[Shell Morphology] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

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Shell Morphology

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Posted by: Garrett Neske

Would anyone know of the explicit Mathematica notation that Wolfram used in his graphical representation of various sea shells in Chapter 8 of NKS? I am conducting research on the parametric correspondence between the bio-geometry of sea shells and the amniote cochlea, and it would help to have a few equations as a frame of reference. Thanks.

-G. Neske


Posted by: Martijn

I don't know how Wolfram has done this.
But I would try a fixed U shaped section of n cells and made each cell using 4 nodes.

Than at each step you can ad a new section with all the distances between the connections enlarged by some growth factor. The new section should connect on the nodes from you previous section.

You can probably get some nice variations if you use different growth rates for different connection directions.

To do this I would just use Graphics3D and draw Polygons. Solving the coordinates at each step.
There probably is a simpler solution to do this that I don't see right now.

Good luck!


Posted by: Garrett Neske

Thanks, Martijn! Actually, any methodology would help right now since I'm learning Mathematica graphics in the process of using it in research. I'll try to put your suggestion to use.

-G. Neske


Posted by: Martijn

If you get stuck with the code, I can try and help. Just tell me whats wrong and send me something to work with..


Posted by: Todd Rowland

Garrett,

You can look at p.1008 the Notes, and use the code there. Or download it from the
programs download page

The parameters relate to some of the metrical differential geometry of the actual growth.


Posted by: Martijn

HI

I keep underestimating the notes in the back of the book.

Funny thing is that the suggestion made in the nodes looks like OKS to me. (No Offence It just looks like a clasical model to me) I have done something like this before reading the book / NKS summer course as a exercise on how to use different plot types.

I think it can be done without “analytic-functions”. I don't think that this will give any different results. It would just be nice to see that it is not necessary to have a function to generate the curvature.




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