Brad-san, thanks for your comment. As you commented, one of the best things about Lego is the 3D. When I was a child, my Lego was mostly just square blocks, and I remember they came in six colors: black, white, red, yellow, blue and gray. Despite the restriction, I was hooked and built many buildings, vehicles, etc.

All parts (tile round) in my Lego Art set are not stackable, but other sets include stackable parts (plate round with solid stud), so one may be able to try 2D+ first.

FYI : The Great Wave created with only tile round

Hi, Kotaro Okazaki, fun post, very colorful. Not everyone is on the anti-Lego side for environmental reasons, and there's honestly a lot worse we could do with petroleum products. There's an ongoing story of Lego becoming again one of if not the favorite toy of Kids and Adults. Part of that story is diversification, which might even be describable as "language development". Lego's development over the last twenty years has seen a lot new pieces. For example, I'm fairly sure that I never had a flat, circular 1x1 tile in my collection as an adolescent or even as a teenager. Although I definitely had 2x2, flat circular tiles.

At some point LEGO group made a good decision of listening to its user community, and now there are a lot more smooth pieces, hinges, and joints than ever before. Consequently, there are a lot of new awesome sets like The Insect Collection and Auspicious Dragon. These official sets are programmatic to recreate, and every bit as good as what Dicken Liu has come up with recently.

It would be really awesome to see your idea go into three dimensions. For example the input could be a CAD model of an articulated android figurine, and the output is a piece list and instructions how to build. I doubt Lego themselves can even do such a thing, and don't want to diminish what you've done here. Starting with essentially one piece is a good idea. If you or anyone else wants to continue the project, I have a "next step" to propose. It would be a fun project for our yearly summer school too.

Aside from smooth pieces, the other thing that is needed for expert "Studs Not On Top" constructions are small pieces that can re-orient the building surface by 90 or 180 degrees. I think the oldest such piece is #4070 the "headlamp brick", which also seems to be the opinion in this article with a more extensive list of useful pieces. The article gives an interesting, inspirational example of the the creator symbol, which is comprised of six headlamps.

How many different ways can six headlamps be combined?

If it was even as simple as asking about poly-pentagons, we could use the tools and methodology of Stephen Wolfram's latest blog post on Multiway Aggregation systems. We honestly could have spent more time on this one, and if we had, the "six headlamp" question would have made a nice section for all the Lego-experimentalists out there. The problem is not only that we haven't finished PlanarPolygonFragmentation, but also that we haven't even started in three dimensions. For the three-dimensional question, we would need something like PolyhedronFragmentation. Enthusiasts are welcome to try with Regions, and it might work to a decent numerical approximation without kernel crashes, who knows.

So it seems 3D is still too difficult for us, but there are some other interesting ways to build up to 2+D as is seen in Vincent van Gogh - Starry Night or the Hokusai - The Great Wave. Once you start using slant or curve pieces in a plane, then something like PlanarPolygonFragmentation is needed to make sure they fit correctly. If even that is too much, Jeroen van Veen (or someone in his camp) has developed a new style of building not much worse than painting with numbers, see the cover art for Lego Music and Preludes. As far as I know, no one has ever successfully used Lego to recreate a Kanji calligraphy or even an enso (circle painting). But it seems the world is almost ready for such works to come into existence.