bo
$obo39bobo$ob41obo$bo41bo$2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o!

[masonlgreen]

Hmm, good questions! Thanks for sharing the links, looks like the rule has already been investigated to some extent (although not named). It’s quite interesting that it has spaceships, given that usually patterns just grow continuously.

Addition: In case you were wondering, the bifurcated survival function does seem to be necessary for the behavior I described. I tried out B3/S123 and it does not produce stable crystals (they “dissolve” fairly soon after formation, hence the liquid phase remains dominant). While survival with six neighbors is a fairly rare event in Magnezones, the fact that it does happen seems to be essential for the crystals to “condense” properly.

On the other hand, survival with seven or eight neighbors seems to be optional (thus, B3/S1236 is a variant, as well as B3/S12367 and B3/S12368). It appears that they differ slightly in some ways (particularly how long it takes for the liquid phase to “cool” into crystals), but overall they are rather similar, so they could be referred to as the Magnezones family. Whether it is possible to construct a wall or not may vary depending on which variant we choose.

Whereas, if we allow cells with four or five neighbors to survive, then instead of Magnezones we get Life without Death or something similar to it.

[azulavoir]

Perhaps to extend the Pokemon references, the S7 but no S8 variant can be Magneton, and the S6 but no 7/8 can be Magnemite.

[masonlgreen]

Sounds great! And the 8 but no 7 could be Sandy Shocks, being a “switched around” version of the “Magneton” rule.