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• Sunflower dot pattern

# Sunflower dot pattern

Mentor ,
Dec 23, 2013 Dec 23, 2013

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Anyone know how to go about creating a mathematically precise sunflower pattern of dots in Illustrator? It looks like the basic idea is to create a spiral arm of dots and then rotate copies around a central point, but I'm not sure how far apart to space the dots and how much to rotate each arm to make the dots equally spaced.

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Mentor ,
Dec 23, 2013 Dec 23, 2013

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I'm sure there are plenty of resources or tools out there that create precisely what you're looking for.  But if you want to do it manually, I would try to look into the Spiral Tool combined with making a Brush out of the spirals with circles copied to the spirals.  Each spiral will be rotated about a central point as a duplicate Symbol.  It's very difficult for me to explain verbally because I don't know the names of all of Illy's functions and toolsets but essentially:

1) create a spiral

2) create a circle, square, or other shape to be copied onto the spiral arm

3) make a brush* which contains the shape from step 2 copied onto the spiral arm

4) create instances of the spiral symbol with the shape from the brush onto your artboard

5) rotate each one by a certain increment and make sure you check your math so that you rotate a certain number into a section of 360 degrees, depending on how widely spaced you want your spiral arms to be.

* as far as the brush concept I may be off base but hopefully someone will chime in to correct my methodology listed above.

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Dec 23, 2013 Dec 23, 2013

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Kris,

 a mathematically precise sunflower pattern

Are you sure you wish this level of precision?

http://en.wikipedia.org/wiki/Sunflower#Mathematical_model_of_floret_arrangement

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Mentor ,
Dec 23, 2013 Dec 23, 2013

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That's the image I was trying to create Jacob.  I've done it in Flash before (somewhat closely anyway) But never Illy.

Here's a poor representation of the steps I took listed in my list above.  Note:  The brush I used was a Pattern Brush, not an Art Brush.

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Dec 23, 2013 Dec 23, 2013

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This is in German, but the screenshot says it.

http://illustrator.hilfdirselbst.ch/dokuwiki/tutorials/tipps_tricks/florales_muster_mit_dem_transformationseffekt

It's Effect > Distort and Transform > Transform

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Mentor ,
Dec 23, 2013 Dec 23, 2013

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Monika, your method may solve the problem I'm having with the origin.  However I notice a very apparent linear pattern radiating from the center, which is not what the floral pattern does in reality or according to the mathematical depiction that Jacob pointed out in the wiki article.

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Mentor ,
Dec 23, 2013 Dec 23, 2013

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Here's a second attempt, this time using an Arc instead of a Spiral.  The problem I seem to be having is near the origin where items are bunched together as opposed to evenly-spread-out.

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Enthusiast ,
Dec 24, 2013 Dec 24, 2013

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Hello Kris...almost like the other comments but a little different.

Hereās another way

Create a circle, stroke with no fill

Use the type on path tool

Use font dingbats, weddings etc, to select a box shape and copy and

paste that shape around the circle, but add a space between the shape/font.

Type to āCreate Outlinesā

Delete part of the boxes you do to need, so you get an Arc of boxes

Then divide 360 by the amount of copies of lines/arc you need e.g. 360 divided by 60 equals 6

you may need to experiment to the desired size/fit

Then copy and paste the arc/line around a centred point 60 times

TREX

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Dec 30, 2013 Dec 30, 2013

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you can try this and this

http://mathematica.stackexchange.com/questions/20924/spiral-pattern-and-fibonacci-numbers

and

function phylo ( N:float,k:int):Vector3{

//N=numpts  k=currentpt

var inc =  Mathf.PI  * ( 3 - Mathf.Sqrt ( 5 ) );

var off = 2 / N;

var y = k * off - 1 + (off / 2);

var r = Mathf.Sqrt (Mathf.Abs(y))  ;

var phi = k * inc;

return Vector3(Mathf.Cos(phi)*r*10, 0, Mathf.Sin(phi)*r*10);

};

i only do the look upt till N/2in the above formula i use N/

this is perhaps even better:

function sflo ( N:float,k:int):Vector3{

var n = k;

var r=Mathf.Sqrt (n);

var t=137.5*pi/180*n;

return Vector3(r*Mathf.Cos(t),0, r*Mathf.Sin(t));

}

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Community Beginner ,
Jul 30, 2019 Jul 30, 2019

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how do you apply that on illustrator?

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Jul 30, 2019 Jul 30, 2019

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Follow the steps in post #54.

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Dec 31, 2013 Dec 31, 2013

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you cant just create a spiral (using the illy spiral tool) as your starting point. you need to create an arithmetic spiral (archimedean spiral)...

here is a quick example, with a brush (dot) ... obviously you can perfect the settings to suit>

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Mentor ,
Dec 31, 2013 Dec 31, 2013

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Lots of great resources! Grant, how did you go about creating your Archimedean spiral?

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Dec 31, 2013 Dec 31, 2013

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i used the polar grid tool with no radial deviders set in options. and 20 concentric deviders.

then I cut the bottom half, pasted in front selected all, ungrouped everything. selected the bottom half moved one ring increment to the right, selected the segments of the first spiral, joined. did the same with the other.

/G

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Mentor ,
Dec 31, 2013 Dec 31, 2013

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Of course!

This might just be the easiest and best-looking method I've seen in Illustrator. I was able to create this beautiful, evenly spaced and uniformly sized pattern in no time:

Thanks to everyone!

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Dec 31, 2013 Dec 31, 2013

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Mentor ,
Dec 31, 2013 Dec 31, 2013

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One thing I did differently, though, was I used a dotted line (rounded end caps, 0pt dash, 9.25pt gap) instead of a special brush. I am able to adjust the size and spacing of the dots on the fly that way.

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Dec 31, 2013 Dec 31, 2013

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yep, many dif ways...  and tweaks etc... but you need a sound base to start.

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Mentor ,
Dec 31, 2013 Dec 31, 2013

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Using the mathematical model greyleaf provided (which derives from the wiki article that was posted) you can achieve an animated result in ActionScript which could be replicated with JavaScript (which I am not versed in).

Click on the thumbnail of the image to see the animated version.

Message was edited by: markerline

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Community Beginner ,
Feb 16, 2018 Feb 16, 2018

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Soā¦ how dd you end up making that shape then?

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Mentor ,
Feb 16, 2018 Feb 16, 2018

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Well, it's been four years, but it looks like I created an Archimedean spiral and then applied a repeating dot pattern to it with a dashed stroke.

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Mentor ,
Jan 04, 2014 Jan 04, 2014

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Some Code for you (Javascript for Illustrator)

 var docSel=app.activeDocument;var docSelSel=app.activeDocument.selection[0];//translate([deltaX],[deltaY]);for (var i=1; i<400;i++){        var r=10*Math.sqrt(i);        var t=137.5*Math.PI/180*i;        var newSel=docSelSel.duplicate(docSelSel);        newSel.translate(r*Math.cos(t),r*Math.sin(t));        }docSelSel.remove();

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Mentor ,
Jan 04, 2014 Jan 04, 2014

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The code I posted produces a sunflower in the following way:

1.  Create a small square using the Rectangle tool

2.  Open the Script (.js or .jsx extension) that contains the script above and run it.

3.  You get the resultant picture

I was able to get this result with a little knowledge of ActionScript and refactoring the code to JavaScript using the JavaScript for Illustrator Reference Manual that is available online.  It was tested using CS6 but I think it will work in CC as well.

Thanks for the formula greyleaf!

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Jan 04, 2014 Jan 04, 2014

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It was tested using CS6 but I think it will work in CC as well.

Works in CC as well. Also works with round dots. Thanks a lot!

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Mentor ,
Jan 04, 2014 Jan 04, 2014

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i am no hero in this post.  i just got lucky that greyleaf posted code that i could interpret.  but i am happy that you are able to use it too, Monika.

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