DrJB

Agree, need a bit more clarity here ... You're right. Intuitively it makes sense. I was thinking of it initially from a mathematical standpoint, and was not sure a rotation matrix can 'always' be written as the product of two reflections matrices. It might very well be that the solution could at times be not unique. When I mentioned 'commutativity', I has in mind full rotation in 3D space, and there, for sure the rotations do NOT commute i.e., rotation about x then y axes is NOT the same as rotation about y then x. Thinking of rotation matrices again, if we change the order of matrix multiplication, we get a totally different result. Now, all of this is true in 3D space (and beyond if we're comfortable with that). In 2D space, there is only one axis of rotation (Z, normal to the 2D plane). There, when a rigid body is subjected to two rotations, they are both about the same axis, and as such, they do ADD. In 'my' terminology, one cannot speak about commuting rotations in 2D ... again, pure terminology. PS. Thanks for a trip back in time ... This reminds me of a graduate course in Dynamics many years ago, and of all the subjects, 3D dynamics is often NOT intuitive ... especially when you include gyroscopic effects. That's not fair ... what am I going to do with all the parts I ordered from BrickLink? :(

The other option, which I find rather slick, is to use a gimbal-stabilized camera. I got the DJI osmo recently and rather pleased with the 'stability' of movies it produces. Careful though, as the 4k videos it produces won't run on just any PC/laptop. Now, if you're into building your own little camera (forget zoom and other features), you can try a Raspberry PI with a Camera Module. Be prepared to invest some serious time programming, to get it to do exactly what you're after. Again, both options (Raspberry Pi and Osmo) have no mechanical zoom/Tele capability.

now you lost me ... '77 ?? ah ... the year the first Technic models came out? My dad bought me the red tractor and yellow forklift.

lol ... no objection there :) I was merely referring to the build style.

I believe these apply only to FLAT patterns (i.e, 2-dimensional only). Once you move to the third dimension, no succession of mirror reflections can produce a rotation. It only works in one special case, when the pattern has one plane of symmetry. Translations are commutative (can change the order without changing the outcome). Rotations however are NOT commutative, the specific sequence of rotations CANNOT be altered.

Exactly ... somehow very similar to 8070

The GoPro Session (small cube) is ideal for many such applications. It retails for around US $150, and it includes both an SD card and a handheld stick. Not sure about the price in Australia though :(.

Very nice. So the yellow is a translated/rotated version of the red, and that results in two planes of symmetry. You really have a knack at doing pentagons inscribed inside hexagons

You're right ... obviously your memory is better than mine :). Though in all fairness, the older thread was primarily about panels vs. no panels. In this new thread, I was motivated by another reason (highlighted in the first post) The reason for this 'newer' thread is that I was a bit 'frustrated' by connectors becoming rare (my other thread you're contributing to). I'm ok with panels, but I do not want them to come at the expense of other parts/connectors. Yes, I agree fully that a clear/transparent' model would be a nice offering. The picture you chose clearly illustrates that what's inside a car matters a lot ... ;). In fact there are already 'few' technic parts available in Trans colors (15L beam, few connectors, and 1 panel). I wanted a while back to ask that same question (in a dedicated thread) but we do not have a large collection of parts yet.

Speaking of variations (of the above), here are two more, that now result in three 'distinct' tiles

Very nice, I like those. Thinking of the wallpaper groups (simplifying the math), the only 'transformations' allowed/possible are: 1. Translations 2. Rotations 3. Symmetries (mirror images) about 1 or more planes It appears the rotations/translations are relatively easy to achieve. The symmetries however are not so trivial. Here are three more, I call them 'Variations on a Theme'. The first is symmetric (three planes), and the other two are its 'twisted siblings' (i.e., no longer symmetric). Yet all three of them still obey translation and rotation.

Yes, I did the math too and, surprisingly, this works very well in LDD, no complaints whatsoever.

Beautiful. I knew you'd join us ... sooner or later :) Here is another one, the so-called 'chicken-foot' pattern. It's often seen on fabrics/curtains/wallpapers ... p4 I think

Yes, I remember that day VIVIDLY ... she was the 'proof' that anyone can make it, to be an astronaut.

Found two more, moving away from p6 to p2/p4 (need to check terminology). The first one is rather 'trivial'. I like the second one, it's starting to look like Moorish Zellige (Tiling/Tesselation) with more than one basic shape.

Very nice ... I need to go read a bit more about the 17 Groups :) I tried few more iterations in LDD and most/all figures I came up with have the p6 symmetry. Essentially, all figures can be reduced to a hexagon with some curvy/crazy edges. This for sure has to do with the parts available to us. Then I discovered a NEW (to me) part on Bricklink. By combining the two parts below, we can then do p4 groups. Pushing this further, we can even try tesselations of 2 groups of shapes. I can't try the combinations below as the part does NOT exist in LDD yet ... but, I just placed an order for few of them. The holidays for sure will include sometime with Lego. + By combining the above two parts, we essentially have the 4-branches equivalent of . One can try this other part ... but I have none. Correction: Found it, in fact, I have 50+ ... that I got some time back from the PAB wall.

I stand corrected :)

Here is another one, using the 'same' basic elements as aeh5040 ... though less compact.

Whatever happened to McAuliffe? What were the criteria to select some women over others?

Regarding the various shades of blue, I'd love to see more of the Dark Turquoise we had in the 8450 Mission and some other small bionicle sets.

Beautiful, thank you for sharing. One small comment if I may: The unit might shake a bit less if the 2L ++ half-width lift-arms (attached to the motor) are replaced with cams (below) can be replaced by I also like how 'physically realistic' the motions of the waves and the swaying of the palm-tree are NOT synchronized. And this is TRUE in real life as well. The two motions are due to two different physical phenomena :)

As much as I agree with many of your points, I am not sure I've seen discussions like these accomplish much with TLG. Do not get me wrong, there are many things I wish the TLG did differently, though in the end, they are driven by their own 'strategy' to ensure you and I (and countless others) keep on buying their sets (no issue with that, it is a personal choice/addiction) ... yet I've seen VERY FEW times TLG listen to the community. In the end end, it's ok to dream and wish, especially this time of year ... Happy Holidays.

Beautiful! We have 3 solutions so far. I'm working on a BL order ...

Thank you for the kind words ... and sorry about the added expenses. On the plus side, many of those connectors are now available 'primarily' in monochromatic colors (grey/white/black) and one needs not invest too much. That said, I'm collecting parts to reproduce your kinetic sculpture (beautiful work) but difficult to get the orange connectors, especially over this side of the Atlantic. And, for 17 groups, another geometric fascination of mine, I found the app below (iOrnament) sometime back. One can literally spend hours on it. I have not attempted to understand the math behind the reason for only 17 though. In the paid version, he extends the 17 groups to projections on a sphere. https://itunes.apple.com/us/app/iornament/id534529876?mt=8

First time I see this part in blue