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Dave Bowman'SAGRADA FAMILIA STEPS' . Spiral staircase inside one of Sagrada Familia’s steeples, designed by Antoni Gaudí, showcasing its intricate geometry. . <a href="https://dave-bowman.pixels.com/featured/sagrada-familia-steps-dave-bowman.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://dave-bowman.pixels.com/featured/sagrada-familia-steps-dave-bowman.html</a> . <a href="https://mastodon.social/tags/photography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#photography</a> <a href="https://mastodon.social/tags/photographersunited" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#photographersunited</a> <a href="https://mastodon.social/tags/architecture" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#architecture</a> <a href="https://mastodon.social/tags/monochromephotography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#monochromephotography</a> <a href="https://mastodon.social/tags/spirals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#spirals</a> <a href="https://mastodon.social/tags/wallart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#wallart</a> <a href="https://mastodon.social/tags/BuyIntoArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BuyIntoArt</a> <a href="https://mastodon.social/tags/GiftThemArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GiftThemArt</a> <a href="https://mastodon.social/tags/ArtMatters" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ArtMatters</a> <a href="https://mastodon.social/tags/AYearofArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AYearofArt</a> <a href="https://mastodon.social/tags/artistonmastodon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#artistonmastodon</a> <a href="https://mastodon.social/tags/AYearForArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AYearForArt</a> <a href="https://mastodon.social/tags/fedigiftshop" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fedigiftshop</a> <a href="https://mastodon.social/tags/MastoArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MastoArt</a> <a href="https://mastodon.social/tags/interiordecor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#interiordecor</a> <a href="https://mastodon.social/tags/homedecor" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#homedecor</a> <a href="https://mastodon.social/tags/homedecoration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#homedecoration</a> <a href="https://mastodon.social/tags/creativetoots" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#creativetoots</a> <a href="https://mastodon.social/tags/artbooster" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#artbooster</a> <a href="https://mastodon.social/tags/davebowmanphotography" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#davebowmanphotography</a>

Professor Ben KenobiResearch suggests the prevalence of spirals in natural structures may be intrinsically connected to entropy. This insight provides a deeper understanding of how energy distribution and structural efficiency manifest in the universe. <a class="hashtag" href="https://bsky.app/search?q=%23spirals" rel="nofollow noopener noreferrer" target="_blank">#spirals</a> <a class="hashtag" href="https://bsky.app/search?q=%23entropy" rel="nofollow noopener noreferrer" target="_blank">#entropy</a> <a class="hashtag" href="https://bsky.app/search?q=%23nature" rel="nofollow noopener noreferrer" target="_blank">#nature</a> <a class="hashtag" href="https://bsky.app/search?q=%23physics" rel="nofollow noopener noreferrer" target="_blank">#physics</a> <a href="https://phys.org/news/2025-03-nature-spirals-link-entropy.html" rel="nofollow noopener noreferrer" target="_blank">phys.org/news/2025-03...</a> <a href="https://phys.org/news/2025-03-nature-spirals-link-entropy.html" rel="nofollow noopener noreferrer" target="_blank">Why does nature love spirals? ...</a>

fheusaigCornish cliff snail<a href="https://friendica.ungzeit.de/search?tag=spirals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#spirals</a> <a href="https://friendica.ungzeit.de/search?tag=cornwallcoast" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#cornwallcoast</a> <a href="https://friendica.ungzeit.de/search?tag=cornwall" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#cornwall</a> <a href="https://friendica.ungzeit.de/search?tag=england" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#england</a> <a href="https://friendica.ungzeit.de/search?tag=uk" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#uk</a> <a href="https://friendica.ungzeit.de/search?tag=greatbritain" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#greatbritain</a> <a href="https://friendica.ungzeit.de/search?tag=snail" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#snail</a>(Ursprünglich am 24. Juli 2019 auf Instagram gepostet.)

Splines<a href="https://pixelfed.social/discover/tags/SeeFeelTouchHug?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#SeeFeelTouchHug</a> In both <a href="https://pixelfed.social/discover/tags/art?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#art</a> and <a href="https://pixelfed.social/discover/tags/engineering?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#engineering</a>, one must be able to both <a href="https://pixelfed.social/discover/tags/see?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#see</a> and <a href="https://pixelfed.social/discover/tags/feel?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#feel</a> things that might not be there (yet). We were able to "see" the outlines of the <a href="https://pixelfed.social/discover/tags/scroll?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#scroll</a> surface from <a href="https://pixelfed.social/discover/tags/imageScans?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#imageScans</a> of <a href="https://pixelfed.social/discover/tags/Vignola?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#Vignola</a>'s sketches in <a href="https://pixelfed.social/p/Splines/793169876757012827" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/793169876757012827</a> and <a href="https://pixelfed.social/p/Splines/793215298082967733" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/793215298082967733</a>. Vignola's images are on a 2-dimensional surface, as are the outlines we extracted from them. We believe the scroll surface also exists, but it is not yet manifest in 3-dimensional space. So, like a visually impaired person, we try to "feel" our way to the scroll surface using the outlines as our <a href="https://pixelfed.social/discover/tags/walkingStick?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#walkingStick</a>. This diagram is identical to that in <a href="https://pixelfed.social/p/Splines/793493316852849994" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/793493316852849994</a> but with the rear ends of the horizontal <a href="https://pixelfed.social/discover/tags/primaryCurves?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#primaryCurves</a> marked with R1, R5, and R3, which are paired with F1, F5, and F3, respectively. We know that the scroll surface must <a href="https://pixelfed.social/discover/tags/touch?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#touch</a> the tangent points T1, T2, and so on in front, as well corresponding tangent points in the rear (not shown here to reduce clutter). In <a href="https://pixelfed.social/p/Splines/792906324854792619" rel="nofollow noopener noreferrer" target="_blank">https://pixelfed.social/p/Splines/792906324854792619</a>, I mentioned that a scroll starts with a volute in front and is <a href="https://pixelfed.social/discover/tags/modulated?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#modulated</a> by as many as six volutes of different shapes and sizes as it reaches the back, with the scroll surface tightly hugging the volutes at EACH contact point in ALL 3 dimensions. In other words, it is not sufficient for the scroll surface to "touch" the <a href="https://pixelfed.social/discover/tags/volute?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#volute</a> <a href="https://pixelfed.social/discover/tags/spirals?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#spirals</a> just in the front and rear. It must also "hug" the intermediate <a href="https://pixelfed.social/discover/tags/modulatingSpirals?src=hash" class="u-url hashtag" rel="nofollow noopener noreferrer" target="_blank">#modulatingSpirals</a>. I will first show this technique with 4 modulating spirals using rectangles M, N, P, Q, and R as their frame, and add more later on. Intuitively, we know that if we use curve F3-R3 as our walking stick on the straight vertical extrusion of that curve, we will feel the scroll surface *somewhere* on that extrusion along every point from front to back. We can narrow it down further by excluding portions above and below as we approach rectangle R in the rear.

MicrofractalIt's <a href="https://mathstodon.xyz/tags/fractalfriday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractalfriday</a> again!<a href="https://mathstodon.xyz/tags/Space" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Space</a> This is my longest render produced by my program so far (not rendered continuously, total time approximately 2 Days I think)Formula: \(z_{n+1}=z_n^2*\frac{z_n^2}{z_n^2+0.001}+c\)Coordinates: x: 0.1762135480324081201348 y: 0.5722332100694445424486, size: 2.25e-05Original resolution: 7680×4320, 400 Samples per pixel<a href="https://mathstodon.xyz/tags/fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractal</a> <a href="https://mathstodon.xyz/tags/fractalart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractalart</a> <a href="https://mathstodon.xyz/tags/mandelbrot" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mandelbrot</a> <a href="https://mathstodon.xyz/tags/pattern" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pattern</a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/art" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#art</a> <a href="https://mathstodon.xyz/tags/spirals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#spirals</a>

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