phyllotaxy

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What you are viewing in each of the above videos is a solid 3D printed sculpture spinning at 550 RPMs while being videotaped at 24 frames-per-second with a very fast shutter speed (1/2000 sec). The rotation speed is carefully synchronized to the camera’s frame rate so that one frame of video is captured every time the sculpture turns ~137.5º—the golden angle*. Each petal on the sculpture is placed at a unique distance from the top-center of the form. If you follow what appears to be a single petal as it works its way out and down the sculpture, what you are actually seeing is all the petals on the sculpture in the order of their respective distances from the top-center. Read on to learn more about how these were made, and why the golden angle is such an important angle.

*Note: the exact value for the golden angle is irrational. Here it is to five decimal places: 137.50776º

© edmark, 2014

http://www.instructables.com/id/Blooming-Zoetrope-Sculptures/

https://www.youtube.com/user/johnedmark/videos

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What did I do with all the WIPs I have going? Start 2 more, of course!

LEFT: Beginning of Phyllotaxis Hat using yarn given to me as a Christmas gift by my sister (”Glimmer Alpaca” by the Alpaca Yarn Company); and 

RIGHT: Beginning another Ripple Shawl by Andrea Jurgrau using another Schoppel Wolle Zauberball by Skacel in a combination of blues, indigos, and purples.

“Karl Blossfeldt (1865-1932) was a German artist and teacher who immersed himself in plant morphology by photographing nothing but plants for 35 years. He devised a self-made system to shoot close-up photographs of flowers, buds, seed pods, tendrils, and more–in order to study their form and design in detail. His photographs were originally seen as teaching material and only later presented as autonomous art works. Urformen der Kunst (Art forms in Nature) was published in 1928”

“Three photographs seen from above of typical phyllotactic patterns formed by ferrofuid drops for different values of the control parameter G [11, 12].  (a) For G ≈ 1 each new drop is repelled only by the previous one and a distichous mode is obtained, φ = 180º. (b) For G ≈ 0.7 the successive drops move away from each other with a divergence angle φ = 150º (between drop three and four).  Drops define an anti-clockwise spiral shown as a dashed line with parastichy numbers (1, 2).  © For smaller G values (G ≈ 0.1) higher order Fibonacci modes are obtained.  Here φ = 139º and parastichy numbers are (5, 8).”

Figs. 27–38. Outermost part of mature staminate flower in Figs. 27–30 and intermediate part in Figs. 31–34. Phyllotactic variation in staminate flowers. Numbers in figures follow the initiation sequence of primordia (SEM micrographs). 27. Flower with trimerous-like configuration. 28. Flower with tetramerous-like configuration. 29. Irregular phyllotaxy. 30. Irregular configuration. Three stamens extraordinarily expanded. 31, 32. Trimerous-like configuration, but size of each stamen differs. 33, 34. Tetramerous-like configurations, but symmetry differs. 35–37. Innermost part of three flowers with successive spiral initiation. 38. Innermost part of mature staminate flower with Fibonacci spiral configuration. Scale bars = 500 μm (Figs. 27–30), 50 μm (Figs. 31–38)