Sierpinski Triangle Pattern Along Surface

Hello,

I'm trying to discover how I can create a Sierpinski Triangle pattern along any given surface. The importance of the pattern is that you could select triangles that do not touch vertices to vertices, but rather vertices to center of edge.

This would allow me to begin trying to create a tensegrity model from any surface. My first attempts started with Lunchbox because of how easily it allows you to panel any surface, but haven't got much further since. I'm imagining it will take some manipulation of data tree structures, but I am not very familiar with doing such things.

Thanks for your help!

Steven

Attachments:

sierpinski.png, 9 KB

Replies to This Discussion

Permalink Reply by Steven T. Putt on May 29, 2014 at 11:41am

Here's another image that is close to what I'm trying to achieve.

Permalink Reply by Steven T. Putt on May 29, 2014 at 2:38pm

See image and links below for progress.

Again, I'm trying to utilize Lunchbox's paneling components to begin. The steps I've taken thus far are as follows:

1. Panelize surface with Lunchbox.

2. Split list of surfaces into two.

3. Cull edge panels of first list.

4. Get centroids of panels in second list.

5. Find three closest curves in first list to centroids in second list. Take three curves and get three midpoints.

6. Scale panels in second list.

7. Use midpoints in step 5 and find closest point from new midpoints created from scaled panels.

It works okay for now, but I know it will have limited applications that will likely be a problem in the future when I want to use a more complicated surface condition.

Attachments:

surface_tensegrity.3dm, 287 KB
surface_tensegrity.gh, 15 KB

Permalink Reply by Steven T. Putt on May 29, 2014 at 3:38pm

Here is some more progress. I've offset the initial triangles and then connected them in a way to create modules. I would like to see the offset be a little more intelligent based on the curvature of the surface. This is something I could do, but I would first like to study what depth in a tensegrity system means. I still have not resolved the modules on the edge of the system that are either floating or are only connected to one other module. Additionally, I still have yet to prove this works on an even more complicated surface.

One other thing I need to research is how to control the UV division so the triangles fall within some range of values. This would help me in the fabrication process when I need to stay within certain material lengths.

Permalink Reply by Chris Crosley on June 9, 2014 at 10:40am

Steve,

This looks awesome! A few questions:

Are the tensegrity modules inter-connected in this script?

In the tensegrity modules, are the top and bottom triangles supposed to be rotated ~60 deg?

I hope to have time to look at your script this week. At a glance however, it seems like there would be a better way to sort curves and centroids than by calculating distance. Shouldn't there be a relationship in the set organization?

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