foldworks<p>Carved stone screen, Agra, India, 19th century, copied from earlier models, Victoria and Albert Museum, London</p><p><a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TilingTuesday</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>tiling</span></a> <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>design</span></a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MathArt</span></a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>photography</span></a> <a href="https://mathstodon.xyz/tags/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>architecture</span></a></p>
#mathart
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Completing the quartet of brass display models, "Threefold" realizes part of the Bryant-Kusner parametrization of the real projective plane.
This 90mm unpolished brass piece was made by Shapeways in winter 2024 using lost-wax casting.
#Math #MathArt #3DPrinting
3D DUCK
3D DUCK
(3rd dimension = time)
(
= abs(1/ʒ)+c(
division))
Continued thread
In the following artworks the corners of the polygonal lines are rounded.
#mathart #algorithmicArt #AbstractArt
These artworks are based on a generalization of Lucas sequences for complex numbers, defined as:
Z(0) = 1
Z(1) = 1 or i
Z(n) = shrink( e^(iθ)·Z(n-1) + Z(n-2) )
Where shrink() is a function which decreases a complex number into the two-unit square or the unit circle centered at the origin. In these works I use three different versions, based on taking out the integer part of the real and imaginary parts (or the integer part minus 1), or of the modulus of the number in polar form.
Figure 1 depicts the 128 values walk using θ = π/5 and Z(1) = i, and the shrinking function which takes out the integer part of the real and imaginary parts.
In the three artworks that follow, the lines connecting successive values toggle between being drawn or not. See the alt text for more information related to the artworks.
#mathart #math #algorithmicArt #AbstractArt
hmmm yes, I'm going to call ðis ðe "Ain't nobody need the Amazon when we have Amazon at home" #tiling 
#TilingTuesday - #Tiling with triangles and squares.
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Now squares increasing by the golden ratio
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Looping animation of silver rectangles with sides decreasing by 1/√2.
Looping animation of squares with sides decreasing by golden ratio.
♋︎Astral
Sorcery♋︎
Fractal with decagonal symmetry for #FractalFriday .
#fractal #mathart #algorithmicArt #geometry
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@ark_brut Another approach is to roll paper into a tube and cut notches. I might try this later https://www.youtube.com/watch?v=65BM4K1k77U
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@ark_brut A bit beyond my current skills, so I looked for something much simpler: https://www.youtube.com/shorts/g0-eD9c5uog. I used four lolly sticks and two rubber bands lying around the kitchen.
The only tricky part was cutting the notches with a craft knife and a self-healing mat.
I might try other tensegrity structures, but some need holes like the bed slat structure which is a step up in terms of equipment and skills.
Tiles on a temple wall, Bangkok, Thailand
#TilingTuesday #temple #geometry #tiling #MathArt #photography #architecture #design
#TilingTuesday Flowery tetradecagon dissection into rhombuses and stars.
Over my years in academia, I helped create a variety of free online mathematical materials. Pirouette is a Spirograph clone that runs in a web browser. I hope you and your students enjoy the software! Read more:
https://www.diffgeom.com/blogs/free-online-math-materials/pirouette/
Continued thread
And a generalisation that needed more to work to do.
#animation #loop #CreativeCoding #IslamicPattern #geometry #geogebra #tiling #MathArt #pattern #GraphicDesign #design