Geometric Drawings · How-to

Gifs & Adobe Illustrator/Photoshop

Pentagons, ebb and flow
Pentagons, ebb and flow

I figure out how to do things, then I forget.

Making a GiF in Photoshop CS6 from artboards created in Adobe Illustrator is one of those things that I have to relearn every few months. I always panic when I have to learn it again. This post is mostly for me, to help me remember. Unless  this is something you want to do, just enjoy the pictures, especially the one at the bottom of this post.

Pentagons converging in color
Pentagons converging in color

Most of the GIF’s I’ve made have something to do with shape transformations. For instance, I’ve done a bunch with pentagons converging towards the center. I start with basic outlines then add effects. This post is about creating the gif from the artboards, not about making the images for the artboards. I leave that for you to figure out. But to give you an idea of my workflow, so that it makes sense for the rest of the post, here’s a screenshot of what one of my sets of artboards look like:


48 artboards
49 artboards

After I am happy with the Illustrator files I save, label and close my AI file.

Next, I open this Adobe Illustrator file in Photoshop. Since the AI file has lots of art boards. a box, which is labeled “import PDF” pops-up in the middle of my Photoshop workspace. Just ignore the reference to the pdf. Make sure the Pages option is picked. Pick your resolution. By default it’s at 300. Depending on my image, I sometimes can’t get a 300 resolution to save. I usually change this to 72.

Nothing is to scale here. Just highlighlighting what's needed
Nothing is to scale here.
Just highlighting what’s needed

To get ALL of the AI artboards to open SHIFt-CLICK the first and the last pages that are loaded in that little window. This will select all the artboards. Press OK (which I forgot to draw, but it’s in the lower right hand corner of the box).

Once the layers panel is full of your images you will need to close them. Oh, this is when I remember that I need to put a new file on my desktop, labeled New Gif. So make that now.

THEN CloseAll your files using the CloseAll command under the file menu.  A menu will come up, you tell it to SAVE and check the box that says apply to all, pick that New Gif file you made to save the images in, and, one by one, they will go into the folder, and you have to press save for each image as it goes in.

One Artboard Image

NOW OPEN your new gif folder in BRIDGE. Bridge is a great program that is packaged with Photoshop. SELECT ALL the artboards. At the top of the Bridges workspace go to Tools>Photoshop>Load Files in Photoshop layers.

Now sit back and wait as the Photoshop’s layers are populated with the artboards.

Almost done.

Next, make sure the Timeline option in checked under Window. At the center of the bottom of the workspace there is a box. Choose then  click on Create Frame Animation. One of the artboards will appear on the timeline. Open the fly-out menu on the timeline. Click: Make Frame From Layers (this is the 11th item on the list, and will only show up if Create Frame Animation has been clicked,  not merely chosen).

The timeline will populate, probably backwards. If so, click Reverse Frames on the fly-out menu.

The positions of all these things that need to be clicked can be found in that drawing above.

The Gif is now basically done. The timing can be changed by clicking on the sec option below the frame. Shift click two frames to select everything between them.

NOW SAVING is a whole other thing.

Click on SAVE FOR WEB under the file menu. Choose the 2 (or 4) up tab on the upper left of the save box. On the right hand side of the save box JPEG will probably be in the second box from the top. Change this to GIF. Choose the file size you want to save. I usually pick the 2nd to the biggest file. Click Save, name your file and be proud.

Here’s the one I made last night:

Click on this to see it go
Click on this to see it go OR click






Spiraling Paper Ornament

I came across this complicated looking but simple paper structure and have been happily playing around with it for days.

I’ve been able to locate only once source for these, which is at, an exquisite site by German artist Manja Burton. Fact is, her site has enough about these globes that, really, no one else needs to ever write about them again ever, but, oh well, here I go.

Manja calls these Triskele Globes. I have no idea whether these are a traditional paper-folding design, or if she developed it herself. “Triskele” is a symbol which depicts three interlocking spirals. These paper globes appear to be interlocking spirals, but the spiraling is simply a wonderful illusion.

Bonus Update: just as I was about to hit the Publish button for this post, I received a note from Manja, responding to my questions about this structure.  I’ve added her response at the end of the post.

Three rectangles that will become globes
Three rectangles that will become globes

The globes are made with three interlocking strips. 

After interlocking the strips, the arcs are folded in. It really helps to pre-score the curved fold lines. Here’s a short video:

I made three different pdfs for paper strips, which will be at the bottom of this post. Each page will make two ornaments. My templates are a bit smaller than the ones on Manja Burton’s site. I like this smaller size mostly because I think it work so well with standard copy paper.

I’ve embellished with the paper with simple shapes, so that it’s easier to distinguish the strips from each other, otherwise it can be confusing to see what’s going on with the construction. I’ve also provided a pdf below that has no embellishments, so my shapes won’t interfere with your own vision.

Image of template for paper strips to make spiral paper ornament
Image of template for paper strips to make spiral paper ornament. Look for PDF below

You’ll notice that there are triangles on the template. These triangles are hidden in the final product. I put them there to help orient the designs, hopefully making it easier to see how the rings of paper strips are aligned to each other.

If you don’t have access to a copy machine, it’s absolutely possible to construct your own template for these paper strips. Here’s a grid that can be used to understand the proportions of the shapes.

The Paper Strips for the Spiraling ornament, mapped on a grid
The paper strips for the Spiraling ornament, mapped on a grid. The strips are 48 squares tall (plus two more for the tab), 10 square wide, and the circles have an a radius of 8 squares, but only 1/3 of the circle is on the paper strip. There, that should get you started.

I liked the look of the grid so much that I made a PDF of templates that includes the grid.

Grid on paper strips
See PDF for this at the bottom of this post

I’ve had such a great time with these. I’m  surprised every time I see the transformation happen as the strips of paper become a spiraling globe.

Here are the PDF’s of the strips.

Spiral Paper Ornament strips with shapes

Spiral Paper Ornament strips plain

Spiral Paper Ornament graphed strips

and here the PDF of the grid so you can construct your own strips without a copy machine:

Spiral Paper Ornament strip construction  (will be much  easier to use if you have graph paper)

A Bevy of Paper globes
A Bevy of Paper globes

Have fun. Use bling. Be colorful. Experiment with different papers, different designs. Make them into dice, fortune tellers, add quotes. Go wild.

Here’s the bonus update: I wrote a note to Manja which said.

Manja, I am enchanted by the Triskele balls, and am currently writing a blog post about them, which will include links to your site. Can you tell me something about history of these balls? did you invent the form or did you come across it in your travels? Many thanks for your beautiful work.

She wrote back, saying:

It is a couple of years back now that I saw an image of one of these globes and all I knew was that it was made out of three strips of paper. I spent a whole day on figuring out how it works… I never found that picture again online. I did do some more research on it back then and couldn’t find anything. So I asked the Hattifant community to help me find a name. And that was absolute fun and we in the end came up with Triskele Paper Globes.  Today, I have seen more of them and also in the Scandinavian area… there they seem to be called “click balls”. So please I would love to know more, too!  If you find out more do let me know!”
Okay! If anyone knows something about the history of these balls, let us know!



Books Made from one sheet of folded paper · How-to · origami pamphlet · simple book binding

Four Books Students Can Figure Out How to Make on Their Own

PDF version

For years, until she retired, I worked with an enthusiastic classroom teacher named Anna who loved seeing her students make books. Instead of teaching bookmaking skills she created a bookmaking corner in her classroom that included a little display of books that I had taught her how to make. These books were accompanied by written directions and a stack of paper. Anna’s third grade students had a great time making books independently.

Last week I received a note from Lana, a teacher in Canada who I follow and who always has insights that I value. Here’s what she wrote:

I started a personal history project with my kids today, with  the big idea that our histories are different but we learn about each other because we are a community. Students start with creating a personal history of 5-10 important events in their lives. What if I open it a bit and let kids work with paper in 3 dimensions? Someone wants a line, someone else a book, a spiral, a tree, a flexagon?

I was wondering if there are some formats that you could recommend that don’t require too much pre-teaching. Ideally kids can follow template/video.

Origami books made from a multiple folded papers, to create a Star Book and a Cascading Book, aka Origami Caterpillar Book
Origami books made from a multiple folded papers, to create a Star Book and a Cascading Book, aka Origami Caterpillar Book

Thinking about Anna’s bookmaking corner, I want to suggest a few books to Lana.

I decided to take this opportunity to finally get around to creating the StarBook/Cascading Book tutorial (at the top of this post) with video accompaniment:

This modular origami book can be tricky, but it is totally doable, The folding needs to be done precisely, folds need to be sharp, and it’s important to pay attention to the orientation of the modules as they get glued together.

Fact is though, that it looks tricker than it is. It’s a structure I highly recommend because it’s so dynamic.

Bookmaking by Paula Beardell Krieg

The next book I want to highlight is the Origami Pamphlet. This is the #1 book that I would like every person in the world to know how to make. Here’s the link to my post 

Another set of these directions that I like belongs to Tim Winkler, and can be viewed at

Mike Lawler made a 24 second video -Voila!- showing a piece of paper transform into the origami pamphlet 

Books made from one or two pieces of paper

The biggest problem with the origami pamphlet is that if you’re using regular copy paper, the book will be rather small,  If this bothersome there are two good variations that result in a larger book (other than just finding a larger sheet of paper):

You can link two of the structures together with a rubber band. That’s what’s going on with the lilac/blue booklet above. Well, I guess it’s not actually a larger book, it’s just longer.

Making a larger origami pamphlet by linking two halves together
Two Book Bases linked together to make an origami pamphlet

A way make a larger origami pamphlet is to use two sheets of paper to make two halves, then attach them together (use glue, tape, paper clips, staples? whatever ) like in the photo above.  I call this half-or-an-origami pamphlet a book base.

An advantage of making a book this way is that, if composition paper is used, the lines will be going in the correct direction for writing on.

There are so many fabulous inventive book structures students can make, but sometimes it’s great to just fold a bunch of papers in half, secure them together, and be done with it. The problem here is that it is not obvious how to secure the pages together. A doable no-needle way to sew pages together in a classroom setting is to use a bit of string or yarn to do a modified pamphlet stitch.

Modified Pamphlet Stitch
Modified Pamphlet Stitch

There you have it, four books:

  • the Star Book,
  • the Cascading Book,
  • the Origami Pamphlet (with two variations) and
  • the Modified Pamphlet Stitch book

Lana’s note mentions a spiral. I’ve been playing with some spiraling pages lately, and I have something wonderful that I want to share, but the spiral deserves its own post: which will hopefully show up here in the near future.



Geometric Drawings · How-to · Math and Book Arts

Moires: A Reason to Tile

Balloon with Moire
Balloon with Moire

Just before Valentines Day the usual group of suspects who capture my attention with their outrageously playful exploration of ideas once again were posting images that stopped me in my tracks.  I have to say that when I saw what they were doing I made a decision not to participate because I was busy-with-other-things.  But then they started using HEARTS in their images and I just couldn’t resist. What they were doing was  creating moire patterns, mostly digitally. Moire patterns are that cool effect you see when two identical screens are laid on top of each other, then shifted.  I started out making some with my Illustrator program, then my attention shifted towards making them in the real world, engineering paper rather than working on the computer.

Moire patterns can start with a repeating tile, a tessellation, which is a shape that can be repeated forever. Here’s a photo of one of the explorations that I saw going on, by Mike Lawler’s family:

Tesselating in the Living Room
Tessellating in the Living Room

Then Dan Anderson started doing a series of outrageously beautiful interactive images on his Open Processing page:

Dan's Moire
Dan’s Moire

Then Martin aka GHS Maths started making moires with straight lines in the on-line graph program Desmos.

You really must visit some of these links in order to get the full sense of how stunning these images are.

My first response to these image was to make a  few gifs myself.

My Illustrator Heart Moire
My Illustrator Heart Moire (click on image to see the gif)

What I wanted to do, though, is make some movable paper structures. I didn’t really know how to do this, but I know someone who does: book artist extraordinaire  and paper engineer Ed Hutchins. The biggest deterrent for me was that it seemed that it would include lots and lots of paper cutting and I don’t feel like doing that right now. Destiny interceded: I came across some transparency paper for copy machines at the local thrift store (50 cents!) and now I was almost ready to proceed.  Most of the rest of this post is one way of making the copy, cut and paste moire pictured at the top of this post.

Moire Materials
Moire Materials

I wasn’t truly sure that using transparency paper and prints would work, but, as it happened, Dan Anderson invited me to visit his tech lab at the high school that he works at, which is just a short drive from my house (amazing good luck for me, considering the other two conspirators collaborators live thousands of miles away). He printed up some of his images on transparency papers and we were able to immediately see how well this worked.

A Repeating Pattern : Tiling; Tesselation
A Repeating Pattern : Tiling; tessellation

I came home and tried out, oh, about 15 different kinds of images, some in color and some in black and white, and settled on a hexagon kind of tiling. Dan had done some colored moires, which , when on the computer screen, knocked my socks, but the yellows and oranges faded out in real life. There were things I could do to work with color but I chose to work with black and white for now, but then shamelessly decided to use screenshots of Dan’s work as part of the background for my moire.

Moire from D.Anderson's OP
Moire from D.Anderson’s OP

Nice, huh?!!

Circle Rectangle Card Compass
Circle Rectangle Card Compass

First thing I did was cut a four-inch circle from the paper that my tiling was printed on, then I cut a my card from the glorious image above (about 4″ x 8″), and cut a 3 7/8″ x 6″ rectangle from the printed transparency paper.

Shapes to start with
Shapes to start with: 1 inch circle, 1-3/8″ square with a 1″ hole cut out, 2.5″ circle, and an egg cup to hold my straight pin.

I am also unbelievable fortunate to live near Ed Hutchins, who graciously agreed to show my how to do the paper engineering for moires. I thought that it would be a quick kind of thing, that he would just be able to say “snip here, glue there” and we’d be done. Three hours after sitting down with him I sort of had the idea of what to do. Honestly, what I am writing here is mostly so that I can remember how to create what I went to learn. Ed’s skill with cutting tools is far beyond my ability, so I’ve altered what he showed me. There is one major concept that remains intact,the hub; exactly  how to make and insert it is a matter of preference.  So I started with the tools above. The hub is the  little bright green circle in the center. This is the basis of a spinning hub. My hub is a one-inch diameter circle.


The hub fits into a smaller hole, which in this case is 5/8″ wide. There are four snips in the hub, cut just so that it fits snugly into the hole  and can turn without wiggle room or too much friction.

Hub Balloons
Hub Balloons

I made some hubs with a square, some with balloon shapes. There just needs to be enough room around the hub so that the larger piece can be glued down without interfering with the ability of the round piece to turn.

One and five-eighths away from the edge
One and five-eighths away from the edge

After the hub is together I put a straight pin through the center of the circle to help me get everything else centered together. I also cut a hole through my card, large enough to allow the hub to show through, but small enough so that the piece around the hub can be glued to the back of the card.

The Hub showing through
The Hub showing through

Here’s how the inside of the card looks. My egg cup is waiting there for my straight pin, so that it doesn’t land on the floor then in my foot. But for now, the pin stays in the card, waiting to pierce the center of the dark circle. The dark circle will be glued on the hub only, which still turns freely.

Adding the Moire
Now the 4 inch patterned circle will be glued on to the smaller circle


A word about the papers I am using: for the hub I need something that is strong , and that folds and glues well. I started out using regular copy paper but was unhappy with how it behaved, so I switched to using some thin but sturdy wallpaper paper, from a sample book that I had around. The dark circle is also a strong, lightweight paper. This piece may not even be necessary, but I decided I wanted a lighter paper to glue to the hub, because my printed paper, which is heavy Hammermill 80 lb color copy digital cover paper, seemed like it would stress out the structure. I could be wrong, but this was my work flow.

Almost Moire
Almost Moire

Now the printed pattern of hexagons is glued on. I used the straight pin to make sure all the centers were lined up. The pin in now back in the egg cup. You can see I added a cut-out on the front of the card. I like the way a cut-out shape frames the pattern when the card is shut.


Now, with some white glue I glued down the transparency paper. You can’t see the full effect of the moire in a static picture. Here’s a link to the video I uploaded of this. You can’t hear much of what I say, but don’t try: I’m giving instructions to my husband on how to hold the card while I am holding the camera. If you don’t want to watch a video, here’s the front, middle, and back of the cards…

three cards
Enter a caption


…and here’s another of my gifs:

Click image tp animate
Click image to animate

And, finally,

here’s the video that started this round of visual explorations, a Numberphile video called Freaky Dot Patterns

another fine example of moires in desmos by Martin

and a video that shows what the Lawler family did with their moire-that-wasn’t