I found a pdf crease pattern at origamitessellations.com that kinda caught my eye. Eric Gjerde and his book are what originally inspired me down the path of folded tessellations in the first place. If not for him and his book, I doubt that I ever would have discovered the genre that I now enjoy so very much.  The pdf and instruction were for offset triangle twists. An idea that had never occurred to me, but looked intriguing.  So I went ahead and folded it.  It felt very similar to other triangle and hex based twist tesses.  It was pretty easy as far as the actual folding was concerned.  The result was not far off from standard triangle and hex twist folds. But definitely worth doing. If only to maybe discover new possibilities in the grid. 

Here's an odd little tessellation that kinda just happened. I really don't recall anything in particular which inspired me to start down this road.  Basically, it's just rectangles folded across a square grid. The rectangles bisect the gird lines rather than following them.  It's just one of those interesting patterns that was hiding in the paper waiting to be found.  I consider this first pic the front.  But the other side is a pretty compelling pattern in its own right. It kinda reminds me of a tile floor or a stone patio.  Pretty straightforward to fold assuming small intersection folds are not a problem for you. I use a blunt point metal nail file to help with difficult and/or small creases.  Just take care to arrange your overlaps in an orderly pattern. They don't have to all flow in the same direction, but something orderly looks best.  

This is a square grid tessellation that I came up with while I was thinking about other people's square grid tesses.  The diamond shapes are folded from the standard Fujimoto clover/hydrangea square collapse.  The points or arrows work the same way.  From there, it's just fiddling with the connections and spacing to get an intriguing pattern.  It's not terribly different from other diamond shaped based tesses, but it's an interesting variation.  The way it lights up is particularly appealing in my opinion. Its exotic appearance belies its humble architecture. 

  I saw this tessellation on reddit that was just diamonds nestled together with no spaces between then. Being in the mood for something less mentally taxing, I decided to go for it. The folder had uploaded a really nice picture and it was easy to see how it had been executed.  The thing about square grid folds is that they are all pre-creasing. By the time you get to the actual folding and collapsing there's very little left to do.  Whether or not tha tis good or bad is personal opinion.  In my version I went with a lower density. My paper really wouldn't allow for anything more. I folded some of the corners differently to get two different sizes diamond shapes instead. But it's the same design. If I were to fold in the corners of my smaller diamonds I would have the tess that inspired this.  The gaps that appear are only because it's a backlit reverse view. Unlit there are no spaces between the squares. It's a not too complicated design that yields a really n...

 I found an image of a really interesting tessellation using google. It was a pretty complex flagstone with many different elements.  The center was the same as is shown here. But then they went with rhombus flowers surrounding it. I started out intending to replicate, but part way through decided to do a simpler variation.  It has some unusual petal shapes off the center open back hex. Then there are elongated rhombuses, which I've not encountered before. But as I was mapping out the repetitions, they showed up in the grid.  I didn't do a great job folding it and it doesn't really back light all that nicely. Even when your folding is a little sloppy, back light usually hides it. But in this case, not so much.  It's an interesting pattern though. And I do have a crease pattern for it. 

  I was messing around with square twists and weave patterns. Square grid tesses are not my strong suit, but they can be a nice change of pace. I know that Eric Gjerde did a very similar tessellation and this is just a riff on that. Just for the fun of it.  The Gjerde tess used just the larger offset square twists. In my case I just combined those with smaller square twists in an alternating pattern.  Not a major breakthrough, but interesting nonetheless.  What is nice about square grid tessellations is that they are usually pretty easy to fold. If you're in the mood for something less intense they are a nice little distraction.  Back side pic and front lit pic included below.

 In an attempt to recreate the tessellation of another, I misinterpreted the structure and created a minor variation on the idea. I've since realized the difference. But what I wound up with is something pretty cool in its own right.  From looking at the photo I thought it was hex twists on the back. So that is how I crafted my design.  Turns out, they needed to be offset hex twists. By the time I realized that I was too deep into it. I just went with what I had.  The result... not a replica of what I'd seen, but rather an interesting cousin to that original design.  New? Maybe. I don't know for sure.  Beautiful? Definitely!

  I've been sticking with the parallelogram shape that I learned from the gatheringfolds website. The photo I found there had four different variations on this shape. So this is another. I really like this one in particular. It's simple, elegant and yet impressive.  It's pretty straightforward once you get used to the underlying structure. The nature of the main shape requires hexes on the back to be offset from the triangle grid.  The parallelograms cross two pleats lengthwise and bisect one on the short sides. Small triangle twists on the rear unite the triads.  It's helpful to draw the pattern out on a piece of triangle grid printed paper beforehand. It really makes it easier to understand.  Large hex twists form as you work the repetitions. .  They occupy the area of the grid between two pleats wide and one pleat wide. I have a crease pattern that I drew, but I'm not sure it's appropriate to share as gatheringfolds is a for profit website.  

Fiddling around on google searching for crease patterns I came across an image from a site called gatheringfolds. It was a single image of four different folded tesses. None of which were crease patterns, by the way, google. Hint. Hint.  The image is copyrighted, so best not to post it here.. But I liked the designs.  When I clicked through to investigate I learned that the site sells their crease patterns and tesses.  I like figuring these things out on my own anyway. So I worked out one of them so far and was able to fold it also.  I have the crease pattern I drew, but since they are  charging for their designs and they have copyrights posted, I don't suppose it's right to publish that here.  If you like the design you'll either have to sherlock it on your own or pony up the money to purchase it from them.  It's an interesting pattern. It's pretty humble on the front without backlight. But when you light it up on the reverse side it really sparkles....

  For some reason I find it harder to wrap my mind around square grid tessellation crease patterns. Hexagonal/triangular ones just make so much more sense to me.  Still, just to add variety, sometimes I try to come up with one or fold someone else's.  In this case I found this crease pattern that Robin Scholz had uploaded for 'Roadkill Rose' by Philip Chapman-Bell.  Apparently Bell did a single molecule and then Scholz tessellated it.  I had to modify it slightly to fit my 32 pleat grid.  In hindsight, I would've liked to space the repeats even closer together. I had pretty weak paper and was still able to get a nice finished product.  It's an interesting design. 

 Here's a new origami flagstone tessellation that might be somewhat original. I've seen similar designs, but not this particular configuration.  It begins with a classic ring of triangle twists around a hexagonal twist on the back.  Then there are those odd polygons which alternate between following the grid and bisecting it.  I've included a photo of my crease pattern and a view of the backside below. 

  This is a literal repetition of the Robin Scholz amizade triangles around a hex twist on the rear.  I believe he's already mapped it and folded it.  But I thought I'd give it a try.  It's a circle of of six triangles twisted gingerly around a hexagonal twist on the back of the paper.  The design naturally repeats by flowing seamlessly one into the next.  No figuring out what goes in the gaps. There are none.  It's a tough fold. Especially when you don't have great paper.  Satisfying to complete though.  Hard to believe that it's just a single, uncut sheet of paper. Yet, somehow, it is.  Oh, those edges. The edges always suffer. I've usually lost my patience by the time I reach the edges. 

 I was messing around with a pattern by Byriah Loper and somehow went off on a tangent which gave me this result.  It's an odd pattern that is hidden in the triangle grid.  It was an accidental discovery.  Reminds me of an old Atari 2600 video game. 

 I saw a photo of a Robin Scholz tess that was alternating triangles and rhombuses around hex twists. I was going to suss it out, but whimsy struck and instead I took the pattern and found a variation on it.  It was a very nice result.  It's a great idea, which I had been playing around with in my head, but hadn't really fully explored. When I saw the photo of a finished model, it really cemented the notion and I just let it take me where it wanted to go.  These are the results.  The combo of rhombuses and triangles form larger triangles.  The negative spaces are oddly offset hex twists.

This is a hexagon of rhombuses and triangles that are nestled together along their matching fold angles. There is a concentric hex collapse at the center.  The tessellation repeats quite naturally. A larger grid and sturdier paper would really have done with model a great service.  We ran out of better quality paper at work, so my tessellations have suffered somewhat for it.                                            Still, the idea is solid. It would be really nice if someone with better paper and a bigger grid decided to fold it.