The task to create tessellation was very interesting and fascinating for me, as it allowed me to understand the essence of transformation and to see how it is realized in practice. I have chosen translation as a basis of my pattern and the figure of a wheel on a square background as an object for tessellation. Below I will justify my choice and explain the way I created my pattern.
Tessellation can be defined as a pattern that is created by the way of repeating certain shape many times in such a way that the plane becomes totally covered without overlaps or gaps (ENC, n.d.). I believe that it is one of the best ways to understand transformations. There are four types of such transformations that can form the basis for tessellations: translation (moving an object without rotation or reflection for a certain distance), rotation (rotating an object, turning it around), reflection (creating a mirror picture of a shape) and glide reflection (combination of translation and reflection, performed in two steps) (BEVA, n.d.). The shapes used in tessellation can also be of various types, but usually some simple geometrical form is taken for a basis.
For this task I have taken the shape of a square as a basis and after changing it a little have added a picture of a wheel inside. While this figure is rather simple, it has everything that is necessary to understand transformation and is quite attractive visually. I have also chosen two colors that are inverted in neighboring elements of the tessellation pattern. In order to create this shape I have drawn the shape of square in Paint and changed its sides symmetrically. Then I have put the shape of a wheel inside to make the picture livelier.
After this I copied the picture and placed it near the first, inverting the colors. Then I continued copying the pictures and fitting them together. The result is shown in Figure 1. By completing the task, I understood the way, in which tessellation works and saw patterns written by different artists, which is why I can say that it can be not only visual representation of math transformation laws, but also a kind of art.
I can but say that I enjoyed this task a lot, as it helps to develop imagination, spatial perception and allows people to understand everything they need to know about transformations. I am sure that it will be also interesting to try working with other shapes and kinds of transformation, which I am eager to do in future. Thus my first work is based purely on the principles of simplicity and visual attractiveness. I believe that after certain practice patterns will become much more interesting. The task to create a tessellation pattern is not too difficult today due to many different computer programs and resources on the web. I think that after some time this process will become even easier, as we can witness progress in all spheres of our life, math being one of the most important in them.
BEVA. (n.d.). Transformational geometry. Retrieved from http://www.beva.org/math323/asgn5/oct31.htm
ENC. (n.d.). What is a tessellation? Retrieved from http://mathforum.org/sum95/suzanne/whattess.html