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#tiling

8 posts7 participants0 posts today
Public *
Dani Laura (they/she/he)

Artworks based on dividing a rectangle/square into two rectangles, by splitting the larger side in a fixed proportion, and iterating recursively. Colors are computed from the shapes of the parent rectangles. (Procedure similar to
mathstodon.xyz/@DaniLaura/1140 ).
The first two pieces use the inverse of copper ratio (sqrt(5) - 2) and e^(-pi/2) respectively. The other two use the golden ratio, notice in the first how the splitting is more regular albeit not periodic (the colors here are just related to the shape of each rectangle so that it becomes more apparent). The last one was divided more in depth and the borders were not drawn to produce a texture.
#MathArt #Mathematics #modernart #ArtistsOnMastodon #mastoart #GenArt #tiling

Artwork of shapes with right angles, colors black, white and shades of yellowish orange and violet.
Artwork of rectangles of different proportions, colors black, white and shades of violet.
Artwork of rectangles of 5 different proportions/orientations, each different one using colors white, red, pink, light and dark green. The structure is more regular than the previous albeit not periodic.
Texture using black, white, and shades of red, orange and yellow.
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Jocelyn Etienne – research

I'm wondering: #physics makes a lot of use of #periodic functions, in particular it is very useful to solve space-dependent equations in representative volumes with #periodicBoundaryConditions.

However I've only seen it done with periodicity along orthogonal directions, aligned with a Cartesian frame.

Do you know of work, e.g. #PDE resolution, in nonrectangular #periodicDomains? E.g., in a #tiled hexagon? (but with a sufficiently generic setting, not exploiting regular hexagon symmetries) Even better if the periodicity parameters themselves are among the unknowns.

(Maybe I'm completely missing something obvious there, I'm in my first steps towards defining what I want - any random thought on the topic highly welcome!)

#tiling people?

Public
R.L. Dane :Debian: :OpenBSD: 🍵

Something I miss from #Tiling wms/compositors like #i3wm and #sway when I'm on #KDE:

I use #Yakuake on KDE #Plasma to have a terminal that's easily accessible, but stays out of my way when I don't want to see it.

On tiling setups, I use disappearing windows (I forget the actual name of the feature) that will pop up when I hit super+-, appear one at a time, and then disappear.

Yakuake lets you do tiling as well within its window, but I kinda miss the ability to cycle through a bunch of windows very easily. I mean, I've got the keyboard shortcuts set up very nicely, so it's just F12 to make the window appear and disappear, and then control+tab to cycle through tabs or control+pgup/pgdown to jump between panes, but somehow the tiling setup is just a bit easier to do. Less thinking, just super+-. ;)

I don't know if I'll continue to use tiling setup too much longer, though. It's too aggravating to figure out how to get the occasional gnome program to work properly. There's always some kind of fancy library initialization that I fail to get right. It's easier to just use a DE and whittle it down to nearly tiling levels of productivity.

:BlobCatDerpy:

Public
Alex Feinman

Has anyone seen a game (video, board, strategic) that is played on a grid OTHER than squares, hexes, or tris?

Yes, those are the only regular #tiling on the plane, but there are other really interesting semi-regular and other ones.

Public
Dani Laura (they/she/he)

These two art pieces are based on the deformation of a hexagonal tiling into a topologically equivalent "tiling" composed of parts of concentric circles, all parts having the same area (third image). Selecting one hexagon as the center, we transform it into a circle of radius 1. Next concentric circle will hold the 6 adjacent tiles as sectors of rings. And so on, the circle of level n will have radius sqrt(1+3·n·(n+1)) (difference of radius when n tends to infinity approaches sqrt(3)). This map can be coloured with three colours, like the hexagonal tiling. For the artwork, suppose each sector of ring is in fact a sector of a circle hidden by inner pieces. Then choose a colour and delete all pieces not of this colour. Two distinct set of sectors can be produced, one choosing the central colour, one choosing another colour. Finally recolour the pieces according to its size.
#MathArt #Art #Mathematics #geometry #tiling

Artwork in yellows, oranges and reds, like an explosion.
Artwork in multiple colours, radial 3-symmetry.
Deformation of a hexagonal tesselation into concentric circles.
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