|
|
|
|
|
|
Welcome to the fourth installment of the Snippets series of articles on tessellations! This month we’ll offer tips on color strategies you can use when hooking tessellations. You don’t need a math background to get started – just some lined index cards, tape, scissors, ruler, and a pencil. A tessellation is an interlocking, geometric shape that repeats without overlapping or leaving spaces, forming a continuous pattern. Squares, hexagons, and triangles are examples of common tessellating motifs and each can be modified to form an infinite variety of shapes that tessellate. Tessellations are everywhere, from honeycombs to quilt blocks, and throughout history, they have been incorporated into art and architecture. Tessellating designs offer several distinct advantages to rug hookers:
Color Strategies for Tessellations Tessellating designs provide a great way to use up odds and sods of wool, and since the hooking itself is repetitive, your challenge is really about contrast and color. One strategy is to think checkerboard. First, hook your grid (see white lines in picture, below) rather than outlining individual motifs:
Then color alternate motifs with complementary colors (shades of orange and blue, yellow and purple, or red and green), or those that are light and dark, warm and cool, or bright and dull. Another option is to create additional color slots by breaking up the internal space of your motif. In the following tessellation, which was used for Trials and Tessellations, point X was placed outside the outline and a ruler was used to draw radiating lines through that point.
Arrange your swatches from light to dark (or warm to cool, bright to dull, or solid to plaid), and maintain that progression in each of your motifs. That’s not to say that you need to repeat the same five swatches in all your motifs – quite the opposite! Just place all your lightest swatches in position #5, next lightest in position #4, etc. Alternatively, you could use the same color strategy as above, but divide the interior space with more freeform lines:
Another approach was used for Scraphappy, illustrated below. After the grid was established, several contour rows were hooked within each shape from the outside inward, and then an additional swatch was chosen to complete each center. Not only did that project make a dent in my scrap bags, but it provided quite a lesson in the relativity of color!
Representational Tessellations
portray recognizable objects. M. C. Escher, considered by many to be
the Father of Tessellations, was a master at portraying humans, birds,
frogs, and fish in his tessellations. To view his work, visit the official
M. C. Escher website at
www.mcescher.com. In Everywoman, the lady motif was created by modifying a square with two glides. (See Tessellations Based on Squares.) The resulting shape was fleshed out with details like a hat, hair and simple facial features: You can nudge a promising tessellation by adding interior details that relate to the outside shape of your motif. Try rotating your piece 90˚ or 180˚ to see if it doesn’t suggest something to you. Does it look like a bird or cat or does the outline suggest two or three items nestled together? (This is a great place to get kids involved!) Alternatively, you can add interior details and then erase the grid lines of your motifs. In Swirl, a floral spray was added to the tessellating motif. (The main flower has been outlined in purple so you can track it in the Swirl rug below.) Six repeats of the motif were combined to form the center of the rug: Then the design was embellished by adding bows and by varying some of the floral sprays. The six large purple flowers in the rug below are a visual clue to the underlying tessellating structure:
The Swirl motif is the same one that was used for Trials and Tessellations (see Tessellations Based on Equilateral Triangles for construction info), but by utilizing the tessellating motifs as a layout tool, and then erasing the outlines that define each unit, a less obviously geometric pattern was created.
Tessellations Based on Equilateral Triangles Equilateral triangles are tessellating shapes that have all three sides of equal length and each corner forms a 60˚ angle. To construct an equilateral triangle, use your ruler and draw a horizontal line that is 3” in length. Find its midpoint and draw a line through it that is perpendicular to your first line. Then line up the end of your ruler with one end of the horizontal line and pivot it until the 3” marking on your ruler hits the perpendicular line. Repeat for the other leg of the triangle. Midpoint rotation A mid-point rotation occurs along one side of a triangle.
You can draw the same line for each mid-point rotation or draw different ones for each of the three legs.
The above example was used to create Trials and Tessellations: Rotation around a corner A rotation around a corner utilizes two adjacent legs of a triangle.
If you wish to modify the third side, apply a midpoint rotation to it.
Tessellations Based On Squares Cut a 3” square from your index card, and then apply any of the following transformations to create a unique interlocking motif. You can only modify each side of your square once, and try to draw directly into each corner and cut accurately, rather than lopping off the corners. Midpoint rotation
You can continue to modify the other three sides with midpoint rotations, and they can be identical (as in the example below), or you can draw a different type of line for each leg of the square.
The above motif was
used to create Scraphappy: Rotation
around a corner
Translation
Glide
By adding interior details, this tessellating shape became the basis for Everywoman:
Once you have a pleasing tessellation, you can trace around it directly on to your backing. If you have used a glide, you will need to alternately flip the shape upside-down and back. You may also want to lay out a 3” grid and line up each of the corner points of your motif with the corners of the 3” grid squares because repeated tracings create distortion.
| |||||||||||||||||||||||||||||||||||||||||||||||||||||
The
two remaining sides can be modified with mid-point rotations, with another
translation, or as illustrated at right, with a glide (G2):