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The infinite tiler problem

The tiler can never find the correct matter for dimension transitions.
  [vote for,

So the tiler has point tiles with point mortar and can make perfect lines. They also,in their material repertoire, they have 2D tiles and its respective mortar and this is true for any dimension required by the client. No problem when the client is working with a distinct n dimension . But you know clients, they want cutting edge stuff. And the sales team,using those ever flexible virtual mathematics tiles and mortar, sell it to them.

The problem comes when the tiler is asked to make a transition edge. They never look right, no matter what dimensional material is used. Take a transition from 3D to 4D, the filling the transition with 3d tiles and mortar leaves gaps, looking from 4D it would almost look fractal. Using 4D tiles and motar, looking from 3D has a ragged cut edge of sliced 4D tiles and motar.

Does anyone have a transition beading of N>N+1 dimensions to make an edge that designers and architects require in this age of smooth slick design? The marketing team have been saying that there is this new topological tile that stretches the span between the dimensional difference but I'm not that sold. And I don't think a 3n/2 tile would work either. It would stick out like dogs balls. Patchwork does.

The tiler is stumped. For the 3D to 4D case, when a 4D tile edges through the 3D design space the difference is noticeable. It's not like looking at a 3D tile. Some clients don't notice but the fussy ones, well.

Maybe, it's an energy thing.

<Idea for [2fries]>

wjt, Jun 27 2019

3D tesselation tiling
I don't really understand problem being addressed in the idea, but this one may be relevant. [xaviergisz, Jun 28 2019]


       Just use curved tiles - if you're tiling a 2d floor, and want to break- out into 3d and go up the wall, you can apply a set of curved transition tiles that start off 2d, and then smoothly bend 90 degrees out to start the same pattern going up the wall. This is fine when the edges of your tessellation are aligned with the orientation of the wall, but if you start going off square, can get tricky rather quickly. Also, 3d spaces are less tiled, more "filled" if regular tilings are used (or semi- regular, i.e. whatever the 3d analogy to 2d-Penrose tilings might be) or, if you're not too bothered about having zero inter-tile distances, then I think the nomenclature is "packed", which I think that extends to 4+ dimensions as well.
zen_tom, Jun 28 2019

       Can a 2D object be functionally stretched to 3D object? Not sure about that one.   

       This is the infinite tiler, though. true 2D tiles , not 2D surfaces of 3D tiles in the 3D realm where all objects are 3D. Same could be said of faux 3D tiles in 4D. In our space it's all 3D objects and effects. I don't think the flatlanders can have a zero z dimension rather 1 unit z.
wjt, Jun 28 2019

       What is the halfbaked idea here?
xenzag, Jun 28 2019

       What you need is tiles with a Hölmsheutz dimension. That way, they can be 2D from one side, but 3D when viewed from the other. Or 3D/4D etc. You could even have tiles that were 2, 3 or 4 dimensional depending on which side you viewed them from.   

       Grouting is going to be a pain in the arse, though.
MaxwellBuchanan, Jun 28 2019

       You should hire Serpinski Tiling Services. They have a talent for this sort of thing.
8th of 7, Jun 28 2019

       //point tiles with point mortar and can make perfect lines//   

       Are the lines of zero length? Or are you counting the grout too? In which case the line is actually a line of grout, not a line of tiles.
pocmloc, Jun 28 2019

       If you use Mandelbrot tiles, they will have an infinite perimiter, so you will require a correspondingly infinite amount of grout ...
8th of 7, Jun 28 2019

       //Hölmsheutz dimension//   

       Until the bot gets to this page, that's not even a googlewhack.
Loris, Jun 28 2019

       Not in this dimension, admittedly.
MaxwellBuchanan, Jun 28 2019

       I'm still waiting to hear what the idea is here. I can see a question bein presented, but not an idea. The HB is about presenting halfbaked ideas, and not about asking hafbaked questions...... (hovers over mfd identification)
xenzag, Jun 28 2019

       // I'm still waiting to hear what the idea is here. //   

       Of course you are. This is quantum ; the idea does not exist until you observe it, thus collapsing its wave function and fixing its state.   

       This requires you to make a preemptive decision to observe the idea. Look, we'll demonstrate the method with this sealed box and this cute kitten ... <sniggering/>
8th of 7, Jun 28 2019

       The idea, I was badly trying to install, was the unit of a n dimension and the change between it and the n+1 dimension's unit. What ever the number of dimensions of the universe, it seems all objects have those dimensions. Even the flatlanders had a 3rd dimension even if it was only, maybe, planks constant or under.   

       We maybe 4D or higher beings. Not that there is any good transition.
wjt, Jun 29 2019

       I still don’t see an idea here.
xenzag, Jun 29 2019

       True, it probably is the question(purely of distance dimensions), is there any unit that spans n and n+1 dmensions. My thinking is reality is stuck with all things having same number ofspacial dimensions but we perceive and act in the 3 distance dimensional space.
wjt, Jun 29 2019

       //I still don’t see an idea here.//   

       Some people obtain greatness while others have groutness thrust upon them.
AusCan531, Jun 29 2019

       There once was a Mandel bread recipe
that involved Tessler's blocks in three dee.
But when the helm of Holz added a dimension
which caused Max's cannon to shoot out a mension,
niether Xen, Zen nor Xavier could tessle them to C an I D.
pashute, Jun 30 2019


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