Astonishing!

 From: Frenchy Pilou (PILOU) 14 Jan 2017  (1 of 19)
 Beauty of the complexity of the simplicity! EDITED: 14 Jan 2017 by PILOU

 From: TpwUK 14 Jan 2017  (2 of 19)
 8265.2 In reply to 8265.1 The wonderfully complex world of Mother Nature - I enjoyed this post, thanks for sharing Martin (TpwUK)

 From: bemfarmer 15 Jan 2017  (3 of 19)
 8265.3 In reply to 8265.1 After 3 hours with google, a method for generating these spiral quadrilaterals was not found. They cold be measured from plants, or traced on the Fibonacci script? I did locate professor Scott Hotton's gif, (and several mathematically esoteric papers with hyperbolic geometry.) http://scotton.freeshell.org/phyllo/lattice_5_8.gif The central "beginnings" and expansion factor are unclear. Perhaps a rotated scaled Fibonacci curve?? As time permits, I may try some curve fitting in MoI. Or read some of the papers, including finding the "center point" of "pinecone" curves. It is an interesting homework assignment:-) - Brian This site seems promising: http://www.math.smith.edu/~phyllo/About/Lattices/SpiralLattices.html EDITED: 15 Jan 2017 by BEMFARMER

 From: Frenchy Pilou (PILOU) 15 Jan 2017  (4 of 19)
 8265.4 In reply to 8265.3 Bon courage! --- Pilou Is beautiful that please without concept! My Gallery

 From: bemfarmer 15 Jan 2017  (5 of 19)
 8265.5 In reply to 8265.4 Yikes! :-) "Each spiral lattices can be seen as a discrete subgroup of the complex multiplicative group, with the generator Geid. Indeed, in complex notation, points of the lattice can be written as Gkeikd. These form a group isomorphic to the integers (the isomorphism is k-> Gkeikd). Parastichies correspond to cosets of the subgroups 8Z and 13Z in the example given here." - Brian

 From: bemfarmer 17 Jan 2017  (6 of 19)
 The three applets on the Smith site can be run and viewed, on Windows 7, by loading the current Java program, and modifying it by adding to the Exception Site List. After installing Java, Under Configure Java/Security/Edit Site List, add http://www.math.smith.edu to the exception site list. Java apparently has some security risks... The cylindrical phillotaxis applet uses mouse picks, or a "2D Mouse slider," for the parameter space. Some voronoi patterns resemble a pineapple pattern. Can MoI do a 2D slider, e.g. with Mouse or Mouseover? The spiral applet uses a hyperbolic parameter disk with mouse picks, or "hyperbolic mouse slider." There are an "infinite" number of possible phillotaxis results depending upon Growth rate and Divergence angle. Using nearest neighbor, and next nearest neighbor, the parastichy curves are created, which show the 4 curve-sided quadrilaterals. The display seems to be a bit cramped. It should be possible to do some MoI script(s). - Brian Also located some Croatian script...The code is in English, comments translated with Google Translate. Needs more study... EDITED: 17 Jan 2017 by BEMFARMER

 From: bemfarmer 17 Jan 2017  (7 of 19)
 Doing a 2D mouse slider in a NodeEditor window, along with a javascript program, with phyllotaxis in the MoI window might work? - Brian

 From: Michael Gibson 17 Jan 2017  (8 of 19)
 8265.8 In reply to 8265.6 Hi Brian, > Can MoI do a 2D slider, e.g. with Mouse or Mouseover? There isn't any prepackaged control for doing that, but it should be possible to implement a custom one, you would want to put an onmousemove="" handler on an HTML element to do that: http://www.w3schools.com/jsref/event_onmousemove.asp - Michael

 From: bemfarmer 17 Jan 2017  (9 of 19)
 8265.9 In reply to 8265.8 Thank you Michael. - Brian

 From: Karsten (KMRQUS) 19 Jan 2017  (10 of 19)
 8265.10 In reply to 8265.3 Hello Brian and Pilou, Thanks for sharing the video - great stuff, but it took a while till I understood it. So like Brian I can't withstand and so I made also some experiments. I started with a expansion factor k is for the main curves given by the construction of the golden spiral. For a 1/4 turn the golden number = r = exp(k*PI/2) -> k=4*log((sqrt(5)+1)/2)/(2*PI) Ok - that's not new and already known by WIKI and the rest of the world. But it's not necessarily. But I didn't find that: If you use this k_1 for the main spirals e.g. 13 and have 8 counterclockwise ones, you can use a k_2=k_1/golden number. I think that's the best choice, because you get a minimal distorted element. What do you think about? Have a nice day Karsten EDITED: 20 Jan 2017 by KMRQUS Attachments:

 From: Karsten (KMRQUS) 22 Jan 2017  (11 of 19)
 Hello Brian, I'm working on a loxodrome node. I think that makes it possible to go to the 3rd dimension. For undistorted elements the intersections between clockwise/counterclockwise can be calculated by the logarithmic spiral function with a angles n*2PI/next fibonacci e.g. 8S/13S/(21). It seems that everything in this configuration is fibonacci!?! Have a nice day Karsten Attachments:

 From: Max Smirnov (SMIRNOV) 22 Jan 2017  (12 of 19)
 8265.12 In reply to 8265.11 [offtopic] Hi Karsten It seems like you using linux+wine to run MoI. The fonts looks awful. :) Try to edit FontSmoothingGamma setting in ~/.wine/user.reg (set value from 400 to 600) In my opinion the best values is: "FontSmoothing"="2" "FontSmoothingGamma"=dword:00000512 "FontSmoothingOrientation"=dword:00000001 "FontSmoothingType"=dword:00000002

 From: Karsten (KMRQUS) 22 Jan 2017  (13 of 19)
 8265.13 In reply to 8265.12 Hello Max, I've tested the values and it works perfect:-) Thank you very much and have a nice day Karsten

 From: bemfarmer 22 Jan 2017  (14 of 19)
 8265.14 In reply to 8265.11 Hi Karsten, You have an interesting project. Based upon my limited understanding: From the Smith site, of 650 plant species, R. Jean found that "about 92% of them have Fibonacci phyllotaxis." (F0 = 1 and F1 = 1). Some plants follow one particular Lukas sequence with F0 = 1 and F1 = 4. (There are other types of Lucas sequences.) There is a formula for the n'th Fibonacci number. (Haven't seen a formula for the n'th term of the above type of Lukas sequence.) As time allows, I'm still studying for a phyllotaxis script. The Java applets seem very broad and very repetitive and inscrutably "simple," so I'll just start doing some code based upon the given formulas, and Growth rate and divergence angles. Plus more reading and study:-) So you might try a Lukas sequence. Or numbers which are different, the Lucas numbers? So a loxodrome is not a Seifert spiral. - Brian EDITED: 22 Jan 2017 by BEMFARMER Image Attachments:

 From: Karsten (KMRQUS) 23 Jan 2017  (15 of 19)
 8265.15 In reply to 8265.14 Hello Brian, the loxodrome node isn't really a loxodrome creator. It's more a stereographic projection node. It takes various curves and maps it to a sphere. In the example I used logarithmic spirals -> loxodrome. Have a nice day Karsten

 From: Frenchy Pilou (PILOU) 23 Jan 2017  (16 of 19)
 Out of subject :) a very cool book! (exists in English and French also! ;) http://www.bilder-der-mathematik.de/ --- Pilou Is beautiful that please without concept! My Gallery