design · Geometric Drawings · geometry and paper

What to do about Color Combinations


Steal them.

Since I started decorating my own papers with geometric designs (as well as decorating geometric designs) I’ve been flummoxed about color combinations. Some of the decisions I’ve made have been truly horrible. Sometimes they’ve not been so awful, but, even then, it takes way too long to come up with color combinations that look good to me.

I suppose I could take an on-line class about color theory, but somehow I’m just not drawn to do that just now. Abode has a palette-sharing site, but it’s not supported in the version I use. Recently, having spent way too much time having way too little success, it finally occurred to me to try out dipping directly into the palettes of painters who use color in a way that sing to me.

Geometry and Georgia O'Keefe
Geometry and Georgia O’Keefe

I probably wouldn’t write about this if  I could do this only in Adobe Illustrator, since this info would be totally useless to most people. I noticed, though, that more and more people in my circle are using Inkscape, which is a free graphics program, and it turns out that dipping into the palettes my favorite painters is even easier to do in Inkscape than Illustrator.

Fra Angelico
Fra Angelico

Here’s what to do in Inkscape. Find a painting you’d like to dip into. Save it to your computer. Drag and drop it into Inkscape. Select the shape or area that  you want to color. Press F7 or choose the eyedropper tool (second to the last tool from the bottom on the left side) and click on the color on the painting that you want to use. That’s it.

Vectorizing the Image in Adobe Illustrator
Vectorizing the Image in Adobe Illustrator

To do this in Adobe Illustrator, it’s bit more complicated. Place the image into the Illustrator file, then vectorize it  in Image Trace. I generally use the high fidelity photo setting in image trace. This separates the painting into regions, which if you zoom in really closely looks abstract and totally cool (in Inkscape, getting this close just looks blurry).

Up-close O'Keefe
Up-close O’Keefe

Just like in Inkscape, to harvest the color use the eyedropper tool, which has the key shortcut “I”. I’ve been using the live paintbucket tool (k) to fill in the areas that I want to color, but, like Inkscape, choosing the shape then the eyedropper works too.

Even more O'Keefe
Even more O’Keefe

Now, I just want to mention that even though this is the best method I’ve used to choose colors digitally, there’s still a bunch of trial and error. But instead of me doing trail and error with millions of colors, I’m using this more limited palette. Works for me. Am having lots of fun with this.


Harry O’Malley just pointed me towards, which looks like the internet’s free version of Adobe’s Kuler. Yay! Another color resource! (I can use all the help I can get.)





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





Geometric Drawings · geometry and paper · geometry and paperfolding · origami

Pentagons, Paper Folding, Stars & Origami

I came across a lovely way of folding stars. It was in a youtube video by someone named Tobias.

As lovely as these stars are, what really caught my attention was the way Tobias showed how to use paper folding to make a pentagon from a square. This square-to-pentagon transformation was in a separate video, and since it will take me about two days to forget everything I saw in the video I drew out the directions.

How to fold a Pentagon from a Square
How to fold a Pentagon from a Square. For the Video of this that Tobias made, go to


After the novelty (but not the thrill) wore off of making a pentagon from a square I began to look at the angles that I was making and figured that I could make the star with less steps (and perhaps with more accuracy) if I just started out with the net of the shape, so I made this map of the paper star’s fold lines:

Lines for a Folded Paper Star
Lines for a Folded Paper Star

If you make Tobias’s stars, after you get the hang of which lines fold in which direction, I highly recommend printing out lines above, score the lines with an inkless ink pen, and make that same star using just its essential folds.

The back of the paper sta
The back of the paper star

The photo above shows the backside of these stars. Quite a nice backside!

I’m sure that there are all sorts of things to do with pentagons, but something I want to mention is something that is fast and impressive, sort of the pentagon version of snowflake cuts. If you cut off an angled slice at the bottom of the folded up pentagon (step 12 in my tutorial drawing) there are all sorts of star possibilities.

36-54-90 triangles, with cutting lines on their tips
36-54-90 triangles, with cutting lines on their tips

These little beauties turn into:

Stars in Pentagons
Stars in Pentagons

The stars inscribed into these pentagons were made by cutting through all layers on the tips of the folded shapes.


And look, below there’s something extra for my friends who teach Geometry, and who might like a holiday themed angle activity. Part of the working out the folding pattern for the star was deciphering certain angles.

Find the Angles with degrees of 90, 45, and ~72, 18, 36, 54, and 108
Find the Angles with degrees of 90, 45, and ~72, 18, 23, 36, 54, 63 and 108

I had a good bit of help with the especially tricky parts of understanding the angle relationships. I’m sharing two twitter threads here, just because it was such a pleasure to get help from my friends.


That’s about it for now. Oh, and if you need to directions on how to fold a square from a rectangle, take a look at

addendum March 2018

Here’s someone making this star. She makes it looks so easy!

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