Life3D - in search of gliders. Part 2

In the first part of the publication, I talked about searching for gliders in the 3-dimensional game "Life" (with 26 neighbors in a cage). There were several examples of what was found. But it turned out that the rules with gliders are somewhat larger than I expected at the beginning. Although not much ...

The program, which was looking for gliders, issued quite a lot of “suspicious” launch configurations. But the gliders were not all. In many cases, the troublemakers turned out to be pulsars - periodic constructions with periods that are not dividers 60.

Most often, the period of such pulsars was 8:
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Rule B5 / S2,3:



Rule B5 / S2,6,8:


Rule B6,7,8 / S2,4,8:


Rule B7 / S3,4,5,6,8:



But there were others. For example, a pulsar with a period of 17 (rule B6.9 / S4,5,7):



Here it can be seen that the pulsar periodically touches a stable figure hanging nearby, this temporarily violates its symmetry, but does not affect the overall development.

Let's return to the gliders. One of the gliders was in a completely empty world (rule B5,7,9 / S4,9,10):



The other flies at a speed of c / 3, retaining its shape: at each step it turns 120 grams and shifts along the cube diagonal (rule B5.8 / S7.9):



This airframe consists of 8 cells and looks like a platform 3 * 2 * 1, to which is parallelepiped 2 * 1 * 1. In one of the rules, a “tail” from one point was added to this glider, but I could not find it again.
By the way, pay attention to the "swinging" u-pentamino. This is the most common pulsar in 3D: it exists for rules in which cells are born with 5 living neighbors (but not born with 3 or less), and die with 4 or less living neighbors. For example, under rule B5 / -

Some more or less ordinary gliders:

Rule B6.8 / S4,5,7,9 (the period of this airframe is 10):



Rule B6,7,8 / S3,5,6:



Rule B6 / S3,5,7,8:



Rule B5,8 / S2,5:



Rule B6,8 / S3,4,5:



Under some rules, more interesting objects are formed. For example, in rule B5,8 / S5,9, a one-dimensional object often appears, consisting of 12-cell flat pancakes and calculating the parity of binomial coefficients:



Most often the worlds in which there are such "replicators" are unstable. And quite often they have gliders flying at the speed of light:



Such a glider may occur, for example, when the replicator interacts with something else:



In rule B5,8 / S5,9,10, gliders are even more diverse:









Even more surprising behavior is found in rule B6.8 / S3,5,7. There, the main part of the space quickly stabilizes, but there is an object that multiplies in some plane. When interacting with sustainable objects encountered on the path, its evolution changes, but does not stop. In some cases, new breeding centers may appear, which are perpendicular to the original plane. As a result, the space is filled with a semi-ordered structure with a density of about 1.5%.





This is all that so far has been found in this space. But it turns out that there are not less gliders in the rules, where only 18 neighbors are counted in a cell. You can also consider the division of space into truncated octahedra or rhombic dodecahedra. There, gliders are very rare, but they are still found. And there are signs of the existence of gliders on a four-dimensional lattice of 24-sided. Unfortunately, the visualization for this case is not yet ready.