beanz Magazine

Escher Tiles

Fdecomite

Use SketchUp to create dizzying patterns and shapes, Escher-style.

SketchUp is a free and fun program for 3D modeling. You can use SketchUp to design just about anything, from furniture to a dream bedroom to an entire city.

There is a downloadable version called SketchUp Make, as well as a web-based version which works right in your Internet browser. This version is called my.sketchup, and to use it just go to www.my.sketchup.com.

If you haven’t heard of M. C. Escher, look him up on Google (and Google Images) right now. He came up with all sorts of crazy tessellations, which means shapes that tile; they repeat infinitely to fill a plane, with no empty spaces. You know that this can be done easily with squares, rectangles, triangles, even hexagons. But Escher came up with lizards and birds as well, and so can you. All you need are some basic SketchUp tools and a little creativity.

I’ll demonstrate this project my.sketchup. Once you see how it’s done you can go wild and create your own crazy Escher tiles.

When you open SketchUp, you’re in this view, with Josh standing on the ground.

Josh isn’t needed for this project, so from the toolbar on the left side, click the Eraser (or press E).

Click anywhere on Josh (click on an edge, not on a face) to erase him.

We want to create our shapes on the ground, in Plan view (also called bird’s-eye view). To switch views, click the Views icon from the toolbar on the right side.

Then click the Top View icon.

For our basic shape, we’ll start with a rectangle. From the Shapes flyout toolbar, click the Rectangle icon (or press R).

Click once to place the first corner, then click for the second corner. Your rectangle can be any size.

Now we’ll makes some changes to this rectangle. Activate the Line tool (or press L).

Starting at the top left corner of the rectangle, draw a few zig-zaggy lines. Be sure to end at the top right corner.

This has created a few new faces, and these faces need to copied from top to bottom of the rectangle. But before they can be copied, they need to be selected. Activate the Select tool (or press the Spacebar).

To select multiple objects at once, press and hold the Shift key. Then click all of the faces created from the lines along the top.

Copying is done with the Move tool (shortcut: M).

Press the Ctrl key (PC) or the Option key (Mac), which puts you in Copy mode. Don’t keep the key pressed, just tap it once. You should see a little “plus” sign next to your cursor. For the first move point, click either top corner of the rectangle. Then for the second point, move straight down and click the bottom corner.

Now we’ll do the same to the left and right edges. Add a few lines along the left edge.

Then select the new faces, activate Move and press Ctrl or Option, and copy these faces from left to right. If your new faces overlap with other faces, use Undo (Ctrl +Z or Cmd + Z) and start over with a different set of lines.

Now we have all we need for our Escher shape. With the Eraser, remove all horizontal and vertical edges of the original rectangle.

With Move active and Ctrl or Option pressed, make one copy of this shape anywhere in empty space. Space them so that the shapes aren’t touching.

Now some creativity is needed. Decide what your shapes should be: birds or lizards, strange furniture, even human (or alien?) faces. Then use the SketchUp drawing tools to fill in the shapes.

Press C to make circles, A to draw arcs, L for lines. Any closed shape you make will form a new, separate face.

Adding color makes this even more interesting. From the toolbar along the right side, click Materials.

There are lots of material categories from which to choose. To see the list, click the Browse icon. You can use solid colors, or some of the various patterns provided.

Here’s my example after painting:

Before connecting these shapes to one another, it’s important to make each one a component. This does two things. First, it prevents shapes from “sticking” to one another. Second, components make it easy to make copies, and also make changes to those copies.

To make the first component, activate Select and drag a selection window that encloses one complete shape.

This selects everything inside that shape: faces and edges. Right-click on any selected face and choose Make Component.

Name this component whatever you like, then click OK.

Repeat for the second shape. Each component is now a separate object – a set of edges and faces that acts as a single object.

Now let’s start tiling these shapes. Activate Move once again, and on one of the shapes, click a corner that you know meets a corner of the other shape.

Move that point to where it meets the other shape.

But these two shapes aren’t enough – we need more copies. And it’s always a good habit to select in advance the object you’re going to copy. Make sure one of the shapes is selected.

Activate Move and press Ctrl / Option, and click a corner you want to meet the other shape.

Click to complete the copy.

Do the same for the other shape.

Keep going until you have as many copies as you like. You could go on forever, these will tile infinitely!

And here’s the beauty of components: change one and you change them all. To see this, right-click on any shape and choose Edit Component.

The component you’re editing appears in a dotted-line box, and everything else appears faded in the background. The only things you can change now are what’s in the component itself. Everything else is off-limits.

In this example, I erased the yellow stripes and replaced them with some dots.

When your editing is finished, right-click anywhere outside the component and choose Close Component. (Or you can activate Select and click once anywhere outside the component.)

The rest of the components come back into full view, and all identical components show the same change.

What crazy shapes can you come up with?

Learn More

SketchUp Make

https://www.sketchup.com/download/all

my.sketchup

www.my.sketchup.com

Other SketchUp activities

https://www.kidscodecs.com/sketchup-build-box-round-corners/
https://www.kidscodecs.com/sketchup-cheerios-box/
https://www.kidscodecs.com/sketchup-jigsaw-puzzle/

Also In The June 2018 Issue

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A phone and tablet app exposes the invisible waves that connect our computers.

How AI technology is helping fans keep the magic alive for one more chapter.

Use Scratch to become the architect of your very own digital metropolis.

Use SketchUp to create dizzying patterns and shapes, Escher-style.

Whiz around your computer’s folders and modify files at lightning speed like a pro.

Use micro:bit and cardboard to create a Jedi knight that sounds the alarm when evil approaches!

Learn about the infamous Enigma machine and how its “unbreakable” code was finally defeated.

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How daily coding puzzles with constant feedback can be a useful tool to help students master text-based languages.

Scientists draw inspiration from nature to create remarkable specialized robots.

Links from the bottom of all the June 2018 articles, collected in one place for you to print, share, or bookmark.

Interesting stories about computer science, software programming, and technology for June 2018.