Organic forms out of Maths

[Frank Beister]

Johan Gielis, a Belgian biologist, has modified and extended the formula of a superellipse, which was found 1818 by the French Mathematician Gabriel Lamé.
It discribes in one simple formula a large group of different organic forms. From a square about a circle up to very complex amorph looking objects.
Gielis has founded a company to develop and market software, based on this formula.

Because the formula results 2 dimensional coordinates by an iteration process it is predestined to convert it in a GDL-object. I've done this and you can download the object from below.

How the parameters work:

width/hight:
The widht and hight of the object are the parameters a and b of the formula.

Rotations:
The shape will be calculated by the formula using polar coordinates. Beginning from center to the right (0°) the object coordinates are produced counterclockwise. To get a closed shape, you hat to rotate once (=1 =360°). But some shapes change in the 2nd, 3rd or i'th round, so you can adjust here the complexity. Filling this more than once rotated shapes is producing irregular polys in GDL, so pay attention.

Number of iterations:
Sets the number of coordinates, which are taken to produce the poly.

n1, n2, n3, m
This are the parameters, which describe the shape. Theres much finetuning to get a decided form. You have to try. Don't play too much, I think you have to work something else too. Some general settings you can take from one of the links below.
There are two checkboxes to lock the n-parameters, which is helpful in some cases.

fill:
the shape can be filled. Use the settings of the section-attributes of the object.

area:
You can automatic calculate the area, if you use a closed shape and rotation set to 1. Just use a fontsize larger than 0 and it will be printed with the object. (unit as the general settings of your actual project)


Related Links:

Where I found the formula and got inspired - attention, german. :
http://www.heise.de/newsticker/meldung/45863

Explanation and coding base of the formula - who else - Paul Bourke:
http://astronomy.swin.edu.au/~pbourke/curves/supershape/

Some further articel on math sides:
http://mathworld.wolfram.com/Superellipse.html
http://www.nature.com/nsu/030331/030331-3.html
http://www.sciencenews.org/articles/20030503/mathtrek.asp

Johan Gielis and its company:
http://www.genicap.com/
http://www.geniaal.be/

[Anonymous]

Hi Frank,

I tried to download the object, intrigued by this belgian invention...

I dezip it but AC can't recognize it... what am I missing ?

[Frank Beister]

It's a zipfile containing the gsm and the gif. Works for me on MacOS9-ie5.1-expander-AC7.

[Anonymous]

F. wrote:
It's a zipfile containing the gsm and the gif. Works for me on MacOS9-ie5.1-expander-AC7.

It's probably due to the fact that I'm on PC : when dezipping, I get the gsm file and the gif file. The gif file is OK, but AC 8.1 tells me it can't recognize the file.

Could you post it as a cross-platform PLA ?

[Oleg]

Geoffroy wrote:

F. wrote:
It's a zipfile containing the gsm and the gif. Works for me on MacOS9-ie5.1-expander-AC7.

It's probably due to the fact that I'm on PC : when dezipping, I get the gsm file and the gif file. The gif file is OK, but AC 8.1 tells me it can't recognize the file.

Could you post it as a cross-platform PLA ?

I sometimes meet such problem for MAC's ZIP archives.
I use old Aladdin Expander 5.0 for Win. It unzips such archives correctly.
It was on www.aladdinsys.com, probably it is not present now, but probably they has new free-of-charge expander for Win.

[Anonymous]

Oleg wrote:
I sometimes meet such problem for MAC's ZIP archives.
I use old Aladdin Expander 5.0 for Win. It unzips such archives correctly.
It was on www.aladdinsys.com, probably it is not present now, but probably they has new free-of-charge expander for Win.

This was it, I had tried with : WinRAR, 7-zip, Windows included zip support -> same (bad) result : file unreadable... I used Aladdin Stuffit to decompress the file and it worked !

Frank, did you script this object for a specific usage or just by curiosity ?

[Frank Beister]

did you script this object for a specific usage or just by curiosity ?

Both. I thought its an remarkable easy formula and with the object one can try to play a bit with its parameters.
On the other hand AC does not offer a lot of help for organic forms (not that I'm a great fan of them). This object could be a little help to expand the possibilities. Theres obvisiously a possibility to expand the formula to 3D. When I published it here, I hoped, that someone can share time to integrate it into the object. Maybe there are still some code maniacs out there. 😉

Two minutes after publishing the first version on our internal server a colleague asked for fills, because he just wanted to use it for defining a playground zone he was working on. Sometimes one does not know, what one is working for.