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Thursday, August 17, 2017

Back to snowflakes

I switched back to tatting snowflakes, so I haven't made any more progress on the large magic square. Maybe I will have more of the magic square to post next week, depending on how the snowflake project is coming along.

Here are a few of the designs that I've been diagramming, proofreading, and tatting:


The two on the left are inspired by Joëlle Paulson's Crystal Star. The one on the right is from my experiments with onion rings.

Thursday, August 10, 2017

Magic Square Path

Yesterday, I was asked if I could create a diagram to go along with the large magic square I am tatting. I don't think I could, without lagging Inkscape so badly that it would be virtually unusable. What I can do, however, is provide a photograph with some numbers and arrows that show the path I am taking as I tat the square:


I've labeled the onion rings only, and have drawn arrows between them to show how I got from one onion ring to the next. Here is the unedited photo for comparison:


It will be another few weeks before I am at the point where I have one repeat finished (four repeats will make a square). I'll make a post with a new picture when I get that far.

Wednesday, August 9, 2017

Magic Square, in Color

I've been working on diagramming, proofreading, and tatting snowflakes and wanted to start on a more relaxing side project. I decided to tat another onion ring magic square, this time in two colors. Here's my progress so far:


For this project, I'm using Lizbeth size 40 Ocean Teal Medium, and DMC size 40 white. I filled up two large clover tatting shuttles and was able to get to the point pictured above, before running out of white thread on the first shuttle. I'll need to rewind several times to finish this square (I'm only about an eighth of the way done).

To make a square this large, I have gone beyond the diagrams and am tatting in triangular sections. To keep my place I have to regularly refer to the section I have just completed, and tat a mirror image of it. This will get trickier as the square gets larger, but it shouldn't be any trouble.

I talked about this method of expanding magic squares a few weeks ago, and you can refer to that post if you'd like to join in on this challenge :)

Wednesday, July 26, 2017

Designing Magic Squares

Today's post is a little overdue, and is about designing magic squares. I will be adding a link for this post at the top of my Tutorials page, so that it can be accessed at any time. If you haven't already, please take a look at my previous post about deconstructing magic squares. The first part of that post (small squares) is especially relevant, and I will be expanding upon that idea today.

In today's post, I will be sharing my method for designing magic squares. Keep in mind that there are other ways to do this, and feel free to diverge from my instructions as needed.

Part 1: Requirements


To design a magic square, you will first need a repeatable square. (A repeatable square is a square that can be connected to other identical squares, similar to granny squares in crochet.) This repeatable square needs to be completed in one round, and cannot involve climbing out to a second round.

Here are a few examples of squares that are made in one round:


You can find one round repeatable squares by searching through existing tatting patterns, or you can design a square of your own. Mary Konior's Patchwork is an example of an existing pattern that I converted into a magic square. My triangle variation magic square and onion ring magic square are examples of squares that I designed on my own.

The simpler the square, the easier it will be to turn into a magic square. You can transform more complicated squares, but I would only recommend that if you are very comfortable and have prior design experience.

Part 2: Finding a Path


Once you have found a square that you like, it's time to create a four square mat. This mat will help us find a path to construct a magic square.

You can make your mat virtually (through apps, computer programs, or drawings), or physically (actually tatting the squares together). I prefer my first run through to be virtual, so that I can make sure that the pattern is viable, without spending too much time tatting.

To virtually assemble a four square mat, I start with a photo of one tatted square, taken from a bird's eye view:


I use a collage app called Photo Grid, which is free and is available on several different platforms. With this app, I import four copies of my photo and choose a collage that builds four equal squares. I remove any borders, and position the photos accordingly:


There are a lot of other programs that can do the same thing for you, and you don't have to use this particular app. Inkscape and other editing software will work as well. I use the app because I am always on my iPad, and hardly ever on my computer.

After making a visual representation of the square mat, it's time to find a path to connect the squares together. This connection needs to happen in the center of the image, where all four squares meet. Our goal is to find a tatting path that will enable the pattern to be completed in one round.

To brainstorm a path, I like to use a second app called You Doodle. You Doodle is an app that lets you draw on top of photos. It's free and is available on several different platforms. Again, you don't have to use this particular app if you find another program that can achieve the same result.

After importing my photo into You Doodle, I use the brush tool and choose my background color (in this case black) to cover up a section of tatting. I want to cover the section in the middle of the mat, as seen below. This will give me a blank canvas for redesigning the center:


The portion that you cover up will depend on the design that you are working with. Cover whatever you think is necessary to recreate the center of your mat.

With that step complete, it's time to draft a new design. Using the color of your tatted sample and the brush tool, try drawing different centers until you find one that you like. The objective is to create a tatting path that travels smoothly, from one square to the next. Here's what I came up with:


As you draw your new center, ask yourself this question: Can you trace a path from one square to the next, without stopping? If so, then you have a successful magic square prototype! 

You can play around with a lot of different ideas for the center, as long as they all accomplish the same goal. I often have many saved photos and choose the one that is most visually appealing.

If you don't have access to these apps, or you don't want to create digital prototypes, you can find other ways to brainstorm. Perhaps tatting the four square mat, and covering the center with a small piece of paper would work. You could try drawing a new center on the paper to see if you can find a continuous path. The main point is to get creative and to use the tools that are available to you. There are no "wrong" ways here, so please feel free to experiment!

Part 3: Tatting the Center


After you have drawn a new center it's time to turn your prototype into tatting. For this step, I like to start with a tatted four square mat (without the new center). It helps me to size things and line them up during the redesign. Here is my square mat:


I will be using this square mat as a guide for creating a new center. As I tat the new center, I will hold it up to the mat, to make sure that everything fits as intended. If you use this method, remember to stick with the same size, brand, and color of thread in all of your tatting. It helps to keep things as consistent as possible.

For this redesign, I find that it saves a lot of time if you only tat the center, and lay it on top of the square mat as you go. Lining it up to the original mat will help to determine if the new center will fit in the overall pattern. Tat just what you need, and don't worry about mistakes. Here is my center design in progress, next to my sample of four squares:


Here is a photo of the center placed on top of the square mat, to ensure that everything lines up:


This part requires some design ability and a lot of trial and error. You might find that you go through several tatted samples before you find a center that works for your pattern.

When you find a center that works, it's time to incorporate it into the overall design. Try tatting a sample of your four squares, but this time, connect them together using your newly designed center. 

Follow the basic magic square path to guide you through the pattern:


As you are tatting your magic square, it is very important that the new center creates a straight line (this line will run diagonally through the square). This is because the center will serve as a corner for a second version of your magic square (seen in Part 4: Expanding the Square). You can double check by holding a piece of paper next to your tatting as you go:


My square was slightly off where the two rings meet. I needed to scrap the sample above, and start again with larger rings. Here is the completed square:


Part 4: Expanding the Square


After you have successfully created a small magic square, you have all of the stitch counts necessary to make a magic square of any size! Let's look at a second "inverted" version of the magic square pictured above.

Remember when I talked about the importance of the new center forming a straight line? This is because it will serve as the outer corner for a second, inverted version of the square. You can see part of the inverted square, outlined in green below:


Here is a tatted sample of the inverted square:


If you follow my method for creating magic squares, you should be able to find an inverted square within your design as well. When expanded, this inverted design will create a new magic square:


This magic square can be visually broken down into four of the inverted squares, connected continuously in the center of the mat:


The continuous center in this large magic square is composed of the corners of the very first square we began working with. As a result, there is no need for redesigns or recalculations. Simply use the stitch counts contained in the original square pattern.

Here is the original square, hiding within the large magic square:


Pretty neat, huh?

Well, that's all I can think of to add to today's post. Be sure to let me know if you have any questions about the process or if anything is confusing. I hope that the information presented here is clear enough for some of you to embark on your own magic square journeys :) 

Thursday, July 6, 2017

Mix and Match Snowflakes

I have one more magic square post that I want to make, but I'm taking a little break from it this week.

So, here's a more casual blog post: a couple of snowflakes with an interchangeable center.


One center is made up of layered rings while the other is a simple six ringed flower. I still need to make a few small tweaks to these designs. The layered rings are a new concept for me, and I didn't realize that they would cause the center to stretch. As a result, I need to enlarge the regular center to better match up the second round of each snowflake.

Thursday, June 29, 2017

Deconstructing Magic Squares

Today I'm going to talk about deconstructing magic squares into smaller shapes. I think this information is helpful for both designing and tatting magic squares. Later on, I'll make a second post to show how I designed the onion ring magic square.

Muskaan also has some posts about magic squares, which you can read by clicking here, and here. If you are interested in the origin of the magic square, scroll down to the bottom her second post.

There are two ways that I like to visualize magic squares. The first involves looking at the pattern as a group of four smaller squares, connected in the middle.


Small Squares


This type of visualization is helpful for designing magic squares.

Let's use my recent onion ring square as an example. Here is one square by itself:


And here are four squares connected together:


For a magic square, the trick lies in redesigning the center, where all four squares meet. A magic square will have one continuous path that connects all four squares together:


Using a simple diagram, the path to tat a small magic square looks like this:


I find that it is best to begin tatting at the corner of the square. It's easier to finish the tatting on the outer edge, and this starting position also allows the square to be built up to any size.

Here are a few more examples of magic squares broken down into four smaller squares. I have boxed one small square in blue for clarity. Notice how the smaller squares connect in one continuous round in the center of each magic square:



So, what happens if you take four magic squares and connect them together, using the same method pictured above? You get an even larger magic square!


This large magic square can be visually broken down into 16 small squares (boxed in pink) or into 4 magic squares (boxed in green). All squares flow together in one continuous, and somewhat confusing round.



Triangles


This type of visualization is helpful for tatting magic squares.

As magic squares grow, the path to tat them becomes more and more complicated. For this reason, I find that it is extremely helpful to visualize magic squares in a second way: as a series of triangles.

If you begin tatting in the spot designated "A" on my diagrams, you will find that the pattern is built up in triangular sections.

I'll go through this step by step, using my onion ring magic square as an example. The same basic stitch count is used throughout. (Please note: in the following example, "clockwise" and "counter clockwise" refer to the direction of the tatting in the photos. In practice, because tatting is worked from the front and back side, actual directions may vary).

The first section of the pattern looks like this:


From here, I have a choice to make. I can turn counter clockwise to complete the square or I can turn clockwise to build a larger triangle.

A counter clockwise turn uses an onion ring to corner, and results in a completed small square:


On the other hand, if I had chosen to turn clockwise to build a larger triangle, I would need to tat an inward-outward facing ring combination to corner. Here is the resulting larger triangle:


After creating the larger triangle, I am faced with the same decision again. This time, tatting in a clockwise direction will finish the square:


While tatting in a counter clockwise direction will build a larger triangle:


Note that each clockwise turn uses inward-outward facing rings to corner, and each counter clockwise turn uses an onion ring to corner. This rule is consistent throughout the pattern.

Moving on from the expanded triangle, I can turn counter clockwise to form a square:


or I can turn clockwise to build a larger triangle:


I can keep building this way indefinitely, creating larger triangles until I feel like turning to make a square. For this particular pattern, I stopped at the image below, which involved a clockwise turn to complete the square:



Lines of Symmetry


When expanding magic squares, it can be tricky to keep your place in the pattern. Something that I've found to be helpful is to use lines of symmetry as a guide.

Let's look at some of the lines of symmetry in the large magic square pictured below:


Some of the lines deal with the overall square, whereas others are for smaller sections. There are more lines of symmetry than what I have drawn. Depending on where you are in the pattern, the most prominent lines will change.

This is easiest to visualize if we use the triangle expansions that I talked about earlier. Let's start with the smallest triangle and expand it into a larger triangle. I can use this edge as a guide:


First I have to tat the corner, and then I can tat a mirror image of my previous work. The result is a larger triangle:


To expand this into an even larger triangle, I can use the new edge as a guide:


I make an onion ring corner, and then tat the mirror image of my previous tatting to form a larger triangle:


If I want to turn this into a square, I can use the other edge as a guide:


Again, I need to tat a mirror image of my previous work. The result is a square:


Using this technique, you can memorize the basic stitch count to tat triangles and squares without referring to the diagrams. It takes some practice, but I've found that this method works much better than trying to keep my place in a diagram.

That's all for today's post. It contains a lot of information, hopefully not too confusing. If you have any questions or find that something isn't clear, don't hesitate to ask in the comments below! For my next post I will talk in depth about how I designed the magic square pictured above.

Thursday, June 22, 2017

Onion Ring Magic Square Pattern

The onion ring magic square pattern is now available. You can access the file by clicking here, or by going to my free patterns page. I have test tatted and proofread this myself, but if you notice any mistakes please let me know!


To keep everything consistent, I ended up tatting these squares in white thread. However, I think this pattern would look more interesting in two colors.

I've made this pattern free as I really want to share the idea of designing magic squares. I love that these patterns can be made all in one round and would be very pleased if more designs cropped up in the future.

I still need to write a few posts to show the design process. If all goes well, I should have a post about deconstructing the magic square next week, and a post about how I designed the square a week after that.

Thursday, June 15, 2017

Onion Ring Magic Square #2

Here is the magic square that can be created using the hidden square from last week's post:


Notice that the onion rings appear on the inside of the square. In the previous magic square (lower left in the photo below), the onion rings are on the outside. Each time the magic square is built up to a larger size, the onion rings will flip (from the outside to the inside, and vice versa).


If you look at the large square, you can see several of the smaller squares within it. Using the same basic repeat, the pattern can be built up to any size, all in one round.

I won't be tatting any larger squares as I'm just using it as an example of how to design a magic square. I should have more detailed posts about the process in the next couple of weeks, and will also be sharing the pattern on my blog.

Thursday, June 8, 2017

Hidden Square

Here is the square that was hidden within last week's magic square:


Look at the bottom right corner in the picture below. You can see half of the hidden square, outlined in green:


The final step is to make a magic square out of four of the hidden squares. The stitch counts are all contained in the first magic square, so no new calculations need to be made. However, it will take somewhere between 12 and 15 hours to tat. More on that in the next week or two.

Thursday, June 1, 2017

Onion Ring Magic Square

Well, it's time for the big reveal. This is what I've been working on for the past few weeks:


It's another magic square, this time made with onion rings. If you've been following along with my last two posts, you will remember that I started with a small square and then connected it into four squares. The last step was to redesign the middle to enable it to be tatted in one pass. Here are the three images together. Can you see how one builds off of another?


This is only a small version of the square, and it can be built up to any size from here. There is also another square hidden within this pattern. My next post will show the hidden square and then I will work on completing another magic square based off of the hidden square.

I received several guesses in my previous posts about what I was making. People were very close, and the guesses of a square doily, mat, or shawl are technically correct because this pattern can be used to make all of those things. However, I was thinking about the design in more of a conceptual way, and less so as a finished project.

My end goal is to compile a post showing how to design a magic square. I think it's a really interesting concept and would love to see other magic square designs pop up, though I know that's wishful thinking!

I will also be sharing the pattern on my blog so keep an eye out for that. It should be ready in the next month or two and will be available as a free pattern.