Fibonacci Spiral?

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 From:  OSTexo
7356.1 
Hello,

I am having trouble finding the script for Fibonacci spiral creation. I have the excellent Fibonacci seed script but thought there was one that created curves. If the script was able to output both the curves and points that would be great, but I'd be just fine with the curves as well. If anyone can point me in the right direction I'd appreciate it, thanks.
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 From:  Michael Gibson
7356.2 In reply to 7356.1 
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 From:  OSTexo
7356.3 
Hello Michael,

I don't recognize any of those as being the script I was thinking about. It could be that I'm mistaken and there wasn't a script in the first place. I thought the Fibonacci seed script started out as a curve drawing script then later seeded the points in along the curves. If I'm mistaken I apologize for sending anyone on a wild goose chase.
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 From:  bemfarmer
7356.4 In reply to 7356.3 
Hi OSTeo

The "sunflower spiral" has points on a particular Fermat (half) Spiral.
There are a couple of Fermat Spiral scripts.

H. Vogel did the sunflower equations.
Vogel's paper is being sold. I very rarely buy a for sale paper. But the math is also here:
http://ijear.org/vol4spl2/9-Amanjot-Kaur.pdf

The Sunflower Spiral and the Fibonacci Metric:
http://archive.bridgesmathart.org/2010/bridges2010-483.pdf

Sunflower Array Antenna:
http://downloads.hindawi.com/journals/ijap/2009/624035.pdf

I've been reviewing the math. It tends to get confusing comparing the different papers
The "golden angle" is involved, lowercase phi, capital phi, irrational numbers with sqrt of 5...

Are you trying to connect the different whorls of smaller spirals, such as the clockwise and anticlockwise subspirals, such as 5,8 or 8,13?
I've been trying to make sense of these subspirals, to see if there is some formula...

A script can feed points into a curve factory, or interpcurve factory, to make a spiral...

- Brian

http://www.degruyter.com/view/j/cris.2014.2014.issue-1/cris-2014-0001/cris-2014-0001.xml?format=INT

EDITED: 21 Apr 2015 by BEMFARMER

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 From:  futagoza (STEFAN)
7356.5 
Hi OSTexo,

i created a Fibonacci Spiral long time ago, by hand, in Shade 3D. Should be really simple to do that in MoI too, without a script. The second link then shows you how to create from the Fibonacci Spiral a sunflower.


https://www.google.de/search?q=drawing+a+fibonacci+spiral&biw=1680&bih=887&tbm=isch&tbo=u&source=univ&sa=X&ei=q043Va2JGsbhaoSygIgM&ved=0CCMQsAQ

http://www.atpm.com/10.02/images/design-sunflower.gif

Best regards
Stefan
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 From:  OSTexo
7356.6 
Hello,

Benfarmer,
Connection of the whorls is one option, I'm curious how the points are generated in the seed script? Are they actually points along the spiral or something else? I'm not the best mathematician so you'll probably go way over my head quickly. I found this link and the seed head optimal packing and the subcurves created from the mathematically closest points looks interesting.

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#seedsIMA50

Ideally what I'm looking for is a way to intersperse the curves between the seed points, or if the seed points are derived from the curves then I could just double up the amount of points to create the interspersed curves if that makes sense.

Futagoza,
It could be that's what I was remembering, the only challenge being that I need the combination of points and curves, and not knowing how the points are derived, or even if there is any correlation between the curves and points is making it difficult to wrap my head around.

Thank you both for your insight.
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 From:  bemfarmer
7356.7 In reply to 7356.6 
Each seed is placed using polar coordinates, consisting of an angle from the x axis, and a radius, or distance from the origin..
The radius is converted to Cartesian coordinates, x and y, using cos and sin.
An angle 360 degrees is the same as an angle of 2*PI radians.
222.4922 degrees plus 137.5078 degrees, equals 360 degrees.

Point 1 is located at 222.4922 degrees = (-1) * 137.5078 degrees. Radius = sqrt(1).
Point 2 is located at (-2) * 137.5078 degrees. Radius = sqrt(2).
Point 3 is located at (-3) * 137.5078 degrees. Radius = sqrt(3).

- Brian
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 From:  bemfarmer
7356.8 
Here is a redone, fast, Fibonacci "Sunflower" script, with option to do the Fermat spiral passing through the
seed points. The spiral works with up to several thousand seeds. With unchecked spiral checkbox, a test with
100,000 seed points worked. The calculation used 2*pi*phi, avoiding dividing by 2 and then multiplying by 2,
so the seed points are very slightly different than the old script. The script uses the fast "Hilbert Curve" style of
code in the .htm file. A possible drawback is hanging up if a huge number of seeds are used.
I was unable to get the Fibonacci seeds calculated in a separate Function.
I was unable to puzzle out calculating forming the curve segments for each seed, with nested loops.
Seeds may start at any integer count, leaving a donut hole, but the spiral always starts at the origin.

- Brian
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 From:  OSTexo
7356.9 
Hello benfarmer,

Thanks a million for this, I really appreciate it. I don't think I'll be approaching 100K seeds anytime soon.
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 From:  Frenchy Pilou (PILOU)
7356.10 
No possibility to use randomly these points for deform the curve in the Z direction for example ?

---
Pilou
Is beautiful that please without concept!
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 From:  bemfarmer
7356.11 In reply to 7356.10 
Here is version 02, with the curve plotted from seed to seed, with nested For loops.
(See .htm file for some explanation.)
Index (j+1) is equal to the seedID number.
Index i in fraction formula (i / (numpoints-1)) is added to j to yield t.
Nesting the For loops was easy, although I could not figure it out last week :-)

This scheme would permit ramping the value of z up and down between (randomly) selected (sequential) seeds.
The i fraction could be used for the ramp.
(This code has not been done yet.)

- Brian

Now to make it play music...
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 From:  Frenchy Pilou (PILOU)
7356.12 In reply to 7356.11 
Keep the good work!
---
Pilou
Is beautiful that please without concept!
My Gallery
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 From:  Frenchy Pilou (PILOU)
7356.13 
French Version ;)
http://moiscript.weebly.com/geacuteomeacutetries-par-bemfarmer.html

Here on the left Points of the Fibo_Fermat are used for the _voronoi by Max Smirnov ! :)



@Bemfarmer
Can you Add the "Z" altitude on the right Fermat Curve above ? (because I am not dexterous with this language! :(

//>>>> Insert z value formula here, with z value changing depending upon
// randomly selected j value. z value could ramp up from 0 to the next seed,
// and then ramp down to 0 to the next seed.
// Pass z value to Polar2Cartesian function.

EDITED: 25 Sep 2015 by PILOU

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 From:  bemfarmer
7356.14 In reply to 7356.13 
Hi Pilou,

I'll have a look...

- Brian
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