New Geometric Patterns

A couple of years ago we began drawing some small, simple geometric patterns which could easily be repeated to make larger, more complex designs.  These were designs that could be adapted for many different crafts — not just needlecrafts.  Designs could be repeated a number of times just as they were in the picture, or they could be reversed, rotated, even taken apart and put together in new configurations.

Let's look at the three patterns at the top of the page. Here is the first one, a very simple design in a single color on white. In the larger version, the original pattern has been rotated to make a design of squares. This one can be continued outward as far as you want to go.

Now let's consider the pattern at the other end of the line. You may remember this one.  Later we showed you how to change the design from a square pattern to a rectangular one by elongating the internal squares either vertically or horizontally.

Vertical & horizontal  versions

I was trying to make two points. First, that, since this was an all-over pattern, it was not necessary to start in the middle of the canvas. I started the piece on the left at the upper right-hand corner of the design and expanded it both horizontally and vertically as far as my canvas segment allowed. Second, the pattern can be worked to fit rectangular projects. They do not have to be square, as the 4-way bargello designs do need to be.  I suggested that viewers might want to do a sample using the 3-stitches-over-4-threads formula that I used for this sample, which elongates the squares into rectangles vertically. The third sample elongated the squares to rectangles horizontally. The result is definitely rectangular — and large. It is probably not a good design for a 4-way bargello unless you are using much smaller squares of canvas. It would probably work on # 14 needlepoint canvas, however.

The middle pattern can be repeated just as it is, of course, but I want to play with it a while. How you approach this pattern depends on whether you want to place the emphasis on the heavier "North/East/South/West" part of the square pattern or the more delicate diagonal components. I will start with the heavier aspects. Here is the result. You can change this from a square pattern to a horizontal one by simply adding another repeat of two of the smaller squares to any side of the original.

I returned to the design, this time concentrating on the slender lines that formed the diamond shapes inside the frames.

These designs made from the small corner squares have proven to be popular. For that reason, I am giving you some more of them to work with. In each case, the original square that was rotated is shown in its proper position and is emphasized by a black outline.

Suppose you are ready to enlarge a design but are not sure how to proceed.

Take a clean sheet of graph paper and mark its center both horizontally and vertically. Repeat your desired pattern (diagram above) on top of the horizontal line, starting just to the left of the vertical line. Now repeat your pattern in reverse to the right of the vertical line. Turn the paper upside-down. Repeat what you just did below the horizontal line above the horizontal line now. Now you have a 4-way starting pattern.  Each colored square represents a stitch or a square of stitches in your pattern. Empty squares can be worked in white, black, beige, etc. Work the four parts of your design in the center of your canvas, then decide how you want to "grow" your finished pattern.

The samples I usually show on these posts are done on #7 plastic canvas. I recommend this for practice and to make pattern samples that are meant to be filed in a box for future reference. If you are working in tent stitch, this is the pattern square, with one stitch for each square of the pattern. It is also done on #7 canvas. These patterns are very versatile. If you do latch-hook, for example, you can use a pattern like this one by putting in a knot for each square of the pattern. This would work as both a four-way pattern, perhaps for a pillow, and an all-over one for a mat or rug. Beading and mosaics could also be done with such a pattern.

When working a multicolored pattern like this, I recommend using a separate needle for each color. This cuts down on the time spent in threading needles and decreases yarn waste. Secure each color often on the back of your canvas. Do not carry long strands of yarn across the back of your canvas while moving from one colored segment to the next.

This two-color pattern is suitable for an all-over design, but perhaps is not as good for a 4-way design.

A word of caution about colors. What I see on my screen in the office is not necessarily what J.D. sees on his screen in the workshop or what you will see on your device. And if you are printing something out, there are even more possible differences. Use your own color choices on any of these designs.

Before we leave the 12-square designs above, here are the three designs as I have expanded them to 16-square designs.

The first one is done in the same way I changed the smaller squares to 12-squares. I took more liberties with the second one, repeating some parts of the design and modifying others. Bear in mind that none of my designs are the only way to "grow" the designs. You need to find your own ways to do that to make designs that please you. I have taken even more liberties with the third design, repeating none of either the dark or light elements exactly as I expanded the design, while keeping the "feel' of the design.

Letter chart

There is another way to record graphed designs, and this one can be done in any color combination that you desire.  Instead of filling in colors on a design sample that you like, put in alphabet letters for each of the colors that you used.  You can then experiment with different color combinations and record alphabetically the ones you want to keep. This diagram will show you what I mean.

Each of the little squares in the design could represent a single stitch on canvas or even-weave fabric, a square of upright gobelin, a much larger square of fabric, or even a floor tile. Let's revisit one of those designs. Instead of taking one of the little squares as the basis of our design, this time let's consider the entire three-inch square as a single, repeatable part of our design. I chose to make this design in analogous colors (colors next to each other on the color wheel) because I wanted to make some points about color combinations. Analogous colors reflect wavelengths of colored light that are closely related Since these colors are closely related, we are pretty well assured of a pleasant design. I chose blue-green, blue, and blue-violet for my color combination, but you need not use those colors if you want to try others. For a trio of warm. bright colors, you might choose red-orange/ orange/ yellow-orange (the exact opposite of the three I chose), for example.

Notice that I have used one light color, one medium color, and one dark color (a tint, a tone, and a shade) in each design. I do this to make it easier to place each color when I begin "growing" the design. Each color is in the same set of squares on all three versions of the design; only the intensity of the colors changes. As you can see, which color is emphasized most does alter the design — a fact you will need to consider not only when "growing" your design, but also before choosing the yarns, fabrics, paints or other materials for your final project. Changing the positions of the colors as well as the intensity will give you even more varied results. I "grew" all three of the blue-green/blue/blue-violet designs. Here are the expanded designs.

Annake at work

Somewhere in the midst of all this, J.D. slipped up behind me and snapped this picture of my worktable, with the designs in progress. (He says he wanted to show you how much work I do before I publish anything for my readers. I think he just wanted to show what a mess my worktable usually is!)

This design technique is called tiling. It is an ancient art form used originally for creating inlays and mosaics. It was used in Mediterranean civilizations long before those of the Greeks and Romans. The earliest known mosaics were made in Mesopotamia before 2,000 BC (BCE)  Just recently there was news of a remarkable mosaic discovered in the ancient city of Hippo.

Of course, I do a lot of preliminary work on the computer to save time.  One place where this comes in handy is in choosing the background color for a geometric center design.  What J.D. does is put up the center design on screen and then "flood" the background of the design with a variety of colors to see how they compare. J.D. did this electronically.  Here are the ones we liked best.

We often show pieces of finished work without showing the design patterns.   Here are three that are suitable for tiling in one or more of the ways we have discussed in this article.

So far we have worked with patterns based on small squares or rectangles because they are so easy to duplicate on standard graph paper. When we return to this topic in the future, we will discuss other base shapes like triangles and hexagons.

Have fun with your design experiments.

 This post by Annake's Garden is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Designing Realistic Flowers for Projects

Daylily rug, by Annake

I love flowers! That is why my business is called Annake's Garden and my blog is called  “Cuttings from Annake's Garden”. More of my work involves flowers than any other single subject. I am a great admirer of Georgia O'Keeffe's giant flowers and her determination to get people to really look  at flowers. While my individual flowers don't approach the size of her paintings, I do like to work larger than life. Actually, this goes back to a time when I was teaching fifth graders about Georgia O’Keeffe. I made several oversized flower pictures in various media to show the students, along with samples of O’Keeffe's work, before I asked them to make their own large flower pictures. Their favorite sample was a study in pastels and crayon of an orange daylily. Several students asked me to make computer copies of the picture for them. I did that, filed the picture, and essentially forgot about it.

"Day-glo Daylily", needlepoint by Annake

After I retired, I cleaned out my files and came across the original drawing. I decided to make a rug, using the sketch as a basis for my design. It was the first rug I ever sold. Fortunately, J.D. had already been archiving photos of my work, so I can show you what that piece looked like (above).  I've also done a daylily as a large needlepoint (right). The colors came from my imagination; however, I see one in this year's catalogs that comes very close to my imaginary one.  Is art imitating life or is life imitating art?

Sample card

In both cases, I was working on a scale considerably larger than life. Doing this frees you to include as many details as you like — whether or not those details existed in an actual flower. There are many instances, however, when this is either not possible, or when it not desirable. Sometimes less is really more. Sometimes it is simply a matter of space. Suppose you are making a series of greeting cards.  The entire card may be smaller than the flower you are depicting. Instead of cropping the flower to fit, why not do a depiction of the flower that fits the card and eliminate unnecessary details?

Sunflower project materials

Once again the size of the finished project dictates what you can and cannot do.  Take, for example, a sunflower that I decided to do in needlepoint in a round frame that was only 9 inches in diameter. Now, I love sunflowers. They are large and complex. They are not dainty, shy blossoms. They are large, bright,  and kind of in-your-face. They never fail to cheer me.

Before I began working on the design, I collected pictures of sunflowers, fabric decorated with them, live flowers, all kinds of materials.

After tracing several examples of both the inside and outside edges of the frame, I worked to get a sunflower center that would be in correct proportion for the ring of petals. These proportions differ between sunflower species, as we discovered from planting Central and South American species. I found a combination that I liked and filled in details of the center. I didn't attempt to put in all the seeds, just suggested them. Then I determined how many outer petals I could arrange around the center, making them similar but not identical.  I shaded petals that were overlapped to indicate depth. At that point, I was ready to start on the actual project.

Finished sunflower needlepoint

I prepared my needlepoint canvas (#14 white mono) and ran colored threads horizontally and vertically through the center. Then I centered the canvas over the drawing and traced it onto the canvas with a fine-lined permanent marker. Once it was dry, I rubbed the lines vigorously on both sides with a paper towel to pick up any bits of ink that might discolor the yarn and I pulled out the centering threads. With the color areas of the picture completed, I filled in the background in a neutral color. Finally, I began back-stitching around certain segments with a single strand of yarn. (This is traditionally done on counted cross-stitch pictures, sometimes using a single color for all the back-stitching.)  When I use it on needlepoint, I prefer to use lighter, darker, or grayer yarns to emphasize the features I'm outlining. Purists won't do this sort of surface stitching on conventional tent stitch. I'm not a purist. I'll not only use back-stitching, but also any surface embroidery that will enhance the canvas work and make it match my mental vision of the piece.

When making a pillow in folk embroidery on gingham, I made a less realistic sunflower, concentrating more on texture. Backstitching here gives the center a different appearance.

Sunflower pillow with detail

Sunflower center

Incidentally, sunflowers should delight the readers who enjoyed our Roots, Leaves, and S.T.E.M. post (February 29, 2020), because they represent both Science and Mathematics.   A sunflower is not a single flower, but a composite of masses of two entirely different kinds of flowers. What we think of as petals are actually individual strap-shaped ray flowers whose bright colors attract pollinators. The central disc is made up of large numbers of disc flowers which, when pollinated, will produce seeds. These flowers are arranged in curved lines which follow the Fibonacci number sequence. The sequence is 1, 1,  2,  3,  5,  8, 13,  21, 34, 55, 89, and theoretically continues to infinity. Each number is the sum of the two previous numbers. The sequence is found many places in Nature — out to the structure and motion of spiral galaxies.

I do a lot more work from quick sketches and studies in pencil, watercolor, pastel. and marker and from handmade charts than I do from photos. However, I've done enough to offer some advice. If you are planning to sell your projects, be sure you have not used anyone's copyrighted material. I work from my own photos and those of J.D. and J.J. (with their permission, of course). If accuracy is important, take lots of photos from different angles, distances, and lighting effects. Be selective about the parts you use. Leave out anything that does not improve the composition. Let me show you what I mean.

Original photo

This photo of poppies has several things going for it. The lighting is interesting. The poppies show up well against the dark background. The red of the petals is complemented by the green stems. But look at the gray, dead leaves at the lower left. They do not help the composition at all. Now look at the picture after J. D. has modified it. Cropping and/or otherwise altering a photo can add a great deal to its appeal.

Poppy photo, edited

On the other hand, sometime a picture needs to be expanded. Look at these two pictures taken at the same time. See how much showing the full petals makes the picture more interesting? That is why taking multiple shots is valuable.

I do, however, want to show you how to modify an outline pattern so that it works more easily as a chart. The first thing to do is to transfer the pattern to quarter-inch graph paper. I use either dressmaker's carbon or a sheet of paper which I have colored heavily on the back with a graphite pencil. Aligning one major straight line in the design with a line on the graph paper, I transfer the design by going over the outline with a ball-point pen that has used up all its ink. Once the transfer is complete, I draw straight lines, square corners, and forward and backward diagonal lines to come as close as possible to the curved lines in the original design. The resulting new design, shown here in red, can then be enlarged or reduced to fit any size of graph paper. (It can also be simplified if you wish.)

Squaring off an outline

 
Before I use or store the pattern, I trace it once again with a permanent marker. Some uses for this type of pattern include:

    a counted cross-stitch design
    a panel of ceramic tiles
    a collage
    a felt applique with cut-out pieces glued or sewn to a background
    a wood carving
    a needlepoint or quickpoint   
    an embossed piece of copper foil
    tooled leather
    the center panel for a patchwork quilt
    a mosaic
    an afghan put together from "granny squares"

Simple iris pattern graphed two ways

Occasionally I enlarge a small or medium-sized design laid out on quarter-inch graph paper to a size suitable for making a latch-hook rug, a wall hanging, quilt blocks, etc. The easiest way to do this is to draw around a block of four squares of graph paper for each of the single squares in the smaller design. I tape a number of pages of quarter-inch graph paper together and lay them out on a large table. Beginning at the center of my design, I draw the 4-square block that represents the center square of the original design. I then work outward in all directions from that center square. I number or color the blocks as I go. The finished pattern will not match either #3.75 or #5 rug canvas exactly, but it will come very close. Count the number of horizontal and vertical squares on your pattern and mark the same number of squares on the canvas. Mark the center of the canvas and draw the outline of the entire design around it. When you cut the canvas, always allow an extra 4 or 5 squares of mesh on each side to turn under before you begin putting in the strands of rug yarn.

You can reverse the process, changing a graph to an outline drawing, but it is a bit more difficult. I suggest that you trace the squared outlines on another sheet of paper so that you don't damage the original. Then work very lightly in pencil, turning squared corners into curves. Stop often to review what you have done, erase where needed, and re-draw.  Be patient and persistent.

Click here to download

Finally, let me leave you with a downloadable outline pattern that you can use in any way you like as it is,  or modify it in any of the ways discussed here.  You can multiply it or reverse it horizontally (or both horizontally and vertically) to make larger, more complex designs.

No matter what your purpose is for capturing the images of flowers, please take time to explore and enjoy their remarkable shapes, colors, textures and fragrances.

 This post by Annake's Garden is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Fool the Eye: Illusions in Textile Art

Three Early American quilt designs

What are "optical illusions"? They are patterns that fool the eye into seeing things that are not really there. These include 3-dimensional objects that appear to extend out from the canvas, “hollow” spaces in the canvas showing depth, textured surfaces, and interwoven areas where sections appear to pass over and under each other. Some optical illusions can be traced back to Early American quilt blocks.

When European settlers came to America, for a long time they were dependent upon supplies of cloth shipped in from Europe.  Therefore, everything needed to be made to last as long as possible. When a garment was no longer wearable, any usable pieces were cut out and saved. When a new garment was made, all fabric scraps were saved. When enough scraps were accumulated, they were sewn together to make woolen quilts like the ones seen here.

A popular pattern was the one shown in blocks on the first quilt in this trio, which was called the "Nine Patch". If you look closely, you will see that each block is made up of nine small squares.  It is an easy beginners' pattern. With the instruction of a patient and loving grandmother, I learned to sew a simple seam and made a little Nine Patch quit for my doll when I was about four years old — and I have been sewing ever since. The second quilt is also composed of small squares, arranged in larger squares which are placed in a diamond configuration. This pattern was commonly called "Sunshine and Shadows". As quilters became more assured (and more competitive) they began to use more complex pieces and designs, like the third quilt shown here, made with sharp diamond-shaped pieces. This is one of many "Star" designs.

Tumbling blocks

Well, these are very pretty, but they don't "fool the eye". This one, called "Tumbling Blocks" does. It forms an illusion still used broadly today.

It appears that you are looking at a surface that is further away than the surface of the canvas. Your eye moves back and forth from blocks that appear to be pointing upwards and acting like stepping stones to blocks that appear to be pointing downwards and coming out of the surface toward you. The effect is achieved by using a bright yarn, a dark yarn, and a light yarn of the same color. The sample was done in longstitch (upright Gobelin) on a #7 mesh canvas. The edges are so sharp that back-stitching is optional. The finer the mesh this is done on, the more distinct the illusion will be.

A tumbling block design in longstitch

The next example shows the illusion of depth. It appears that you are looking down at a surface that is farther away than the surface of the canvas. The pattern starts with a network of light-colored diamond shapes. One of these has been filled in with successively shorter rows of successively darker shades of the yellow color. The darkest shade forms a solid diamond that our eyes tell us is the bottom of a 3-dimensional space. The more layers of color that are used, the deeper that the "box" or "room" appears to be.

Another needlepoint illusion

This illusion is made by making rows of zig-zag pointed patterns which meet only at their highest and lowest points, which are staggered from one row to the next. This leaves small blocks of canvas in between the rows. Since the rows are off-set slightly, the empty blocks are not diamond-shaped as one might expect. These parallelogram-shaped parts of the pattern are sometimes called "lozenges". These are used frequently in bargello patterns.  The odd numbered rows are identical to each other. The even-numbered rows are identical to each other, but slightly different from the odd-numbered rows. This causes the "lozenges" to point to the lower right in one row and to the lower left in the other.  Would such a construction be possible in three dimensions — say using shoeboxes?

The illusion below appears to show two flat striped ribbons twisted around each other.  Notice that the bottom edge of each ribbon is slightly lighter than the matching top edge.  The sample is done in long, straight stitches. It would be a bit more difficult to chart and work in tent stitch, but the illusion would probably be more distinct.

Follded ribbons in longstitch

Bachelor's puzzle construction steps

Here is a step-by-step series of diagrams for an illusion I know only as "Bachelor's Puzzle".  It is derived from a quilt block. Below is a small framed picture of it done in needlepoint.  A collection of several pictures like these is nice for a narrow wall space next to a door or between windows.

Bachelor's puzzle needlepoint

This time we are going to adapt two designs and combine them to make a framed "op art" picture. I started with a pattern I know as "Ring Around the Star".  (Many patterns have multiple names.) I don't know the origin of the pattern, but I suspect it is 18th Century American.  However, I believe it may be derived from a much older English pattern called "King's Cross". The center of the "King" pattern is just to the left below. The center of the "Ring" pattern is next. The last two diagrams are sketches I made to decide which shading gave the effect that I wanted.  I chose the one on the right.

Ring-Around-a-Star development sketches

The two pictures below show the shading I did for the color stitching. You will find a photo of the framed picture at the end of this article.

King's Cross in a rectangle

Square frames are harder to find than rectangular ones, so I have modified the "King's Cross" design to fit a rectangular frame.  I did this pattern for a 5-inch X 7-inch frame (13 X 18 centimeters), but I can show you how to adapt it for any rectangular frame. Turn the frame upside-down on your canvas and draw around the opening with a pencil. Remove the frame. (If necessary, use a ruler or straight-edge to square the corners and make the sides straight.) Leave extra canvas around the rectangle so that you can tape the edges. Find the center of the rectangle and mark it with a dot (O on the diagram), continuing to use a pencil. Find the centers of the top and bottom — the short sides — and mark them with dots (A). Find the centers of the long sides and mark them (B). Mark the four corners (C). Mark the centers of the lines between the A's and the center O (D). Mark the centers between the B's and the O (E). Mark the centers between the C's and the A's (F) and the centers between the C's and the B's (G). Now connect the dots as follows:

1. A-O-A
2. B-O-B
3. Both C-O-C's
4. Both E's on the top and bottom with the nearest D
5. Both G's on the sides with the nearest E. You may then erase the A-D and the B-E lines if you wish to do so.

Now you are ready to begin stitching.

King's Cross sketch

This sketch will work with any three-color combination as long as the white sections are in the lightest color, the pencil-shaded sections are a darker shade of the same or a similar color, and the inked-in triangles are in a very dark color. You will notice that the pairs of triangles are not quite the same. Also, the shapes that were parallelograms in the original pattern are now polygons. These are large areas, so use a heavier yarn than usual or double your regular yarn to cover the canvas completely. Once again, I recommend doing the triangles in basket-weave, starting at the center points and working outward this time. Any irregularities where two colors of yarn join, or at the edges, may be covered by back-stitching if you choose.


Once, as I worked on the design for a 6-way bargello pattern, I told J.D. that I could see an optical illusion forming in one of the designs. He said he could see one, too, but that he would have to erase some of the lines in the design to make it. I suggested that we each draw the design we imagined, to see if we had different illusions in mind. When we compared our results, we had indeed seen different illusions. We were delighted. This “game” continued for some time. Below are two of the more interesting ones, for the benefit of those of you who have taken up this pursuit. You can use black, white, and grays for your shading or you can use various tones and shades of a single color. If you use different colors, you may achieve an interesting design, but lose much or all of the illusion.

Hexagon grid

Working with a hexagonal shape requires us to adjust our thinking just a bit. We are used to thinking in terms of a base of 90 degrees (0 degrees, 90 degrees, 180 degrees, 270 degrees, 360 degrees).  A hexagon, however, is based on 60 degree angles (0 degrees, 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees, 360 degrees). The design is constructed along each axis from the degree mark to the center. Although the hexagon is basically two overlapping triangles, it seems more balanced than any triangle.  On the other hand, it is more versatile and less static than a square or a rectangle. Try starting with a hexagonal outline and building shapes inside it.

In the first example, two overlapping 3-dimensional squares have been fused together to make an angular figure-8 shape.  The most shadowed areas are shaded in black. The intermediate shading is done in a medium green.  The most illuminated areas are done in a light blue. The background is the white of the drawing paper. Once the figure is complete, the little construction lines can be erased, along with the unnecessary bits of the hexagonal outline.

The second figure is made up of small cubes.  You would need to put the construction lines in very lightly because many of them would have to be erased in order to achieve the final illusion. The same three colors have been used to show the amount of light reflected from the surfaces. Once again the white of the paper is the background, but you could put in another very light color if you wished. Study the construction diagram on the top right to determine how the figure was constructed. The finished illusion is shown on the bottom right with the construction lines and unnecessary hexagonal lines erased.

Now that you are familiar with hexagons, you might want to try constructing a six-pointed star pattern.  Here is a hint:  connect 0 degrees (which is also 360 degrees) to both 120 degrees and 340 degrees; connect180 degrees to both 60 degrees and 300 degrees. Two more straight lines will complete the star.

Finally, here is a photo of the finished and framed project that we promised you earlier in this post.

If you enjoyed this article, watch for a new post on the subject this Fall.

 This post by Annake's Garden is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.