Tesselations are often found in architecture.
M.C. Escher, a 20th century Dutch artist, is famous for his work with tessellations -- works that use repeating forms or pictures that fill the whole page or canvas without overlapping or leaving negative space. These tessellations create the illusion of actual three-dimensional space using patterns and shading.
Puzzle Pictures
Basic tesselations use a single pattern.
Tessellations can be as simple as a blank jigsaw puzzle. The pieces make a repeating pattern and fill the entire space, leaving neither empty spaces nor overlapping bits. Each of these puzzle pieces are identical, but a more complex design could use more different shapes and a more intricate pattern
Tesselations Using Organic Forms
Tessellations can also be created using images from nature. Imagine every puzzle piece replaced by the shape of a leaf, swan or frog and you will be imagining tessellations right out of Escher. These sorts of patterns typically involve several different shapes, or one shape than can be flipped or rotated in order to fit against itself over and over in a series. The most complicated examples involve multiple images in a repeating pattern; shapes are repeated first forward then reverse, right-side up, then upside-down, and usually alternate from black to white. The use of color of lack of color, however, does not define a tessellation; the form is defined by the pattern and the way each shape fits tightly against its neighbors.
Tesselations Using Geometric Forms
Tesselation can be based on geometric shapes.
Simpler tessellations revolve around geometric forms; they create the illusion of space using one or more repeating simple shapes in the style often found on tiled floors or mosaic work. The repeating arrangement of squares and octagons found in this mosaic is a tessellation using geometric forms. The designs on the octagons and within the squares are embellishments upon the underlying tessellation.
How Are Tessalations Made?
You will need scissors, colored pecils, a black marker, white paper, and index cards.
You could be the next M.C. Escher! To make a simple tessellation like the one in the mosaic above, use two index cards. Cut one card into a square with 2-inch sides; cut the other into an octagon, also with 2-inch sides. Using a ruler, make sure your shapes are nice and regular so that they will fit together well. Start in the middle of a piece of paper and trace your octagon lightly with pencil. Fit your square so that its bottom aligns with the top of your octagon, and trace it. Repeat this procedure on the opposite side of the octagon, with the top of your square aligning with the bottom side of the octagon. Now trace the square again on the right and left hand sides of the octagon, so that you create a pattern of squares around your octagon as shown in the picture above. Four sides of the octagon will boarder on squares; these will alternate with the other four sides where we are about to add matching octagons. Fit your octagon between two squares and against the first octagon, leaving no space. Trace it and repeat so that four octagons and four squares now appear around the central octagon. Continue in this manner until your paper is full of octagons and squares, some of which hang right off the paper. Next choose one color for your squares, and another contrasting color for your octagons. Finally, trace over your pencil lines with heavy black marker.
