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Looks great - I'll get to work trying this...

Wow, this absolutely phenomenal. I am struggling for words! I have thought about such a thing many times, and concluded that it was in practice essentially impossible! (I was quite happy when I managed to implement a one-dimensional cellular automaton mechanically - see below - but yours blows that out of the water). It would be great to see a grid big enough for some interesting configurations. It may well be worth investigating other cellular automaton rules (it seems that you can implement any totalistic rule with the Moore neighborhood). It's likely that some others can give more interesting patterns on a small grid. (Although of course Life has the advantage of being very well known). Please do make a digital file or instructions. I would be very happy to test or help in other ways. https://youtu.be/_52PX3vEntQ

That's epic! I made a smaller version of the mechanism a long time ago (see video below), but it never occurred to my how perfectly the concept fits with GBC! And here is an astonishing piece of automation by the same builder...

Very entertaining and fun project! This is also the direction TLG is heading! #colorvomit

Very nice. Mesmerizing in its awesome simplicity!

Wow, great experiment and great video! I am amazed that it can take so much weight, but those poor parts! To go even further, maybe you could reinforce axles by running them through 2x2 round bricks, or somehow replacing the axle bearings with technic turntables... He's already done 100kg!

Thank you for the nice comments folks. (I was a bit worried it would be too esoteric for anyone to appreciate!) Yes, exactly. You can hook up as many of the units as you want in a ring (or just in a line). The only thing that would need to change is the geometry of the physical bracing and the chain drive. Currently 135 degree angle connectors are used to get the 8-fold symmetry. Interestingly, if the number of units is not a power of two, it would typically take MUCH longer for the pattern to repeat. E.g. with 10 units I think it takes 8890 steps. No reason why not in principle, although it would be harder. Perhaps differentials could be used. Of course, a Turing complete rule would be good! One thing I would like to improve is to replace the yellow "flags" with something larger and more visible (that moves or changes color). The issue is theat it needs to take very little force to activate it. Any ideas welcome...

Here is my latest endeavour in mechanical computation. Cellular automata are among the simplest possible computers. One of the most famous is Conway's Game of Life which runs on a two-dimensional array of cells, but even cellular automata on one-dimensional universes can be interesting, and some, such as rule 110 are known to be Turing complete (i.e. can do arbitrary computation). As is my wont, I wanted to see if I could implement one of these entirely mechanically. The device implements a version of the XOR rule (or rule 60), an even simpler cellular automaton that produces fractal space-time histories. There are 8 units, each of which can be in the "up" or "down" state. They are scanned cyclically in clockwise order (via the chain drive). When a unit is scanned, if is in the up state then the state of the previous unit is toggled (changed to the opposite state). The pattern repeats every 8x8x7=448 steps (8x7=56 revolutions). Every 56 steps, all units are up, and then all but one are switched to down in succession. So far the device is 100% reliable!

Most important parts of the mechanism are actually visible in the video, although I understand it's hard to see what is happening! The chain contains four wide track links, and the rest is normal chain. When those four pass the knob wheels at the top of a unit, they rotate the central vertical axle by one turn. The central axle has a driving ring (the new 3L type on the smooth Porsche axle connector), so that depending on the position of a changeover catch the central axle it is connected either to nothing or (via a 1:2 gear ratio) to a crank (Bionical weapon barrel) on the _previous_ unit in the circle. That crank controls the changeover catch of that unit - a half turn toggles the changeover catch to the opposite position. Apart from the gearing (which isn't important except that it is a 1:2 ratio), the only thing not clearly visible is a detent mechanism, which ensures that the crank snaps cleanly into one of two positions 180 degrees apart. (That is essential, otherwise errors would quickly accumulate).

That app looks great, but sadly it seems to be iOS only :-(

Several things are a bit confused or potentially confusing here: 1. JonathanM: it's true that any isometry can be produced by composing reflections, but not all these groups can be generated by reflections. Indeed, many of them do not contain any reflections. 2. DrJB: JonathanM was referring to Frieze Groups, which are 2-dimensional (with a 1-dimensional subgroup of translations). 3. DrJB: Not quite. It's always true in any number of dimensions that a rotation is a composition of two reflections. However, in 3 or more dimensions there are isometries (rigid motions) that are neither reflections, rotations, translations, nor glide-reflections. E.g. in 3 dimensions there are screw-rotations, and in 4 dimensions there are compositions of two commuting rotations. 4. Lastly, it's true that rotations do not in general commute in 3 or more dimensions. But in 2 dimensions rotations about the same point do commute.

You guys are on fire! Some beautiful tesselations there. To make things more interesting, for the definitive "17 wallpapers" catalogue, I am going to suggest some extra requirements: 1. The symmetry group should be the same regardless of whether you ignore colors, and whether or not you only look at the overall shape or the individual parts. (So for example, a 3L axle going through a should be avoided, unless you can tell from the rest of the pattern whether 4-fold rotation about this point is intended to be allowed). 2. It should be rigid, not floppy, and reasonably strong. (So should probably be replaced with , while is best avoided). 3. It should be a mathematically exact fit. Here is a relatively lame example satisfying these requirements, with (unambiguous) symmetry group p4m: In a different direction, could we do a Penrose tiling, I wonder? Presumably the pentagon angles would require some approximations. By the way, to anyone wondering what we are on about, I found this classification table useful: http://en.wikipedia.org/wiki/Wallpaper_group#Guide_to_recognizing_wallpaper_groups

Here are p6m and p6:

Nice! And of course the same can be done with 135 deg connectors throughout. Thinking a bit more about the 17 wallpaper groups project: In the case of the first picture in this thread (the hexagonal lattice), there is a possible ambiguity about which symmetry group to assign it to. If we consider symmetries at the level or actual parts, so the brown connector is regarded as different from the LBG one, then I think it is p3m1. If we just look at the overall shape, and don't distinguish between axles holes and pin holes, it is p6m (in particular it has 6 fold symmetry). If we want to do it right, I suggest ambiguous cases like this should be avoided... That's a delightful image, by the way... I wouldn't mind seeing them too.

The other thread was mainly about 3D structures. I think it makes perfect sense to have a different thread for 2D tesselations. Those are among my favorite parts too, and posts from DrJB have an unfortunate tendency to trigger an expensive spending spree! As it happens I have made _exactly_ those two before! I'll see what else I can come up with... One interesting challenge would be to come up with examples of each of the 17 wallpaper symmetry groups.

Definitely looking forward to seeing video of that latest "stepper" - it looks very intriguing! Keep up the good work...

Hi all, Here is my latest kinetic art piece: The nine pods all oscillate at slightly different speeds, so the pattern is always changing, and repeats about every 5 minutes. The two at the ends are directly geared in a 9:10 ratio. The others are driven by differentials which successively average the speeds. This means that the speeds are in the ratios 72:73:74:75:76:77:78:79:80. At various times, it produces 1 wave, 2 interlacing waves, and 3 synchronized color sets. Enjoy!

That's awesome! So simple yet so beautiful.

Awesome - a very nice piece of public service!

Thanks! Amazingly there is very little strain on the motor. It is running only at about half power from the rechargeable train battery and not really struggling at all. (And the smaller version ran continuously for two shows without generating dust). I tried running it from an E-motor and solar cell, which did not quite work with the current gearing. I suspect that would work with another 1:3 or 3:5 reduction.

I made a bigger version, with 17 pods geared in the ratios 80:81:82:83:84:85:86:87:88:89:90:91:91:93:94:95:96. Enjoy!

Wow, just beautiful! Dare I say it, Akiyukyesque.

Indeed, in my experience these 9V batteries themselves are not suitable for high-current applications. I once tried running a buggy motor powering a pneumatic compressor from one - I seem to remember the battery was dead in a minute or so!

Wow - this is just incredible - I'm speechless! (Although I think there is a reason TLG did not make the official set like this ) Please do make some more videos! I think everyone would like to see how all the functions work in full detail. And, of course, keep building. If this is your first MOC I can't even imagine what the next will be like!