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this probably hasn't been discovered yet, has it?

That's a predecessor to lumps of muck, surrounded by two houses. Something this simple has probably already been discovered since Life first became popular in 1970.

Extrementhusiast wrote:That's a predecessor to lumps of muck, surrounded by two houses. Something this simple has probably already been discovered since Life first became popular in 1970.

But could we synthesise that?

Freywa: not impossible, starting with a r-bee on house

the stabilized beehive-like LOM predecessor is just the first generation of the stairstep hexomino, kind of like the similarly shaped bookend and its parent the century. The plan is to find a synthesis of the stairstep, and other gliders that are one generation away will make the houses.

While I don' t think anyone has tried to synthesize this specific still-life, it should probably be fairly easy to do. I would guess that it ought to take around 10 gliders or so. I'll look into it.

we already have a 2-glider synth of the house AND LOM both by you, so it would take only six gliders. The first generation of the lumps of muck might make a handy induction coil that functions similarly to a bookend, house, or cap.

alex79 wrote:we already have a 2-glider synth of the house AND LOM both by you, so it would take only six gliders. The first generation of the lumps of muck might make a handy induction coil that functions similarly to a bookend, house, or cap.

I didn't find either of those. Conway himself traced all the two-glider collisions in the very early days of life. Also, just because one can make object A from X gliders and B from Y gliders, that doesn't necessarily mean you can make A+B in any desired orientation from X+Y gliders. This is true in some cases, but not true in general. in particular, most house syntheses emerge from the edge of their predecessors, and so do most LOM predecessors, gluing one house to a LOM is easy. Unfortunately, I know of no simple LOM predecessors where houses can be brought in from both sides simultaneously. Constructing a LOM incrementally from a still-life is possible, but more expensive.
Here are two syntheses; one from 17 gliders by growing a pseudo-still-life sideways, and one from 24 starting from one house and working end to end. There's probably a way to do it more cheaply; the problem is that most LOM predecessors cause the LOM to erupt forward from one side (making the other side inaccessible), rather than from the side, allowing both ends to be capped simultaneously.

1.If you did not find the LOM and house synthesis with two gliders, how come it says so on their wiki pages?
2.does the predecessor have enough induction coil value to be posted with its relatives the cap, bookend, r-bee, teardrop, etc. on the wiki?

alex79 wrote:1.If you did not find the LOM and house synthesis with two gliders, how come it says so on their wiki pages?
2.does the predecessor have enough induction coil value to be posted with its relatives the cap, bookend, r-bee, teardrop, etc. on the wiki?

I think he meant reactions that would work to build such a still life. The one two-glider collision that produces a LOM is too sparky to be used here. (And no, I don't think two-sided induction coils have that much value.)

alex79 wrote:1.If you did not find the LOM and house synthesis with two gliders, how come it says so on their wiki pages?
2.does the predecessor have enough induction coil value to be posted with its relatives the cap, bookend, r-bee, teardrop, etc. on the wiki?

I don't maintain the wiki, so I can't speak for its contents. I had a web site (currently down) from 1997-2013 that listed many Life objects, and also many syntheses (originally based largely on the work of David Buckingham, whose synthesis lists in turn started with a few that were previously known, plus much of his own work in synthesizing over thousands of additional objects.). Unfortunately, my internal database format uses an older Life pattern file format than .rle, that doesn't support annotation information, so the .rle files on my site contained no annotations about who found patterns, who found their syntheses, etc. As much of this information has been copied around, much has been attributed to me that was actually the work of others. I have done a lot of work in synthesizing objects, but others have done much more (except perhaps for pseudo-objects, which seem to be of little interest to anyone else). The one thing I can claim credit for is the editing (e.g. arranging the object lists,
arranging syntheses in small steps with "before" and "after" images, etc.), which is primarily my own work.

A few months back, I went through all the synthesis files on the wiki (from a downloadable zip) and made some notes about what I remember - in particular, things that were misattributed to one person (frequently me) that belonged to someone else. At some point, if anyone has the time and patience to deal with it, that could be edited back into the various affected wiki files. I'll be happy to provide the information to anyone who is interested in doing this.

As far as two-side induction coils, they do have a place, but they're generally much less commonly used (since at least three components must be involved, resulting in much larger objects). The smallest object that uses such an induction coil is (I think) 15 bits - two blocks on a 7-bit Z. They are also usually harder to construct, and much less likely to occur naturally, e.g. if the chance of one piece occurring naturally has a low probability p, the chance of two coming together is much smaller, O(p^2), but three at once is smaller still - O(p^3). While such things do sometimes happen, it's usually as a result of a one-sided inductor being hit by something else that turns it into a two-sided inductor inducting a new one-sided inductor.

could it be a smaller substitute for two one-side inductors like r-bees?

It's usefully extensible! However the maximum size is limited by the maximum size of the Houses.

alex79 wrote:It's usefully extensible! However the maximum size is limited by the maximum size of the Houses.

It's infinitely extensible. One longer (as you have here) has long houses aka docks. At two longer, an extra bit appears on the houses - they are pairs of siamese bookends. 3 and 4 are similar - further extend one or both sides. At 5, there are two extra bits, 3 spaces apart (i.e. bookend siamese table siamese bookend). This can be continued as far as you want. Synthesizing these can be a bit of work, but it's probably doable, just widening all the pieces a little bit at a time.

For longer inductions, I use bookends with tails, then bookends with R-bees. The bexh, however, is ugly...
P.S. Of course, they are hard to create, but they are classy.