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.

 

 

 

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.

Addendum:

Harry O’Malley just pointed me towards http://www.colourlovers.com/, 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 https://bookzoompa.files.wordpress.com/2018/01/awesome-gif-pentagons.gif

o

 

..

 

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 https://www.youtube.com/watch?v=4kJmJUQVbO0

 

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.

and

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 https://bookzoompa.wordpress.com/2014/12/10/paper-folding-squares-and-equilateral-triangles/


addendum March 2018

Here’s someone making this star. She makes it looks so easy! https://www.instagram.com/p/BfuSgYdnmY5/