Tesselations

Hi, I'm a complete beginner... I've dabbled in Rhino and Rhinoscript and an interest in Escher's tesselations has brought me to Grasshopper!

I think it should be quite possible to create first some simple 2D tesselating patterns with grasshopper and then progress to morphing tesselating patterns.

MC Escher did some amazing drawings by hand and there is plenty of resource documenting the basics... eg. http://www.tessellations.org/index.htm

Can anyone first tell me... Is this going to be a long uphill struggle through the world of Grasshopper, or can I get some good results without having to become an expert user?

Can anyone suggest a good tutorial for me? (I'm working my way through the "Essential Mathematics for Computational Design" at the moment!)

Any suggestions would be great!

http://www.mcescher.com/

Martyn

Replies to This Discussion

Permalink Reply by Damien Alomar on April 5, 2010 at 8:44pm

Well, there are two main parts to tesselations, defining the transformation of the tesselation (ie is it just a translation, or is it a glide reflection, or rotation, etc), and defining the shape to be tesselated (which in turn interacts with the transformation. Transforming the object with GH is not really the issue, its defining the tesselated shape. I would imagine that defining the shape within GH is a possibility, but that's going to depend significantly on what you're trying to create.

The escher example that you have there has the morphing on top of that. It may be possible to do something like that too, but much much more invovled than even creating the tesselation.

Anyway, maybe some specifics about the kind of tesselation that you're trying to do would be helpful if you want anything other than general advice.

Permalink Reply by Andrew Heumann on April 5, 2010 at 9:07pm

http://www.grasshopper3d.com/page/tutorials-1 will direct you to lots of useful learning resources. Andy Payne's GH Primer and the digital toolbox tutorials are among the best, in my opinion.

Here's a stab at some simple tesselations using the "slice method", which might give you some ideas about how to move forward:
http://dl.dropbox.com/u/5805666/simple_tesselation.ghx
http://dl.dropbox.com/u/5805666/simple_tesselation.3dm

This kind of definition could be extended to work for other base tiling patterns, like hexagonal - the principle is basically just the repeated translation of curves drawn in rhino by the appropriate vectors.

Here's an approach to morphing tesselations - it's a little more complex, starts to get into some of the more challenging aspects of grasshopper, like data tree management with grafting + flattening.
http://dl.dropbox.com/u/5805666/morphing_tesselation.ghx

Right now it only morphs between a simple parallelogram and a more complex shape, defined the same way as in the first example, but it could be extended to morph across a range of different tile shapes like the escher example you posted. It is basically calculating all the intermediate steps of each curve first, in the same location, and then distributing them out in an array like the first definition.

I didn't really annotate the definitions especially well, so feel free to ask questions if any part is unclear.

Hope this is helpful in getting you started thinking about these problems in GH terms!

Andrew

Permalink Reply by Martyn Hogg on April 6, 2010 at 2:56am

Many thanks for your responses!
This gives me plenty to be going on with and I will post here for sure, when I have any successes or problems!

Martyn

Permalink Reply by Tatiana Sarkisian on June 10, 2016 at 12:55pm

Hi Andrew,

By any chance do you still have these scripts? I know it's a long shot since this post was started 6 years ago, but if you still have them I would love to check them out. Thanks for your help!

Permalink Reply by martyn hogg on June 10, 2016 at 5:02pm