Life3D - in search of gliders. Part 2

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

    The program that was looking for gliders gave out quite a few "suspicious" starting configurations. But gliders were far from all. In many cases, pulsars turned out to be troublemakers - periodic structures with periods that are not divisors 60.

    Most often, the period of such pulsars was 8:

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

    Back to the gliders. One of the gliders ended up in a completely empty world (rule B5,7,9 / S4,9,10):



    Another flies at a speed of c / 3, retaining its shape: at each step, it rotates 120 g and moves along the diagonal of the cube (rule B5.8 / S7.9):



    This glider consists of 8 cells and looks like a 3 * 2 * 1 platform, to which a parallelepiped 2 * 1 * 1 is attached. 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 / -

    A few more or less ordinary gliders:

    Rule B6.8 / S4,5,7,9 (the period of this glider 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 form. 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, worlds in which there are such "replicators" are unstable. And quite often they have gliders flying at the speed of light:



    Such a glider can 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 bulk of the space quickly stabilizes, but there is an object that multiplies in some plane. When interacting with stable objects encountered on the way, its evolution changes, but does not stop. In some cases, new breeding centers may occur, 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 no less than gliders are in the rules, where only 18 neighbors are taken into account in the cell. You can also consider the partition of space into truncated octahedra or rhombic dodecahedrons. There gliders are very rare, but still found. And there are still signs of the existence of gliders on a four-dimensional lattice of 24-facets. Unfortunately, the visualization for this case is not yet ready.

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