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

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!

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...

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!

Nice find, and thanks for sharing. This looks very useful!

Awesome! I'd be interested to see video of the white version...

I strongly agree with this suggestion. The BWE quarter gears are definitely the way to go. I had a very similar constraint with this MOC, and the those gears were the only way to get close to the required accuracy. I would also avoid worm gears in the gear train - spur gears have much less backlash.

Akiyuki's Pneumatic module uses it: No doubt those who have worked on it can explain exactly what the function is here...

Jason Allemann's Marble Maze made it: http://jkbrickworks.com/maze/ I suppose some might argue that it is not really technic because there is a brick-built component in addition to the underlying technic functionality, but I don't agree with this position. Very interesting model, by the way!

Efferman has developed an extensive catalog:

Among the small sets, the Go Kart is by far the best in my opinion, especially for someone just getting into technic. In fact it is one of the best sets of this size that I can remember over the last 30 years.

Syncing was a big nuisance, and I did not manage to do it perfectly (as you can see if you watch the video carefully enough). Of course, what you want to achieve is that there is a time when all pods are perfectly aligned with each other. Probably the right way to do it would be to line everything up perfectly as you build, perhaps locking the gears in place somehow. However, I did not have the foresight to do this! Instead I had to adjust after the build was finished. Here is how I ended up doing it (which is not ideal). The mesh between the 16t and 40t gear is quite loose. Therefore, if you force the horizontal member that was constructed on p1 UP a bit (perhaps after disconnecting it at the far end), you can click the 40t gear around, one tooth at a time. This proves to be enough flexibility to get it more-or-less right. Some trial and error is helpful for fine tuning. Honestly this is a bit of a flaw with the model. It would be nice if it were easier to adjust.

Awwww. I thought it was real It's a very nice and neat mechanism, and a cool illusion!