Decoration · design

Beautiful Papers

I’ve had my head into making beautiful papers for different projects I’ve been working on. Thought it would be nice to give a peek at the different ways I go about making these papers. This, sadly, is not a “how-to” post, as each technique has so many steps.

The one thing that these all have in common is that I create them using the computer.. While I have great affection for making decorative papers by hand, it’s been my experience that if I want to use the computer to print papers that it’s best to create them on the comupter.

The paper at the top of the post is created in Adobe Illustrator, using patterning I’ve learned from Islamic Geometry tutorials. These patterns are great to when I am teaching folding methods, as I can size the designs so that the designs line up nicely when the paper is folded precisely. This has made teaching certain things so much easier.

Here’s an origami box, folded with my papers. More boxes below. Same pattern, different colors.

I use Islamic Geometry a great deal on my papers, but not always.

Sometimes I just create from the tools that are unique to the programs I am using. Illustrator’s flare tool is very fun to use.

This one is made by overlaying, resizing and recoloring a rarely used tool in Adobe Illustrator, called the flare tool. It’s hidden at the bottom of the menu that contains the rectangle and circles tools. I love having an excuse to play around with flares. This one I used to build a shape in which I placed the design inside the shape so it only showed when the light inside of it was activated.

Another way a create designs is by starting with graphs of equations. Even if I don’t understand the graphs that I’m working with, I have figured out how to play around with equations then work with the resulting graph.

Playing around with graphs isn’t hard once you get the hang of it. You can do it right now. Click this link https://www.desmos.com/calculator/b9bjax0qjf and then click the little arrows to start and stop the animation. See what happens. When I get something I like, I copy get the lines in Illustrator, create tessellations, and add color.

The pattern with the orange in it comes from the desmos graph. The blue pattern uses another set of equations. I like that the colored and uncolored versions are showing here.

This flower-like image is made from trig functions. Gold and silver embellishments were added by hand. This one ended up being a thank you card.

Now might be a good moment to mention that I just put a set of beautiful notecards up for sale in my etsy shop. https://etsy.me/3EGgXY2

While Illustrator is my program of choice, I do dip my toes into photoshop once in awhile.

I’m pretty much a novice with Photoshop. Maybe that works to my advantage? (Wishful thinking.)

I’ve discovered I can lay down a gradient, use some filters and the gradient tool and sometimes make some really gorgeous papers. It’s quite a random activity. Soon as a design shows up I save it. There is no recreating these.

These Photoshop generated papers have become all sorts of shapes.

With the holiday season coming, I’ve been using my Photoshop papers to make these paper ornaments.

I could go on and on with the different ways I put designs on paper. Here’s just one more.

The design above started as black and white lines on Dave Richeson’s computer, which then made its way to twitter https://twitter.com/divbyzero/status/1415049185573879817?s=20 then made its way to my computer. I did the coloring with Sharpies, colored pencils, and other markers. I did try scanning this, but I knew, from past experience, I wouldn’t like the scan. Here’s what I do when I want to make copies of hand drawn designs: instead of scanning the images I simply lay them on the glass of my copy machine and make copies.

Ushexahexaflexagon

Using the copy machine retains the feel of the hand drawing, which can be really nice, as long as no one looks too close.

There, so I’ve shown you the Islamic Geometry designs, the design made from graphs, flare overlays, random Photoshop gradient washes, and using my copy machine.

Now I need to figure out how to package up some of these items that I’m making so I can justify all this ink that I’ve been using! So easy to just have fun, the business part is still in process.

Decoration · design · Frieze Groups · Math and Book Arts

Frieze Symmetry Patterns, introduction #1

Frieze border Book Cover 2002
Frieze Border for Book Cover 2002

I call them borders. For decades I’ve been creating lessons for young kids on ways of creating geometric borders in the books that I make with them in the classroom. Kids love these lessons. They sit quietly, raptly attentive, and can’t wait to get to work.

Frieze Storybook Decoration 2009
Frieze Storybook Decoration 2009

Long overdue, I thought I’d take a closer look at these linear repeat patterns. Thought I’d have it all figured out in an afternoon. That was a couple of weeks ago. Now, deep in the rabbit hole, I’m reporting back. What was going to be one post will be many posts. It’s not that any of this is difficult, but there’s much going on that’s not evident with a cursory look or a single example.

Example of Glide Pattern

What’s just as challenging as deciphering the patterns one can make is deciphering the notation that describes them. There are three separate systems of notations that I will be listing, though these aren’t the only systems. Notation will be filling up my next post.

Here’s the first amazing fact about a pattern that grow along a horizontal strip, which I will henceforth refer to as a Frieze as in Frieze Groups or Frieze Patterns, or Frieze Symmetry:

There are only seven possible ways to create a frieze pattern.

Any frieze pattern you see will be some configuration of only one of seven ways of manipulating a base unit.

Doesn’t seem like this could be true, and if it is, doesn’t seem like it would be too hard to figure out.

It is true, there are only seven possible ways that frieze symmetry happen, and it is not easy to grasp. Some symmetries are easier than others, but each of the seven ways have their quirks that need to be addressed, which is something that I will do in one post after the other until I am done.

Here’s a list of the main resources I have been using:

My resources:

Beautiful Symmetry by Alex Berke

Frieze Group, Wikipedia

Talk: Frieze Group, Wikipedia

Gait Sequence Analysis Using Frieze Patterns, Table 1, Yanxi Liu

Gait Sequence Analysis Using Frieze Patterns, Table 5, Yanxi Liu

 

Geogebra Apps by Steven Phelps:

To be continued…

Decoration · design

Domino: A Shape With Merit

Paper Cut Dominoes
Paper Cut Dominoes

The domino shape just doesn’t get enough respect.

You are likely familiar with the fact that the game of dominoes is played with tiles that are like two squares on top of each other. Much to my delight and surprise, about a year ago, mathematician Justin Lanier enlightened me to the fact that this rectangle, which is twice as long as it is wide, has a specific name and that name is DOMINO.

(pause. paste in Matt Vaudrey’s reaction…

domino Hallelujah
https://twitter.com/MrVaudrey/status/601777262871060480

…ok, continue with post)

This may not seems like such a grand reason to celebrate, but, over the past year, by being able to pull this definition out of my back pocket, both my teaching and my structural problem solving have improved and deepened.  There is something about calling something by its proper name that has value.

Domino  https://en.m.wikipedia.org/wiki/Domino_(mathematics)

students 2002
students 2002

For decades, with thousands of children who have done bookmaking with me, I’ve been trying to figure out how to get students to decorate their books using geometric shapes in a meaningful way. A meaningful way means, to me, getting them to really understand and exploit the characteristics of the shapes. Thousands of children for decades means I can try out one idea after the other, attend to nuance, and maybe even figure out a thing or two.

Cover Made by First graders 2010
Cover Made by First graders 2010

I’ve known for a long time that starting with squares can help reign in the chaos of making decorations for books. I actually use to cut out and distribute piles of squares to students so that they could work with squares.

Lots of cut squares
Lots of cut squares

Yeah, I would spend hours cutting little squares out brightly colored card stock. Even now it’s painful looking at these squares, remembering those late nights of cutting cutting cutting… and then the students would want to  smear glue all over their books and sprinkle the squares like candy on them and, when the glue dried, half of the squares would fall off because the gluing was sub-prime. Ok, I’m sort of exaggerating:  Many turned out beautifully, but I still didn’t feel like the kids were getting the most out of the activity: they weren’t making the connection that I was hoping for with the square.

Dominoes, cut into squares, then half squares, which turn out to be a scaled down domino, then halved again to make small squares
Dominoes, cut into squares, then half squares, which turn out to be a scaled down domino, then halved again to make small squares

Eventually I realized that I could give students the double-square shape, though at this point I didn’t know that it was called at domino. I show students how to line up two of these double-square perpendicular to each other,  from which they cut “on the line” that separates the colors, and snip, snip, they have four squares. If they cut the square again, this time by eye, they have scaled down rectangles, and they can then cut these in half to make baby squares. Yes, baby squares. These are young children and young children like baby squares. I also talk to the about rotating the square, cutting it from point to point to make two triangles, and then cutting the triangles in half to make baby triangles.

Dominoes cut and arranged
Dominoes, cut

Now just this year, during this teaching season, I have a made a point to introduce the double-square shape by name. The students I work with are shape savvy: they know what a rectangle is and they know that the square is a special kind of rectangle, but their eyes light up when I tell them a that a double-square shape is a special shape too, a domino. Does it make a difference for them to call it by name? I answer that with a resounding YES.

Emperor Penguin Book
Lily’s Emperor Penguin Book

It’s been like night and day. Students seem to honor the shape and special qualities of the domino. I know this because, with the hundreds of students that I’ve worked with this year, I saw, for the first time, the overwhelming majority of students being at ease with the idea of working with just the shapes that I talked with them about. There was so much less arbitrary cutting of paper, so much less just slapping down whatever shape that emerged from a hastily cut paper strip.

Thinking hands
Thinking hands

Across the board, with the introduction to the domino, students approached this part of the project with a sophistication that I had never seen before.

pages in progress with cut paper decoration
pages in progress with cut paper decoration

Instead of having to wade through photographs to show the type of work that I think is most valuable to show, I am finding it hard to choose between all the interesting work that these students are making.

Mostly Green
Mostly Green

I look at these and I can sense that the student is connected to the underlying structure. If you don’t know what I mean by that, just look again at these photos.

It seems to me that I even have metric which tells me that this is not just something I’m imagining. One of the other techniques that I show students is how to make paper spring.  This is a challenge for most students, but a worthwhile one, as they love  how it gets used in their books. Though not a domino shape, it is made by having an awareness that the two strips of paper they start with are of equal width, and I show them how to weave and rotate the strips down into a square.

Working hands
Working hands, paper spring made with paper strips that are 8 times as wide they are  long, which, is  I am told by mathematician Paul Salomon,  an octomino

After first showing them the techniques of decoration with the domino it was astounding how quickly the students understood how to do the spring.

Paper Spring, completed
Paper Spring, completed  Interesting fact: my page on How to Make a Paper Spring has been visited more than 16K times

In fact, in each class, these parts of my presentation went so quickly and smoothly that I kept checking my notes, thinking I had missed some part of the lesson because there was so much extra time.

Needless to say, I have much respect for the domino.

For the last few months I have been casually, now more seriously, studying a folded paper structure in Chinese Folk Art, called the Zhen Xian Boa. My plan is to write a number of posts on this structure. It’s not hard to figure out that part of my fascination with the structure is that, from beginning to end, there’s the domino.

Zhen Xian Boa , Chinese Folk Art
Zhen Xian Boa , Chinese Folk Art

Here’s some links to look at about the Domino

Two from Wikipedia:

 https://en.m.wikipedia.org/wiki/Domino_(mathematics) 

https://en.m.wikipedia.org/wiki/Domino_tiling

And here’s a wonderful paper written by Paul Salomon and Justin Lanier, about the ways to think about dominoes and other polyominoes  https://mathmunch.files.wordpress.com/2015/08/moves-proposal.pdf

Justin Lanier just shared this link to a video after reading this post. Perfect. https://www.youtube.com/watch?v=yXL4DP_3dJI

 

 

 

 

 

Decoration · Making Books with children · Making books with elementary students

Adirondack Birds, Books by Second Graders

Adirondack Bird Books by second graders
Adirondack Bird Books by second graders

Here’s a project I did with second graders a number of years ago, but, for a specific reason that I will divulge at the end of this post, I chose not write about. Now, having just come across this folder of picture, I liked the images so much that I decided it’s time write about these  books.

Adirondack Robin
Adirondack Robin

These second grade student chose to a local bird to research. My job was to design a project that would showcase the results of the research, display some generalized info about the life cycle of the bird, have an “About the Author” section, as well incorporate a diorama that flatten, and which included pop-ups and a paper spring.

Adirondack Birds Katelyn's Eagle 2
Adirondack Birds Katelyn’s Eagle

I can’t say for sure (though I will dig up my notes and include this info later) but I’d say that this book stand about 10″ high.  You can see that it opens from the center to reveal the habitat of the bird.

Adirondack Blue Jay
Adirondack Blue Jay

We were able to do two pop-ups; one in the sky and once on the forest floor. The Blue Jay is attached with a paper spring to give the bird some dimension and movement.

On the backside of the habitat there’s ample room for research and everything else.

Adirondack Birds, Chelsea's Hummingbird Book
Adirondack Birds, Chelsea’s Hummingbird Book

Food and Interesting facts go on one of the sides.

Blue Jay book
Blue Jay book

Facts about the bird’s appearance and their habitat are written on the far edges of the paper…

Adirondack Birds Life cycle back of book
Adirondack Birds Life cycle back of book

….with life cycle info at the center…

Adirondack Birds Chelsea's hummingbird
Adirondack Birds Chelsea’s hummingbird

…topped off by information about the author.

Adirondack Birds Chelsea's hummingbird 2. jpg
Adirondack Birds, Chelsea’s Hummingbird Book. jpg

Now here’s some details to notice. To get the front sections to stay together, the rotated center square is glued on half of its surface, the other half slides under the long strip, which is glued down just at its bottom and top.  The details of the decorative elements on the fronts of the books were created with simple, geometric symmetries. I loved the decisions that kids made with the shapes!

Adirondack Owl
Adirondack Owl

Another idea that the students worked with was the idea of using different mediums and methods to make thehabitat. The cloud is foam, there’s cut paper shapes, drawing with markers and crayons, a few shapes created with paper punches (the  butterfly and dragonflies) paper springs behind the owls, and both a one-cut and a two-cut pop-up: all with the goal of creating an interesting, texture display.

Adirondack bird nest made from Origami Pocket
Adirondack bird nest made from Origami Pocket

As you might imagine, these books are made using lots of separate pieces. For this kind of project I generally first have the students make a large origami pocket from a 15″ square paper so that we have  container in which to keep everything organized. The classroom teacher, Gail DePace, who I could always count on to enrich my projects with her own personal standards of excellence, had the idea to ask the students to decorate their origami pockets as if they were bird’s nest, complete with  appropriately colored eggs.

 

 

clay owl
clay owl

The students added another dimension to this project by creating their birds in clay and putting them on display along with their books.

At the beginning of this post I said that there was a reason that I hadn’t written about this project. As lovely as the project is, the teacher, who was a spectacular collaborator on this and all projects that we did together, didn’t love this project. She noted that this structure didn’t work well as a book, that it was awkward for the kids to open to the “pages” and read their work when it came time to do their presentation of the final project.

I’d have to agree that this project works much better as a display than as a book. Oh, and it looks great in pictures too.  Sometimes, though, the display and the documentation are the priorities, so that’s what I’d keep  in mind for this project next time.