What we’re going to learn to day is how to take your computer and create some art, and what you will make will astound you. First things first. What we are going to create will look a lot like wallpaper, with repeated shapes. However, the more someone looks at it, the more they’ll see. In fact, what we shall make are called tilings or tessellations. A tiling is a way to divide up the plane into geometric figures, each of which is of an identical shape (you may also have a few different shapes, but they must repeat in a pattern and fill the plane).
In the text you’ve seen many tilings. One example is with squares. Another one can be achieved with hexagons (six sided figures) and triangles. I’ve created one of my own below.
Note that there are two different variations of one tile, in different colours. I'm going ot describe how to use software to create you own tiling. You'll need a painting program. There are many free ones; we'll use thePaint program available in Windows under the “Accessories” menu.
Start up your paint program. If you’re using Paint, it will automatically open with a blank page to work with. You’ll probably want to increase the size of the page by dragging the bottom right corner of the page out as far as you can.
Now you want to draw a black rectangle, one that is of medium size (in the end, they should be small enough that you should be able to place at least six of the squares across and down without any overlapping). In Paint this is fairly straightforward: After making sure that both "Color 1" and "Color 2" are black (if one iusn't, select it and then select the black box to the right), all you do is click on the rectangle shape and drag out a rectangle on the page (if you want the rectangle to be a square, hold down the Shift key whie dragging).
This is the key step. What you want to do here is alter the shape of your tile from a square to a more interesting one. If you think of what you need to be able to put your tiles together, what you’ll see is that whatever pieces are indented into the left side must project from the right side in the same way, and vice versa. The same is true for the top, and as long as this happens, the tiles should fit together like a hand in a glove!
Here is how to proceed. You need to click on the Free-from selection tool under the "Select" menu (by clicking on the arrow beneath it). Now click with the mouse to the left of the rectangle you’ve drawn, and drag out some closed shape inside the left side of the square, making sure to get a bit of the top or bottom edge (this will make the subsequent alignment easier later). By closed I mean that when you let the mouse up, the end point of the mouse is close to where you started dragging.
Now choose Control-X to cut the piece out, and then Control-V to paste it. You'll need to drag the pasted piece to the right side of the tile and carefully release it so that it is exactly fits. If you click on the page away from the rectangle, you should see how the left side of your tile will fit exactly into the right side. Now go about and do the same with the top and bottom (select, cut, paste and drag a piece from the bottom up to the top, or vice versa). An example is shown below. You’ve just drawn your basic tile.
Now select your tile with the rectangular selection tool (it is the dotted rectangle on the left), drag a rectangle around your tile, and then click down in the middle of your tile and drag the whole tile down to the bottom of the page. You can take your tile and paint on it however you like with the painting tools. If you don’t know how to use the paint tools, ask someone, or just try them out – it’s pretty easy! Make sure all your painting is within the tile. Here is how I painted mine:
Use the rectangular selection tool to select your tile, cut and paste a copy of the tile. Drag it far enough away that you’ve left plenty of space between it and the original tile. Now you can recolour the new tile. One of the best ways is simply to change some of the colours. The easiest way to do this is first to click on the bucket tool. Then select a color for "Color 1". Select the piant bucket tool and click on any colour on your copy of the tile; the colour you selected should replace the old one. Do this several times until you’re happy with how the second tile looks. (You can use Control-Z to undo any choices you regret!)
Select aone of the two tiles with the rectangular selection tool and move it to fit into the other tile; this is your two tile pattern. Move the copy down to the bottom of your window.Then copy and paste it. Move this to the left side to be you first tile. You can then repated paste and drag this combined tile several times to fill in across the page, fitting it in snuggly as you go, and then continue beneath the first row, and so on. Continue to alternate, dragging copies of the two tiles at the bottom and placing them successively across the top so that they fit neatly into one another. The tiles will always be of opposite colour to the ones directly beside it (on all sides).
Save your picture and print or post it. It should look wonderful! Feel free to start all over again. Here are some ideas to explore once you’ve got the idea:
George Escher, M.C. Escher's youngest son, has described a game that his father invented in 1942. You’ll need the same items as described previously, along with a rag or firm sponge and some tissue paper. Here is what you do:
You’ll need a grid, that is a piece of paper that’s covered with squares of the same size. Xerox several copies of the page, or, if you’ve created the grid on your computer, print off several copies. You may want to hide the lines of the grid, and only place dots on the corners of the squares.
What you want to do now is draw some lines (not necessarily straight) across one of the squares, so that when two copies of the square are placed side-by-side, the lines will connect to one another (one easy way to do this is to make sure, for example, that the lines run across from the middle of one side to the middle of the opposite side).
Cut a large single potato right through. Use the knife and one of the squares to pare away more of the potato halves so that each half’s flat portion is a identical in shape to one of the squares.
Take the piece of paper with the square you’ve designed and place it on the flat portion of one of the potato halves. Carefully use the knife to cut through from the paper onto the potato half in order to transfer the edges of the design onto the potato. Then use the knife to pare away the parts of the potato that are to be white when you print (these are the ‘non-design’ parts of the potato half).
Make an ‘ink pad’ by spreading some of the fingerpaint onto a piece of paper, and then use a rag or sponge to absorb the paint (you’ll find using just one colour works best).
Press the potato half with the design onto the ‘ink pad’; the raised parts of your design will be covered in ink. Use some tissue to absorb some of the excess paint.
Press the other potato half firmly against the inked half (aligning them up precisely, of course) so that you get a mirrored image of the design. Use your knife now to cut the second stamp out (you’ll pare away all the non-inked areas); this second stamp is a mirror image of the first.
Now take a new grid page, and use your stamps (after inking them) on each square. You’re free to rotate each square as you like before pressing it onto a square of the page.
You’ll be surprised at the beauty you can create. To create true ‘escher’-like patterns, you’ll need to make a little ‘notch’ on each potato half so that you can keep track of the design’s ‘orientation’. Then you can try any arrangement for a 2x2 set of squares, and be careful to repeat the pattern you use over and over. It’s a little complicated, so if you want to know more, I suggest you go to the library and see George Escher’s article in M.C. Escher: Art and Science.
Copyright©2012 Jason I. Brown