- Tessellation creator. An excellent tool to investigate how angles affect tessellation. Ideas for using this resource Could be used by the teacher to demonstrate tessellation to the class, or to start class investigations.
- Tessellation Patterns & Repetitions: Recursion Recursion: Plant Recursive drawing guided for Plant Design: Snowflake Radial Symmetry focused on Snowflake Design: Pro Unrestricted combination of Radial Symmetry, Tessellations & Recursion. Fine cell adjustment, transparency, SVG export, and much more.
Making tessellations is an easy, creative, and fun way to explore patterns and geometry for all ages!
Overview
Tessellations are a famous form of mathematical art! Making tessellations is approachable by students of all math levels, and with its simple list of required materials, this is a great project that can be done at home or anywhere you need an enriching project. And with a variety of tessellation styles, students can keep exploring new ways to create interesting patterns while also developing spatial reasoning skills!
Materials
Download Tessellations for iOS to create colorful tilings just like Escher.Start with a basic figure like a Square, Square 90, Brick, Triangle and Diamond and create a nice.
Project Background
An interactive drag and drop application to support the investigation of tessellations. Tessellation activities and games. Stem activity for children: make a tessellation. What is a mathematical graphic geometry tessellation? Tessellation Creator. Geometry Angle Games: Classroom Lesson Plan common core math ANGLES. Common core math grade 3-5 lesson plan for measuring angles. Vector Kids - Angles. Common Geometry Formulas.
Definition:
Before diving into making tessellations, let's ask: What is a tessellation?
A tessellation is the tiling of a plane using one or more geometric shapes such that there are no overlaps or gaps. In other words, a tessellation is a never-ending pattern on a flat 2-D surface (such as a piece of paper) where all of the shapes fit together perfectly like puzzle pieces, and the pattern can go on forever.
Examples of Tessellations:
Not Examples of Tessellations:
Now that we know what a tessellation is, how do we make one?
We have four different ways to create your own tessellations!
Getting Started: Beginner Tessellation
No cutting is involved for this starter tessellation design, making it a great starting project for younger artists.
STEPS:
1. Start with a piece of paper and a pencil. We recommend starting with half of a regular 8.5' x 11' white sheet of paper.
2. Divide the paper up into equal width rows (or columns); about 3-4 rows for a small sheet will work very well.
3. In one row, draw a simple shape that spans the entire height of the row (see image above), such as a square, triangle, a lopsided rectangle (parallelogram), or other shape of your choice. Draw that shape again immediately next to your first shape. Do they fit together perfectly? What if you draw a third shape immediately next to the second shape? Do they still fit together perfectly?
4. If your shapes are fitting together perfectly, keep drawing them in each row until your entire sheet is filled up.
5. Color in your tessellation and display!
Step it up: Ready for a harder challenge? Skip Step 2 and just try drawing a shape on a piece of paper. Now try drawing that shape again immediately next to the first shape. Do they fit together? Try creating more complex shapes, like fish, flowers, or even dinosaurs!
1-Step Cutting Tessellation
Great for beginner cutters, and a great next step into more complex tessellation making.
STEPS:
0. Start with five squares of paper that are the same size.
1. Take one square piece of paper and cut a weird shape out of one side of the square. (So if you start cutting from the bottom side of the square, make sure your scissors finish cutting on the bottom side of the square!)
2. Line your oddly-shaped cut-out on top of a second square of paper, lining up the long edges. Trace your cut-out onto the square with your pencil.
3. Repeat for each of the remaining three squares. Ensure that your oddly-shaped cut-out is facing the same way every time you trace it.
You should now have four squares of paper, each with your shape traced out in the same way.
4. Take one of your squares and cut out your tracing.
5. Rotate the square by 90˚(one corner in either direction) so that you have a fresh, flat, un-cut edge of the square facing you. Tape your cut-out shape to that side of the square, lining up the long flat edges.
6. Repeat Step 4 and Step 5 for each of your remaining squares. Very important -be sure to maintain the same orientation of your cut-out shape every time you tape it!
7. Fit all of your new tessellation pieces together to create a beautiful, puzzle-like work of art!
2-Step Cutting Tessellation
These tessellations are nearly identical to the ones just explained, but have an extra step that allow for even more creative designs!
STEPS:
1. Take a small square piece of paper (about 4'x4') and cut a weird shape out of one side of the square, just as before.
2. Tape your cut-out shape to the opposite side of the square, maintaining its orientation and lining up the long flat edges.
3. Pick one of the two remaining untouched sides of the square and cut another odd shape out of that side.
4. Repeat Step 2: Tape your new odd shape to the opposite side, maintaining orientation and lining up the long edges. You should now have a unique shape that no longer has any flat long sides.
5. Trace your tessellation shape onto a piece of paper over and over again, fitting the shapes together.
6. Use crayons, markers, glitter, or any extras you wish to make your tessellation art extra incredible!
'PART' to 'TRAP' Tessellation
Ready for a more complex challenge in creating amazing tessellations? The 'PART' to 'TRAP method is a great way to create a unique shape that you can trace over and over again on paper for an intricate tessellation design!
STEPS:
1. Take a square piece of paper and write the letters 'P', 'A', 'R', and 'T' in each corner.
2. Take a pencil and draw a funky line horizontally across the paper, separating the 'P' 'A' side from the 'R' 'T' side.
3. Draw another funky line vertically down the paper, separating the two sections into a total of four sections.
4. Cut along your lines, yielding four separate shapes, each with a single letter.
5. Re-arrange the shapes such that the letters meet in the middle and they spell the word 'TRAP'.
6. Tape the four pieces together to create a single tile.
7. Trace your tessellation creation onto a sheet of paper. Once your shape is traced, slide your tessellation to the immediate left, right, top, or bottom of your tracing, and trace again. Repeat until the entire sheet is filled up with your amazing tessellation creation!
Discussion
Our brains better retain information when we engage both our hands and minds in the activity. Now that we've explained how to engage the hand, what are some discussion questions to engage the mind during the activity?
1. What is another example of a drawing that is not a tessellation?
2. Where do we see tessellations in the world around us?
3. What are some examples of regular polygons (2-D shapes with all sides that are the same length and all angles equal to each other) that fit together to make tessellations? Do all polygons fit together perfectly?
Supporting Resources
You can learn more about tessellations by just starting with these three great links. Be sure to explore tessellations first through the project guidelines above, and use these great resources to supplement what you've already discovered on your own!:
Tessellations at MathIsFun.com.
Tessellations at CoolMath.com.
Tessellations at MathForum.org.
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TesselMania!™ is a stand-alone tessellation creation program. It will run under DOS, Windows 3.1 ~ WinXP, and Macintosh (68030, 68040 or Power Mac system 7.1 or later). Its drawing toolkit is only slightly less comprehensive than MS Paint (the pixel-based drawing program that comes with MS Windows). These tools and the tools specific to tessellation are above average for a standalone tessellation program. However, users accustomed to the extensive toolkits in powerful drawing programs like Adobe Illustrator, Photoshop, Paintshop Pro, and GIMP may feel frustrated by working with Tesselmania!'s comparatively small toolkit. Those graphics power-users may prefer to look for tessellation plug-ins for their favorite graphics-drawing programs.
Of special note to Windows users: It will work under Windows 95 through XP, though its Windows compatibility shows signs of near-obsolescence. Most Windows users will have to tweak the desktop shortcut's compatibility properties to make it run. We do not expect it to run under Windows Vista.
POSITIVE ASPECTS:
- tessellation tiles can be resized and reproportioned. For example, if your design starts out as a brick-like outline, you can make that brick's height, width, tilt, and height/width proportions change as you draw. This massively useful feature is strangely lacking in many other tessellation programs.
- fairly complete drawing toolkit. There're a'floodfill/paintbucket', several line widths, and a (slightly large) eraser, all of which are tools strangely missing from many other tessellation programs.
- The color palette is a little awkward, but includes many more color variations than the 8~16 colors offered by many other tessellation programs. There's also a selection of pattern-fills, a feature uncommon in tessellation programs.
- You can click on several buttons which will show the current tessellation in several entertaining automatic animations. These animations are NOT savable or distributable without clever use of a 3rd party screenshot program. For this review, I captured one of these animations easily using the shareware screencapture program 'SnagIt', and then converted that data into an AVI video and an animated GIF. You can see that GIF here (300k).
- You can view and edit the design in several different sizes, at the click of a button.
- The program goes to extreme lengths to assist you while you choose a tessellation pattern. This is a vast improvement over the somewhat cryptic tile-pattern menus in other programs. The help here includes examples, colorful arrows, and short animations.
NEGATIVE ASPECTS:
Tessellation Maker Free Printable
Tessellation Maker Free Download
- Without special setup, this program won't run on PCs that display more than 256 colors. The setup isn't difficult, however:right-clicking on the desktop shortcut and set Windows' compatibility-setting to pretend that the PC can only display 256 colors at a time.
- 'Save' is limited to a unique proprietary format, *.TSS. Therefore, to export your picture to another program, you must either use the EDIT >> COPY command (which copies the picture to your Windows clipboard), or hit the 'printscreen' key on your keyboard to copy the current contents of your screen to the Windows Clipboard, use a screenshot program like SnagIt, or use a printer and scanner. (To get something OUT of the clipboard again, use the destination program's 'EDIT >> PASTE' feature. 'PASTE' puts a copy of the Clipboard's contents in whatever program you're using at the moment.)
- File names and directory names are limited to the old DOS 8.3 filename.ext rules, and 'My Documents' may be difficult to find if you're new to Windows.
- You will be unable to run or switch to almost all other programs while running Tesselmania. Screenshot programs are a lucky exception. As a result of Tesselmania's limitations, all programs will be in 256-color mode until you exit TesselMania.
- Smooth outlines are not possible, although you can approximate them by using several sharp corners with tiny angle changes. This is a 'sharp' contrast to most other tessellation programs, which usually allow sharp and rounded corners.
- Although you can toggle back and forth between 'single tile' and 'completed pattern' at the click of a button, you can only edit the picture while looking at a single tile on an empty background. This can hinder you as you toy with a pattern.
- The 'undo' tool only allows you to undo the ONE most recent action. That limitation was the most annoying problem during testing, though it's somewhat compensated by the presence of an eraser tool.
- You can only work on one design at a time.
- The help menu is somewhat limited, and the advice written in it is often clipped-off in mid-sentence because of Windows compatibility problems. However, I've seen worse help menus in tessellation programs.
STEPS:
- To create a tessellation, one must start by choosing a vague pattern from a menu of flips, rotations, and offsets. This can be the most daunting area for a newcomer, though TesselMania makes a heroic effort to explain the choices by offering examples and diagrams.
- The next step is looking at a simple shape (square, rectangle, triangle, hexagon) on a plain white background. In this stage, it's tempting to go straight to the drawing tools, but I don't recommend it. Instead, use the arrow and pushpin tools at the top of the menu bar to distort the shape of the basic tile. Leave the drawing and coloring for later.
In this stage, you can resize and reproportion the tile... a feature that I greeted with a happy sigh, because it seems so essential yet it's missing from the vast majority of other standalone tessellation programs. Thank you, Tesselmania! Without this feature, all your rectangles are squares; drawing a tall, thin tessellation is impossible; all your cats and snakes will be short and fat.
To manipulate the outer edge of your tile, use the arrow-shaped tool for resizing sides and sliding the image left, right, up, and down. Use the pushpin -shaped tool to click on the borderline, thus creating a 'turning point', rather like putting a pin into a string. Also use the pushpin to drag existing 'turning points' to new locations. Use the scissors-shaped tool to remove 'turning points'.
The three main tools you use in this stage will only work in 'normal viewing size'. They will not work when you click on the 'view large version' buttons (x2, x4, x8), so wear your reading glasses. - Now you can optionally begin filling in the interior of the tile with lines, color-fills, and patterns. If you choose to adjust the outline of the tile during this stage, notice that the interior does NOT squish, expand, or move to match the altered outline.
- Once your tile is finished, click on a button to see the completed pattern. Notice that many of the repeating tiles will be in colors that you didn't choose. Yellow parts of your original design, for example, will become bluish purple in some of the other tiles. Let's call this the 'anti-pattern'. The reason for this 'antipattern' is so that it's easy to see where one tile stops and the neighboring tiles begin. You may have to experiment to find colors that look good even in Tesselmania's anti-pattern. This color distortion is neither optional nor adjustable.
- Once you're done making a pattern, you choose how to save your masterpiece.
If you plan on working on this pattern again in TesselMania, then use FILE >> SAVE.
However, in its free 'trial' version, the FILE >> SAVE menu will only allow you to save in Tesselmania's unique *.TSS format, which is incompatible with all other programs of any type. The lack of a JPEG, PNG, GIF, EPS, AI or other common picture format is a serious intentional shortcoming in the free trial version of TesselMania. The free version which Tessellations.org reviewed did not say what file formats are available in the non-free version, but I expect they include GIF and do not include *.PNG. To save the picture in the more traditional formats, you can print it out or use a Screenshot to copy-and-paste the picture into another program like GIMP, Adobe Photoshop, Adobe Illustrator, PaintShop Pro, OpenOffice, MS Word, Powerpoint, or any of a hundred other programs, and then save it. I tested this technique, and had no problem using the PrintScreen key on my keyboard to copy the entire current screen, then paste it into a few other programs...even better, I'm happy to report that I was able to easily use SnagIt (a feature-rich screenshot program) to record one of TesselMania's built-in animation features as a movie file.
Those animations are some of Tesselmania's most unexpected and entertaining features. See my recording of one here.
CONCLUSIONS
How do we rate this program? Good, but not consistently good. It's an average of some very good features and some outdated or weak features. A big 'plus' is the large number of companion books available for it. Although we haven't had the opportunity to review those books yet, and therefore can't vouchsafe their quality, their existence seems a good sign that TesselMania is (or was) a well-respected program. Learning to use the program doesn't require any reading, but the interface is occasionally confusing and requires some experimenting. Even experienced PC users should not expect pretty results in their first three attempts. You can get basic results quickly, but fine tuning the outline is difficult.
Initial setup (installation) is simple, but will not explain how to set up compatibility with Windows versions beyond Win98. For that, please consult Jill Britton's webpage (listed at the end of this article).
In 2006 I wrote: 'If this software gets updated in the near future and upgrades a few features, we can expect it to be very popular. Without a rewrite, however, I do not expect it to run under Windows Vista, which premieres in 2007.' Inexperienced Windows users may be frustrated by dealing with its reliance on very old Windows and hardware standards. On the other hand, if you're using an older PC, this will be a blessing-- it can run on a PC with as little as Win95, Win3.x, or DOS 5.0, 256-color display, less than 5 megabytes of RAM and less than 10megabytes of free hard disk space.
The good news, as of November 2013, is that software author Kevin Lee has created 'Tesselmaniac', a new program and successor to the program reviewed on this page, 'Tesselmania'. Click here to read our review of the new program, 'Tesselmaniac'.
Jill Brixton, the famous tessellation teacher, has written a number of companion books. We hope to someday soon post reviews of those books here at Tessellations.org .
Tessellation Maker Online
There are several books about Tesselmania (and used versions of Tesselmania on CD) at Amazon.com
There is a separate but similarly-named product on the market called 'TesselMania! Deluxe' It appears to be by the same author and to include many more kid-friendly features, but we have not been able to locate a copy for review. If you know where we can find a copy for review or where copies are being sold, please contact us.