Ahhh, good day to you! I see you've come to watch our interview with the artist, Arcadia. Rumor has it that she's going to tell all of us how to do beautiful tessellations, like the ones she's done...well, not quite exactly like those, but, ones similar, perhaps. Let's be quiet now, and listen to what is being said.
| Interviewer: | Now, Miss Arcadia, I'd very much like to thank you for taking some of your extremely valuable time to allow this interview to take place. |
| Arcadia: | Well, it's my pleasure to be here. I find it a great honor to know that my work is so valued and appreciated here. |
| Interviewer: | Would you mind telling your interested audience, please, what exactly is a tessellation? |
| Arcadia: | Of course I wouldn't mind. A tessellation, by definition, is a shape that isused to tile a plane completely, without overlaps, gaps, bends, lumps, folds, or corrugations. Occasionally, a tessellation may contain multiple shapes. Such tessellations as these are called semi-regular tessellations. However, the same principle applies. The shapes, remaining in a set pattern, tile the plane seamlessly, that is, with no gaps, overlaps, folds, bends, etc. |
| Interviewer: | I see. Now, would you then please tell all of us if there are more than one kind of tessellation? |
| Arcadia: | Yes, there are several kinds of tessellations. There are "Translations," "Rotations," "Glide Reflections," and a few combinations, such as "Translation-Rotation," and "Glide Reflection-Rotation." I myself enjoy the type called rotations, though glide reflections are nice to use as well. |
| Interviewer: | I see. Could you describe for us please what these types of tessellations are? |
| Arcadia: | I'd be happy to describe them for you. A translation is a type of tessellation where the basic shape is tiled by sliding it sideways or up and down so that its edges align with the edges of the other tiles around it. The figures in a translation all look about the same, except for tiny variances made by an artist -- that is, they all have the same "orientation." The same part of the figure is always facing "up" or "left" or "right" or "down." |
| Rotations are another type. My picture, "Dancing Ladies" in the exhibit is an example of rotation. Rotations are done by taking a figure and rotating it around a point. Only certain figures can be rotated. If you haven't seen the exhibit, I would suggest looking at it -- it will likely help a great deal in understanding this. | |
| The third main kind of tessellation that I mentioned is a glide reflection. Glide reflections are very much like translations, except that the image is "flipped over." That is, it's orientation, or order of points, is reversed, as compared with the other images in the tessellation which surround it. | |
| Interviewer: | Ahh, thank you. Could you try to explain for all of us the process that you go through in creating a tessellation similar to the beautiful ones that you create? |
| Arcadia | Certainly. The first thing that I do is decide what kind of tessellations I want to do. It's usually rotational -- those are my favorites. |
| After that, I decide what figure I want to use. When I do rotational tessellations, I typically use hexagons, though equilateral triangles, squares, and certain types of kites are also possible choices for figures which would work. Then I get my materials ready. The materials that I use are pencil, pen, paper, compass, ruler, and tracing paper, or wax paper. On a sheet of white paper, I construct a hexagon by drawing a circle, and then using my compass to find the six points of the corners of the hexagon. After I've drawn the hexagon, I'm ready to change it's shape somewhat so that I have an interesting figure to work with in terms of creating a shape similar to something found in real life. | |
| To change the shape, for a rotation, I start by bending the line between two corners of the hexagon. I try not to bend it too much, most of the time, because otherwise it gets difficult to change the lines without having them overlap later. Anyways, I start by bending the line between two of the corners. Then, I take the wax paper and trace the line that I've made. Now comes the tricky part. I take the wak paper and place it under the hexagon, on top of a white peice of paper, so that I can see my line. Basically, I have a stack of three peices of paper -- a plain white sheet on the bottom, the wax paper in the middle, and another white sheet of paper, with a hexagon drawn on it on top. I first line up the lines on the wax paper and the paper on top. Then, I rotate the wax paper to the right until the right endpoint aligns with the next point on the hexagon, moving counterclockwise, and keeping the left end of the line in exactly the same place. I repeat this process going all around the hexagon, which means that I go through it a total of three times. | |
| After I've done that, I study the image, and make lines in the inside of it, to turn the image from a "blob" into something that looks like something from life. Once I've done this, I copy the image over and over on a new peice of paper, to cover the entire page. To finish, I color in all of the areas, as I did with my "Dancing Ladies." | |
| Interviewer: | I see. That has been most helpful. Tell me, are there other ways that you do tessellations? |
| Arcadia: | Yes, I do sometimes use a computer program called Tessellmania to do my tessellations. |
| Interviewer: | Well, Arcadia, this has been most interesting. Thank you for taking the time to allow us to have this interview with you. |
| Arcadia | It's been my pleasure. |