Origami Tessellations

This is a piece that I have been working on for a while now- it’s the latest version of my star twist tessellation. (it will fill the plane, eventually!)

It uses a logarithmic growth pattern to create a sequence of triangles that follow the fibonacci sequence in their growth, or at least as much as I can predict without folding further and further towards infinity.

You can see some additional photos as well as some initial crease patterns for this design on my local photo gallery.

here’s the cut and pasted flickr description text:

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This is based on my original star twist, but is taken quite a bit further.

Have you ever started folding something, which was interesting and complex, only to later realize it was something you had folded before? And you just spent quite a bit of time finding another way to get there?

I realized after folding the star twist version 2 (found here) that it was really the same as my original star twist, but just folded differently to allow for the relatively complex folding sequence. When I started folding my first version back in the spring, I had not explored logarithmic folding or really much of anything yet. Now that I have a few months of research and exploration under my belt, I am able to better recognize what I’m doing. This is a positive thing, in my opinion.

Anyhow, this design uses a pattern based on a lot of triangles, which expand in a logarithmic progression. very pleasing to fold, if not a little bit complicated. Now that I have a few folded, it’s time to disassemble one and build a crease pattern for it. Future attempts should be easier once I know what parts are not required for actual folding, as well as producing a cleaner overall design.

——–

This is based on my original star twist, but is taken quite a bit further.

Have you ever started folding something, which was interesting and complex, only to later realize it was something you had folded before? And you just spent quite a bit of time finding another way to get there?

I realized after folding the star twist version 2 (found here) that it was really the same as my original star twist, but just folded differently to allow for the relatively complex folding sequence. When I started folding my first version back in the spring, I had not explored logarithmic folding or really much of anything yet. Now that I have a few months of research and exploration under my belt, I am able to better recognize what I’m doing. This is a positive thing, in my opinion.

Anyhow, this design uses a pattern based on a lot of triangles, which expand in a logarithmic progression. very pleasing to fold, if not a little bit complicated. Now that I have a few folded, it’s time to disassemble one and build a crease pattern for it. Future attempts should be easier once I know what parts are not required for actual folding, as well as producing a cleaner overall design.

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grabbed from the Flickr photo entry.

I uploaded quite a few pictures of this model, but I find it to be rather entertaining, and certainly quite pretty. I don’t think these photos did the design justic- it looks best backlit by the sun, but sadly there was no sun to be had today!

tweaked some of the folding choices and came out with a better design. it’s actually all a bunch of diamonds, getting progressively larger following a Fibonacci sequence. interesting numbers, for sure. even when I’m not trying to fold something using them, I keep finding them popping up.

This design is a (logarithmically?) growing shape, which gets increasingly larger each time you change sides of the paper. My intention is to find a method of folding this all on one side, but for the time being this is where we are at.

it uses the normal 60 degree precreased grid for one side of the star, and the other side is based on a 60 degree grid that is offset by 30 degrees. This means that the stars are offset to each other, and don’t match up in any way, other than some odd geometry which I don’t quite understand yet.

Like other models (like the Fujimoto Lotus or Hydrangea) this item can be folded infinitely larger, as it keeps expanding to larger and larger sizes. I think, in fact, that it will grow using a logarithmic scale (I guess it must to do this) but I don’t know the details on what number it will be. I have ideas, but I’d rather keep folding and see how it turns out first; although I think it follows the Fibonacci sequence (my personal favorite.)

however, it’s rather neat how the sides go back and forth; this would be a great model folded with some tissue foil- when it’s not pressed flat it looks like a flower blossom.

I’ve been told this looks like my star twist, which is very true. I think this is that design but without all the bungling of extra paper. maybe I should call it star twist v2?

this is a work in progress, but I thought I’d share this interesting item with you. I hope to release an updated version soon. As always, your comments are very welcome.

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(description lifted word-for-word from my flickr post.)

an update on this- it’s an origami display in Barcelona, Spain.

the info from mourazul on flickr:

“It’s in Barcelona, at the end of the “Ramblas”.

Just ask for the “wax museum”, and you’ll find it!”

Flowers (and many if not most things in nature) can be found to have geometric properties that are aligned with the number Φ (Phi). It’s one of those numbers, like Pi, that are endless non-repeating numbers; Phi is, approximately, 1.618034. it really goes on endlessly, though.

The geometry of the pentagon and all related shapes that use the same angles tend to have a natural affinity for both Phi and phi (lowercase) which is equivalent to 1 over Phi, or 1/Φ. this, oddly enough, is equal to Phi-1, or 0.618034.

This is also the number that makes up the “golden ratio”, long known and used for it’s great geometrical qualities.

you can find out more information here, or just do a google search for Phi and the golden ratio.

Here’s a good entry on Phi in plants.

This photo really represents this concept quite well, and it’s something that is so simple for nature but yet so difficult to try and recreate!

I feel there is a lot of undiscovered folding territory in Phi, and I hope to explore this as time goes on.