citiesofsound

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Types of Spirals. Logarithmic Spiral - self-similar spiral curve which often appears in Nature. Spira Mirabilis, Latin for “miraculous spiral”, is another name for the Logarithmic Spiral. The size of the spiral increases but its shape is unaltered with each successive curve, a property known as Self-Similarity. Possibly as a result of this unique property, the Spira Mirabilis has evolved in Nature, appearing in certain growing forms such as nautilus shells and sunflower heads.  Fermat’s Spiral - in the sunflower and daisy, the mesh of spirals occurs in Fibonacci Numbers because Divergence (angle of succession in a single spiral arrangement) approaches the Golden Ratio. The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat Spirals - ideally. That is because Fermat’s Spiral traverses equal annuli in equal turns.  Archimedean Spiral - it is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. The Archimedean Spiral has the property that any ray from the origin intersects successive turnings of the spiral in points with a constant separation distance, hence the name “Arithmetic Spiral”. Hyperbolic Spiral - transcendental plane curve also known as a Reciprocal Spiral. A Hyperbolic Spiral is the opposite of an Archimedean Spiral. It begins at an infinite distance from the pole in the center (for θ starting from zero r = a/θ starts from infinity), and it winds faster and faster around as it approaches the pole; the distance from any point to the pole, following the curve, is Infinite.

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Blooming Vessels

Single-cell genetic and signalling analysis maps the factors and receptors involved in determining cell fate as human blood vessel organoids (lab-grown models) develop – insight for using these models in research in health and in vascular disease, such as in diabetes

Read the published research article here

Video from work by Marina T. Nikolova and colleagues

Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland

Video originally published with a Creative Commons Attribution 4.0 International (CC BY 4.0)

Published in Cell, April 2025

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Japanische Färbeschablonen - 1899 - via Sachsen Digital

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Antti Laitinen, 2D Tree (3), 2017.

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Bobbin-made hanging, designed by Luba Krejci (1925-2005), Czechoslovakia, 1964.

Lace in the collection of the Cooper-Hewitt Museum. 1982.

Internet Archive

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The Descent of Amida, the Buddha of Infinite Light

Sho Amida raigo zu

17th century

MEDIUM/TECHNIQUEHanging scroll; ink, color, and gold on silk

DIMENSIONS149.6 x 105.2 cm (58 7/8 x 41 7/16 in.) (height x width)

CREDIT LINEWilliam Sturgis Bigelow Collection

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Janet McCaffery, ''The Witch of Hissing Hill'' by Mary Calhoun, 1964

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David Burroughs Mattingly, ''Spectrum'', 1994

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Typographische Jahrbücher - 1910 - via Staats und Universitätsbibliothek Dresden (SLUB)

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Frans MASEREEL - Histoire de fou XVI, 1961

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Flying South by Clara Scintilla, 2023

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Irene Chou (Zhou Lüyun, 1924-2011) — Untitled [ink, colour, on paper, hanging scroll, 1991]

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"Southbound ducks on western flyway." Life. September 28, 1959. Cover photo.

Internet Archive

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Phase Two. Rollerball on A3

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Moebius

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Frank Lepold（German）

Satellites, impetuoso    via