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The previous demo made me dig deeper into dithering algorithms. It's something I should have done years ago, as I've been using simple random dithering now and then, and I hadn't even thought of gamma correction. One algorithm in particular caught my eye: Riemersma dithering, which uses the Hilbert curve. Compared to the usual matrices for error diffusion, the curve approach seemed easier to implement in some ways, as it has fewer edge issues.
More interestingly, it struck a chord with my earlier experiments with space-filling curves in image processing. So it was a kind of familiar territory, but it also seemed esoteric enough that I could imagine making some new discoveries. For example, play with other plane-filling curves besides the Hilbert.
The first image uses the boustrophedon curve, which makes the vertical wave patterns I recall from a number of non-dithering demos. The second curve is what I call the diagstrophedon, a diagonal zig-zag starting from the top left corner, and I think its wavy artefacts make a nice match for Venus's hair.
Then in image 3 we have Hilbert, which doesn't seem to make any particular artefacts, and I guess that's a good thing for dithering. Finally 4 uses the Peano curve, which makes some fun wiggles in light areas.
lls,
Shah-i-Zinda, Samarkand, Uzbekistan.
“The Shah-i-Zinda Ensemble includes mausoleums and other ritual buildings of 11th–15th and 19th centuries. ...meaning "The living king" … The Shah-i-Zinda complex was formed over eight (from the 11th until the 19th) centuries and now includes more than twenty buildings.” https://en.wikipedia.org/wiki/Shah-i-Zinda
I've been fumbling around with #openprocessing #logics and #colours and made two sketches demonstrating something like logical combination of colours, applying logical operations to the r, g, b values of the colours to be "mixed". I know this is completely useless but it was a funny prgramming exercise...
You can see (and test) the results in the two sketches
Colour VenDetta:
https://openprocessing.org/sketch/2634928
and Colour VennDango:
Window, Cửa Bắc Church, Hanoi, Vietnam
https://en.wikipedia.org/wiki/C%E1%BB%ADa_B%E1%BA%AFc_Church
#FensterFreitag #tiling #geometry #mathart #photography #architecture
A new (and improved) visualization of what translation looks like under stereographic projection. This is a line drawing, but looks pleasantly like a rendered reflective sphere.
The occasion is, my online shop is moving soon to a new platform. Relocating the math blog was a chance to freshen up some images.
Hexagonal tiling with stars, squares and assymmetric kites for #TilingTuesday
maybe ðere's a reason pentagonal dungeon crawlers haven't been invented yet 
Tessellation with cairo pentagons and hexagons (regular and lengthened). All pentagons have the same shape, the ones joining as in cairo tessellations have different colour than the ones which not.
#tilingtuesday #tiling #Mathematics #Mathart
Another visual refinement to a recent demo: adding seams to the optimized tiling scheme. While it breaks the mosaic illusion to some extent, I think it makes the tile sizing idea much clearer. As before, there's a uniform variant with the same number of tiles for comparison.
Source photo: Mary of Egypt by José de Ribera, in public domain.
Floor tiles, Imperial Citadel of Thăng Long, Hanoi, Vietnam
#Tiling #TilingTuesday #Pattern #Geometry #MathArt #MathsArt #photography
