Geometric Drawings · origami · Zhen Xian Bao

Late for Black Friday: A New Kit

Over the summer I made a 3-hidden boxes packet of these folded paper Zhen Xian Bao with an oceany paper for a workshop in NYC. I put up for sale, then sold out of, the packets that I didn’t use.

In the fall I made more papers for another workshop, but used autumn colors with a design that reminded me of falling leaves. Those are all gone.

Now, here we are, barrelling into winter, so I designed papers that remind me of snowflakes. Just put kits up for these on sale at Etsy, at https://www.etsy.com/listing/744194390/packet-to-make-a-three-section-chinese

I must be delusional. It thought that it would take me only a couple of days to put this project together, thinking they’d be ready for Black Friday. I should know better by now. It has never taken me less than three intense days to design a new paper. Why did I think this would be any faster this time? In fact, it took longer. I couldn’t get the colors to work right, and I struggled with lots about the design.

But I stayed with it, and in the end, FINALLY, today, not two days ago, it finished coming together.

There’s so much about these papers with this structure that I love. It’s full of shapes and colors and patterning that work together in unusual and surprising ways. Really had to work at letting the patterning reveal itself while still keeping it within the boundaries of my own vision.

There’s a bit of a story here.

I had been looking through Clarissa Grande’s twitter post, searching for inspiration. It was the second design in this thread, the one in that is green and gold, that caught my eye.

 

I didn’t realize it at the time, but it is a design I had studied and created quite some time ago while learning from Samira Mian. Samira pointed out that this was one that she had taught as the Chinese Qur’anic Manuscript Arcing Motif.

Now this shows what I like the most about these geometric constructions: the same underlying structure can create such wildly different results. Going more in the direction of Clarissa’s work, I came up with this pattern:

This led me to the final patterns in the top of the post.

What a journey!

I will have these papers in a kit for sale for just a couple of weeks at https://www.etsy.com/listing/744194390/packet-to-make-a-three-section-chinese

 

 

 

Art and Math · design · Geometric Drawings

Copy, Rotate, Reflect and add eggs

In the middle of my arts-in-ed season I’ve kept trying to find time to mess around, trying to make beautiful images.

Today I started a wonderful, week-long math activity folder project with four classes of kindergarten students, am barely able to stay awake right now, but I’ve been wanting to at least throw these  images into my blog here.

I started doing this some time before Easter. Just wanted to make something. Started with a graph that I was able to reduce to just these few lines:

https://www.desmos.com/calculator/gqt97ui6ha

Then I copied, rotated and reflected these lines and came up with a nice tiled surface.

I honestly just loved this image. Parts of it I expected, other parts came as a surprise.

https://twitter.com/PaulaKrieg/status/1117260203421052928

Spent lots of time coloring it in. Mostly used watercolor brushes, SAI Japanese Traditional Colors, but also used some colored pencils.

When it was done, I didn’t much care for the finished result.

It was okay, but didn’t make me as happy as I would have liked.

But then I started playing with it. Put it into Photoshop, isolated squares….

 

…then did some copying, rotating and reflecting…

I kept coming up with all sorts of stuff that surprised me.

 

I kept trying out different combinations…

… and then because Easter was on my mind I started wondering if I could map these on to eggs in Illustrator.

Turns out the answer was yes.

 

These were so fun to do.

I liked how the watercolor translated so well in to the digital environment.

Was very surprised that I ended up with these eggs. But very happy.

OK, that’s it for now. Gotta get ready for tomorrow with kindergarten!

 

Art and Math · Geometric Drawings · group project

Rotational Symmetry project with 5-9 year olds and Moms

I got to spend some time with a group of kids and moms this past Sunday. They had asked me to plan a math/art project for them. Last time we did this we played with shapes scaled according to the golden ratio. This time I wanted to help them make images that are made by rotating a graphic around a circle. We used a circle that was divided into twelve equal sections, and we got to talk about how rich the number 12 is, in that it comes up often in measurement of time (hours, months), quantities (dozen), distance (Inches) and so much more.

Images were made in two ways. One was to connect the dots around the circle according to a rule, such as connect the first dot to the fifth, connect the fifth dot to the tenth, connect the tenth dot to the dot that is plus+5 further around the circle, then continue until you are back where you started from. A star emerges!

Connecting the points around a circle

We started the afternoon by sitting in a circle of eight people, and doing the skip-counting activities that I described above. This was actually a thrill to me, as it’s something I’ve wanted to try out for a long time. As the star shape grew within the circle of people, who were the “points”, everyone was thrilled. They had no idea a star would emerged. I knew, but I was thrilled too.

I had PDF printout of circles and shapes.People cut out shapes that they wanted to rotate around the center, then colored them in if they wanted to.

I think the young man who did this image is about 8 or 9 years old.
I think the young man who did this image is about 8 or 9 years old.

The moms seemed to like this activity at least as much as the kids.

I never know how these projects will go. A couple of the boys didn’t want to be coloring any more after a while. One boy in particular really liked cutting paper, so I got him started with another kind of rotational symmetry: making snowflakes!

Snowflakes have rotational symmetry
Snowflakes have rotational symmetry

I hadn’t thought about snowflakes beforehand, but liked the way I was able to link to something that was already familiar to this group.

After awhile one of the girls was finished with coloring, I showed her how to make an origami pockets that were sized for the drawings to slip into.

Lot of pockets
Lot of pockets

She really liked making the pockets, and made them for everyone. This also let me segue into showing her how to make a square from a sheet of paper.

In the end, we had made lots of images, pockets, snowflakes and our work area was delightfully messy. Everyone helped with the cleanup, especially with the tiny pieces of paper on the floor.

At the end we put our tiles out on display.

Our tiles
Our tiles

A couple of hours later one of the mom’s texted me saying that, on the way home, her kids were asking to do more of these. YAY!

 

Drawings · Geometric Drawings · Uncategorized

Coloring Books and me

Scaling Shapes, Visons of the Universe by Alex Bellos & Edmund Harriss
Scaling Shapes, designed by Professor Chaim Goodman- Strauss, Visions of the Universe by Alex Bellos & Edmund Harriss

I’ve always loved coloring books. Is this true for every kid? I really don’t know. Are coloring books for kids even around much anymore?

When the coloring books for adults became all the rage a few years ago, it made perfect sense to me, although most of the titles on the market didn’t interest me much. I like sense an underlying  rigorous structure, but one that is not simply symmetrical. Naturally, then, I fell in love with the books by Alex Bellos and Edmund Harris.

Patterns of the Universe and Visions of the Universe by Alex Bellos and Edmund Harriss
Patterns of the Universe and Visions of the Universe by Alex Bellos and Edmund Harriss, published by The Experiment

In the interest of full disclosure, I have not been asked to write this post by anyone connected to these books. In fact, the reason I am writing this now is because I am working on something else that won’t be ready to write about for awhile, so I thought that, with the holiday season upon us, the colorfulness of writing about these books seems timely.

Cascading Waves, Read the Sines, Patterns of the Universe by Alex Bellos and Edmund Harriss
Cascading Waves, Read the Sines, Patterns of the Universe by Alex Bellos and Edmund Harriss

I love these books for all the same reasons that I’ve always loved coloring books. They let me mess around with color without having to think too much about form. Just experimenting with color combinations without thinking about much else is a great thing for me to do when I’m wanting to make something but not feeling particularly ambitious. I think this cascading waves is my favorite of all the pages. If the authors happen to be reading this, please make more versions of this one for me, please.

Polyhedra, Cascading Waves, Read the Sines, Patterns of the Universe by Alex Bellos and Edmund Harriss
Polyhedra, Cascading Waves, Read the Sines, Patterns of the Universe by Alex Bellos and Edmund Harriss

I do not recommend using crayons in these books. The image above in started as crayon only, but it didn’t have a look that I liked until I added those crackly lines made with markers. Crayons are amazing when used on paper that is a bit rough, just like the newsprint paper in traditional coloring books, but seems to me that they aren’t well suited for the smooth papers of adult coloring books.

Modular Forms, Visions of the Universe by Alexs Bellos & Edmund Harriss
Modular Forms, Visions of the Universe by Alexs Bellos & Edmund Harriss

Colored pencils work well on these pages, but be advised that not all colored pencils are created equal. The best value for colored pencils are the Crayola brand, but Prismacolor Colored Pencils are just about the only upgrade that makes sense. If I’m using colored pencils on these pages, it’s Prismacolor that I’m using. However, If I am making drawings of my own, using my own designs, I generally use my absolute favorite colored pencils, made by Caran D’Ache.

Petit Fourier 1, Patterns of the Universe by Alex Bellos and Edmund Harriss
Petit Fourier 1, Patterns of the Universe by Alex Bellos and Edmund Harriss

Sometimes mixing up the Prismacolors with markers works out best. This page above, which references color bands used by Georgia O’Keefe in one of her paintings, was done with both Prismacolors and brush markers (an expensive Japanese brand, SAI).

Read the Sines, Patterns of the Universe by Alex Bellos and Edmund Harriss
Read the Sines, Patterns of the Universe by Alex Bellos and Edmund Harriss

I love the way Sharpies look on these pages. Yes, they bleed through like crazy, so I always put a protective piece under the page that I am working on. Otherwise, I don’t care that they bleed through the page. The publishers of these books were kind enough to keep the verso side of the spread mostly blank, so I don’t lose anything that I’m not willing to lose in the interest of using exactly the materials that I want to use.

The Collatz Conjecture, Visions of the Universe by Alexs Bellos & Edmund Harriss
The Collatz Conjecture, Visions of the Universe by Alexs Bellos & Edmund Harriss

My favorite pages, so far, are one that are not full of tiny, tiny details, like the one above, These tiny details require more attention than is comfortable for me.

The Kolakoski Sequence, The Collatz Conjecture, Visions of the Universe by Alexs Bellos & Edmund Harriss
The Kolakoski Sequence, Visions of the Universe by Alexs Bellos & Edmund Harriss

This Kolakoski Sequence has just about the right balance for me of detail and broad areas of color. I’m generally more interested in the description of the form after I’ve colored it, but in this case it was already obscured by the bleed through from the previous image. Oh, well, I still have the internet.

Mechanical Curves, Patterns of the Universe by Alex Bellos and Edmund Harriss
Mechanical Curves, Patterns of the Universe by Alex Bellos and Edmund Harriss

Here’s another one done with both markers and pencils. I didn’t find this uncolored page very compelling, so I challenged myself to use color to make it more interesting to me.

detail Mechanical Curves, Patterns of the Universe by Alex Bellos and Edmund Harriss
detail Mechanical Curves, Patterns of the Universe by Alex Bellos and Edmund Harriss

I was pretty happy wit the way this one turned out.

Dodecapliex, Patterns of the Universe by Alex Bellos and Edmund Harriss
Dodecaplex, Patterns of the Universe by Alex Bellos and Edmund Harriss

The thing I like the most about these books is that I can pick them up and put them down with impunity. I don’t have to remember what I was thinking about or where to start. During the years of raising children and never having any extended amounts of time to work on anything, it still makes me feel happy to have something to do that doesn’t suffer from interruptions.

Spiral Tile,Patterns of the Universe by Alex Bellos and Edmund Harriss
Spiral Tile,Patterns of the Universe by Alex Bellos and Edmund Harriss

This spiral is the first one I did in these books. Took quite a few sitting before I considered to be finished, but that’s fine.

Co-Prime Numbers, Patterns of the Universe by Alex Bellos and Edmund Harriss
Co-Prime Numbers, Patterns of the Universe by Alex Bellos and Edmund Harriss

Here I got to play with trying to create a illusion that these circles were not in a precisely straight line. Sadly, in this photo that illusion seems to be mostly lost, but on the page they do look wiggly.

Graph Theory, Visions of the Universe by Alexs Bellos & Edmund Harriss
Graph Theory, Visions of the Universe by Alexs Bellos & Edmund Harriss

Not all drawings that I do come out great. Some come out well but don’t photograph well, like this one, which I love, but doesn’t seem to like the camera much. Sharpies love the camera.

Those funny shapes to the right of the page are called Sphericons. They are peculiar, funny, and I will making some to give away and some to hang on our tree. They are pesky to try to make out of paper, hence it will be many more days before they get a post of their own. But am happy to have finally made a post about my favorite coloring books.

OH, and if the editors or authors are taking requests, how about a coloring book along the same themes as these, made for kids and printed like old-fashioned coloring books, on newsprint, so that crayons would be the preferred medium? A mathy coloring book for kids, with large, not-particularly detailed patterns sounds like a great idea to me.