Math Encounters — Symmetry, Art, & Illusion — Scott Kim

Also take a look at the ambigram in the background of the poster.

Scott Kim - "Symmetry, Art & Illusion"

The proceeds benefit the “Museum of Mathematics”, opening in Manhattan in 2012. For more information, visit mathencounters.org.

NY is a crazy city and everything here isn’t always the way that it seems. The Ambigram is great way to showcase this mindset because you have to take a hard look to truly appreciate the complexity of the design much like this great city.

Image used with permission from FLIP NY.

2. Why do you think the ambigram logo was appropriate, given the branding of FLIP NY?

FLIPNY encourages people to take a second look at this city… to look closer at the environment and the people that inhabit this crazy place.  The ambigram was a perfect way for us to get the message across with just a logo.

3. What and/or who was your inspiration for the ambigram mark?

It’s funny.  It was actually Dan Brown.  In the early fazes of the marketing plans I was reading “Angels & Demon” which uses abigrams throughout the entire book.  I thought it was the coolest concept I had ever seen.  I needed to use it for this clothing line.

4. An ambigram isn’t usually the first, second, third or even fourth idea for an identity of a company. Was the ambigram concept in the forefront initially, or did it evolve later on in the design process?

Nope, it was the furthest thing from my mind… But like I said earlier, when you have a great idea and you know it’s great, you have to fully pursue it.

Image used with permission from FLIP NY.

5. Do you think the mark accurately represents FLIP NY and its culture?

Absolutely, like I mentioned before, things in this city aren’t always what they seem.  I have been living here my entire life and I am constantly learning new something new.  The FLIPNY Logo is a constant reminder to take a close look at this place and the people  you might surprise yourself…

6. What was the most challenging aspect of the design & development process of the ambigram mark? (here, would you be able to show any possible ambigram sketches, ideas, etc..something to show the evolution process of the ambigram)

Not really once the idea came to mind the sketching portion was pretty simple.  We had multiple concepts.  The hardest part was choosing the concept we liked the best which is the logo you see today which we considered “the classic Goth style”

Image used with permission from FLIP NY.

7. Are there any ambigram artists that you personally admire?

I would have to say John Langdon. Without his work on Angels & Demons, I never would have came up with this idea.

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A big thank you goes out to Todd Aferiat,  President and Founder of the Flipny Clothing Corporation. Take a look at their website and products at www.flipny.com

I contacted the owner of the blog, and they pointed me in the direction the artist Papper & Penna. He was kind enough to answer a few questions about the creation process for the Ektopia logo.  Read on!

1. What type of a blog is Ektopia, and why did you think an ambigram logo was the perfect solution?

Used with permission from Ektopia and Papper & Penna

Ektopia blog is about creative art. The logo wasn’t a commission design. Me and Jay (Ektopia) are friends on “Flickr” and I follow his photostream. In his gallery I saw an attempt of his doing an “reflection” ambigram (see below).  He explained how he needed a new logo for his blog “Ektopia” and that he really wanted it to be an ambigram but had some struggles and was reaching out for ideas.

As soon as i laid my eyes on his drawing I got inspired and thought of how I could improve his design and make the letters work better with each other.  I’ve been drawing letters my whole life but I became really passionate when I discovered graffiti. As a graffiti writer I always aimed for symmetry in my letters. The thing about graffiti is that it’s often meant to be wild and hard to read. But an ambigram is no good in my opinion if it is not clearly legible. I hate ambigrams that look forced into symmetry.

After some doodling pen on paper I soon discovered that the letter combination “ektopia” would work better as a rotational ambigram and not reflectional. Its a fun challenge sketching up letters one by one that should work as other letters up side down. I constantly rotated my paper and it must have been a funny sight if you didn’t know what I was up to.

2. What and/or who was your inspiration for the ambigram mark?

Jay’s sketch.

Used with permission from Ektopia and Papper & Penna

3. The Ektopia ambigram has a very distinct aesthetic to it: the blackletter/gothic look is a fairly common trend in ambigram design. Was that the initial look you were going for, or did you attempt other styles as well?

I think the main reason that the “gothic” look is common among ambigram designs is that the letters often are symmetrical as they are. Gothic and blackletters have very straight-vertical lines which is appreciated when you draw ambigrams. They are also decorative and you can hide or reveal letter-parts among “ornaments”. I don´t know if that answered your question but yeah I wanted the logo to be artsy/aesthetic, but a script font could have worked as well. The important thing is how you alter it.

4. Do you think the mark accurately represents Ektopia and its purpose?

Yeah, Ektopia’s blog is about more than just art and my logo-design is more than just a logo.

5. What was the most challenging aspect of the design & development process of the ambigram mark?

An ambigram is always challenging if the word is not an palindrome obviously. Haha. But if you want me to pin point out a specific detail I guess it was making the “kt” look like a “p” upside down.

Used with permission from Ektopia and Papper & Penna

6. Are there any ambigram artists that you personally admire?

I honestly don’t know any names but a personal favorite is the logo for “Blacksmith management”. It looks so obvious and natural, not forced into an ambigram.  (Take a look at the Blacksmith ambigram here.)

7. What is your background? Are you a designer, fine artist, or a hybrid of the two? Or, is there anything else in the mix that inspires your design and art?

I am a freelance logo designer. Together with a friend I have “Papper och Penna”. I find inspiration in everything from my 3 year old sons drawings to food labels and old signs.

Much thanks to both Papper & Penna and the Ektopia blog for providing the material for this article.

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Here is the link to the Ektopia blog
Ektopia Blog http://www.ektopia.co.uk/ektopia/

Here is the Flickr photo-stream for Papper & Penna. Take a look at some of his wonderful typographic work!
http://www.flickr.com/photos/papperochpenna

It is often said that the reason rotational ambigrams work is because we concentrate on the tops of letters when we read. So when the bottoms of the letters are altered (or even removed entirely) they are still relatively readable. This is a property that even the beginning ambigrammist can take advantage of.

For those new to ambigram design, knowing where to begin can be tough, so the method below is probably the simplest way I can think of to make a basic, rough ambigram (without using automatic generators, of course!) Please note that this method doesn’t work with ALL words/phrases.

The following example is with the word ‘simple’:

A series of vertical lines forms the basis for your ambigram

Step 1: Start by making evenly spaced vertical lines. (Fig. 1)

Step 2: Use these lines as the basis of the letters.  (Fig. 2) Try to include as much of the letters’ defining characteristics as possible, although with some letters (Q, L, etc) this is not possible. It would be a good idea to make several versions, using different cases and styles. After this step, the word should be relatively readable (a second opinion here would be very useful.)

Add the ambigram to itself

Step 3: Take this, flip it over and add it to itself. (Fig. 3) Again, it should still be relatively readable.

Step 4: Now ‘finish off’ the letters. (Fig. 4) As you can see, the bottom of the ‘L’ has been added, and the letter shapes have been tweaked to be as clear as possible. This is the most critical step.

Another Example: The name Robert

Again, this method isn’t foolproof, and shouldn’t be used as a crutch, but it can be very effective.

This ‘vertical line’ concept isn’t anything new- it’s the main reason the ‘gothic blackletter’ font seems to be the most effective font for ambigram design.

The inspiration for an ambigram can come from almost anywhere. It could be a commissioned piece, a gift for a friend, or a ‘just because’ in-the-spur-of-the-moment desire to create something unique and unusual. But, even if the inspiration is instantaneous, you still have to go through the analysis & determine whether your chosen word will make a successful ambigram or not.

In this example, the song ‘Out Of My Mind’ by John Mayer was on the radio. I have always been a fan of blues, and I like Mayer’s music because he can switch seamlessly between the mainstream artist and a classic blues man, whose guitar-playing abilities rival those of Hendrix and SRV. While listening to the song, I wrote down the name of the song and artist, almost mechanically, in my sketchbook.

(click the image to see a larger preview)

Of course, my next thought was ‘Oh!Ambigram!’ since I already had my sketchbook open and had pencil ready in hand. First, I wrote down the words ‘john mayer’ in lowercase, lowercase cursive, and uppercase.

(click the image to see a larger preview)

Usually, I start off with writing the future ambigram in uppercase, but in this case, I decided to write it down in several different cases. At first, I decided to work with all uppercase letters. Uppercase letters are much easier to draw, read, and work with; they have much fewer tails, serifs, ears, and other typographic structural elements that are ubiquitous amongst lowercase letters.

After writing down the words ‘john mayer’ in all uppercase, I wrote it upside down to see how the letters lined up, and then began a more in-depth analysis.

(click the image to see a larger preview)

After looking at it for a few minutes, I realized that my initial assumption that uppercase would be easier to work with was erroneous. When I realized that I also came to a few other conclusions:

- After I decided to use very simplified lowercase letters, I realized that a 1-to-1 ratio would work perfectly for this ambigram.

- I was lucky enough to have a ‘central’ letter, the M, which has an equal number of characters on each side; in addition, the M was very easy to modify to read the same way upside down.

- The words ‘john mayer’ was as close to a natural ambigram as I could come; I had to make but a few slight changes to make it both readable & legible.

In the previous image, you saw a few quick sketches of each letter pair to see how they would look underneath each other. Here is a more finalized sketch:

(click the image to see a larger preview)

After I finished the first complete sketch, I also realized that this would be a perfect opportunity to use an actual typeface to finish the ambigram. Usually, I steer away from using already designed typefaces and always hand-draw the final diagram, then trace it in the computer. However, for this ambigram, I wanted to portray the effortless sound and classy style of John Mayer’s music. I didn’t want a heavy or even a regular typeface weight for this ambigram. So in the end, I decided to go with the tried and true, overused & abused, perfect and boring: I chose Helvetica Light as my typeface weight. After some very minor adjustments, this was the final solution.

(click the image to see a larger preview)

End of process!

Natural ambigrams are ones that don’t require any modifications. Flip them, mirror them, reflect them, and you get the same word, and very rarely, you get a different word. In the world of ambigrams, a rotational ambigram (one that depicts the same word when rotated 180 degrees) is the most common one, followed by some reflective ambigrams, and very rarely, if ever, a symbiotogram.

Let’s take a look at a few examples, shall we?

MOM

This is one of the few natural ambigrams that works as a reflective ambigram in two different ways, as well as a symbiotogram.

Reflection v1

Reflection v2

Mirror (a rare case where the mirrored word is a symbiotogram.)

suns – rotational

This ambigram is pretty self explanatory.

How about a bonus? Eliminate one vertical stroke of the U/N, add a dot, and you have a SINS ambigram!

sos – rotational

When you need to be saved, what better to use then a graphic that can be read the same way in two different directions?

pod – rotational

bid – reflective

Reflection v1

Reflection v2

bud

Reflection v1

Reflection v2

GOD

This ambigram might require some slight modification depending on how you write it, but it is pretty straight forward as well.

But wait…what’s this? Let’s take the G, mirror it, and…now we have a reflective ambigram from the same word!

Reflection v1

Reflection v2

noon

Reflection v1

Reflection v2

anna

Reflection v1

Reflection v2

Note that each one of these ambigrams is sketched on paper in a slightly different aesthetic, then simply held up against a mirror and photographed. I’m no David Copperfield, so these ‘illusions’ are as real as can be!

Now, you may be asking yourself, what good is studying, drawing and redrawing natural ambigrams?

There are several parts to that answer. The first part is blatantly obvious: you do not have to worry about legibility, since it’s already a natural ambigram!! This allows you to focus on aesthetics; thus you can give your ambigram almost any look & feel that you want, without reducing legibility and/or readability. Of course, there are exceptions to the rule, as you can ‘over-stylize’ even the most natural ambigram so that it will be hard to read and understand.

The second part of the answer is simple: you are developing your hand and eye ability to recognize ambigram potential. We have to practice our skills; whether you’re an athlete, musician, poet, writer, designer, etc. you still have to work on honing your abilities. Why should ambigram design be any different? Once you train your eye to recognize and your hand to draw (and stylize) natural ambigrams, you can switch to more complex words and attempt to turn them into ambigrams.

THE AMBIGRAM CHALLENGE

Here is my challenge to everyone: take one of the natural ambigrams you’ve read about in this article, or find one that I haven’t mentioned. Attempt to stylize each one at least 3 to 4 different times so that each version exudes a different style. Do this by hand, not on the computer!! Then scan/photograph the sketches, email them to nikita@ambigram.com and we’ll post them along with a write-up and analysis in one of the future columns.

Happy ambigramming!

As you can see, the title is set in a Blackletter-style Cyrillic typeface, which really has a great aesthetic connection to the dark plot and characters of the book. My first thought was “can I make an ambigram out of the title?”  After asking myself that question, I had two immediate goals in mind: analyze the current title to see if it would indeed make a successful ambigram, and if it was possible, to keep the same ‘dark and sinister’ look.

Analysis

At first what I did was quickly redraw the book title by hand, just to see what my hand does. I know that might sound strange to someone, but think of how you touch clothing in a store to feel the texture of the cloth or you inhale a fragrance to see how it will make you feel. This is no different! Drawing out a typeface allows you to understand it better and to experience firsthand (pun fully intended!) the transition from character to character.

After redrawing it (1), I realized that each character is made up of the same basic shape, some wider characters requiring two of the shapes (2). When I saw how basic the shape is, I realized that it was almost perfectly balanced, which I quickly determined by drawing a rough outline around the would-be word (3). After a few more rough sketches (which I am not including here because they are too rough), I switched to the only problem in the word, which was the letter ‘y.’ Why is it a problem you ask? Well it’s all about that pesky descender of the ‘y’, the only non-symmetrical part in the whole word. As I experimented with three or four various shapes (4) to make the ‘y’ that is read the same way after the word is turned, I became frustrated with the lack of symmetry and decided to switch to the computer to work out the basic vector shapes for each letter and then experiment with the ‘y.’

After finalizing the basic shapes for the narrow (5) and wide (6) characters, I decided to develop those few characters that, in my analysis, proved that they would be perfectly symmetrical.

As you can see above, perfect symmetry! Not a bad first attempt, but the biggest problem was still the ‘y.’ Since I wanted to keep the letters proportionate and consistent, I decided to crop the vertical center part of the first letter and use it as the descender of the ‘y.’ I noted that the negative space between the ‘a’ and the ‘c’ characters (refer to the image below), when combined with the descender, almost formed two perfect ‘y’ letters.

Ok, that looks like a very rough ‘y’, but let’s try it!

Not bad right? Well the symmetry was definitely there, but something bothered me about the way the ‘a’, ‘y’ and ‘c’ were joined together and that the ‘y’ was more implied then strictly defined. So I decided to try to fix that issue.

Much better! But, now the ‘y’ bothered me because it did not look like a ‘y’ but more like a character that would look more at home on the Rosetta stone then in my ambigram! It also looked very separated from the rest of the word and seemed to fill the space rather then complement it. What to do…what to do…what to do…

The solution proved to be very simple. By simple extending the tail of the ‘a’ and the ‘c’, the connection helped define the ‘y’ better and gave the ‘a’ and the ‘c’ better recognition.

And to compare the final result to the original….

Voila! A Cyrillic ambigram!

I would like to focus on these two types of ambigrams:

Rotational – reads the same way when rotated 180º degrees. Certain variations of this exist; for example, one word can be read one way, and when you rotate the word 45 degrees or 90 degrees, you read a completely different word.

Symbiotogram – an ambigram that depicts a different word when rotated 180º degrees.

As I mentioned earlier, in an ideal ambigram (rotational or symbiotogram), there is the same number of letters in both words, all the letters will match up well and you can keep the ratio of letter 1-to-1. So, for what reasons would you want to alter the ratio and combine two (or more) letters?

In a rotational ambigram, just because there is the same number of characters in either direction, does not mean that the 1-to-1 ratio is optimal for legibility & readability. Combining several characters in one direction, while reading them as one character in another direction, could improve the legibility of the ambigram and make life a bit easier for the artist.

The key to creating a successful 2-to-1 ratio is to explore multiple variations to determine which character(s) will work better for which ratio. Sometimes two characters will blend together seamlessly in one direction while forming a perfectly legible single character in another direction. Let me illustrate this point by using an ambigram which utilizes this approach.

For this particular ambigram, I selected the names of my two friends who recently became engaged. Initially, I set the words in Myriad to look for matching stems, crossbars, curves and strokes. Almost immediately, I noted that the ‘u’ would be a problem when matched up to the upside-down ‘i’. The next thought was about how well the verticals in the ‘u’ matched up to both the ‘l’ and the ‘i’. There was my first 2-to-1 match-up!

Ok, so the u/li are matched up well. My eyes were then drawn to the central character of the ambigram, the ‘h.’ Granted I set the word using a lowercase ‘h’, but decided to use an uppercase ‘H’ instead, because that is a natural match to itself upside down. I also noticed how the ‘&’ character matched the curves of the ‘s’ really closely. I knew that I had that problem solved as well and that the s/& would be a good match for each other.

The only letters remaining were the ro/a combination. At this point, there was no choice but to make it a 2-to-1 ratio because I cornered myself by matching up the u/li. The shapes of the ‘o’ and ‘a’ are pretty similar to each other. Now you may think that I need contacts because those letters have nothing in common except for being vowels.

Here, I would like to make a very important point: to determine whether or not a 2-to-1 (or more) ratio will be successful, you need to see it in context of the full word and not just by itself on a piece of paper. Other than some basic curvatures, those two characters are different. Each has a different personality, a different signature if you will. But, combine those two letters, place them in the context in which they would be seen, and your perception of those characters will change. The proper context will not only help you understand whether the ratio is successful or not but will also help you perceive the word, as well as determine the legibility & readability.

At this point, the ‘r’ looked like the odd letter out. There did not seem to be any room for it. But since I had the other letters figured out so well (at least for the time being) I thought that the ‘r’ would fit in later. And…

…it did! If you look at the right side of the above ambigram, the way the ‘r’ merges with the ‘a’ and ‘l’ makes it look like an exaggerated spur of the lowercase ‘a.’ On the opposite side, the merger of the ‘l’ and the ‘r’, along with the slight separation at the terminal of the ‘r’ (see above image), helps define the r/o combination while upside down, it appears as an exaggerated ‘a.’

And, the final ambigram:

In the final version, I ended up using two 2-to-1 ratios; they ended up following each other, and when both of them were combined, they helped make certain letters more prominent in either direction, as well as help disguise other letters. As you can see, 1-to-1 is not always the optimal solution. Even if a word matches up well utilizing 1-to-1 ratios, try to experiment with different ratios; it will train your eye & your hand, as well as your ability to recognize certain character transitions and potential for unique & unusual combinations.

There are books that showcase ambigram design, most notably John Langdon’s Wordplay and Burkard Polster’s Eye Twisters. John Langdon’s book gives everyone a great insight into his philosophy & personal world of ambigrams, while Burkard Polster’s book exhibits ambigrams from various artists across the world. Langdon’s and Polster’s books show examples of wonderful ambigrams and the process behind them, but they don’t teach you how to design them. So, what’s a novice ambigrammist to do?

Well, never fear, because there is a light at the end of the tunnel. That light comes in the form of Letter By Letter, An Alphabetic Miscellany, by Laurent Pflughaupt. This book does not include a step-by-step guide to creating ambigrams nor does it magically transform its readers into professional ambigrammists. So why am I calling it a perfect book for ambigrammists?

If you remember my first post here (and if you don’t, feel free to take a look at it) I discussed what ambigrams are and why they can be so difficult to create (and to create properly!).  We are so used to seeing letterforms in a specific application that it is hard to imagine them existing in any other context. Letter by Letter opens your eyes and helps you see each letter as not just a specific form (with a single meaning) but also an entity that is flexible and can be perceived differently, depending on the context.

First, Laurent starts the book off with a short historical introduction. He covers Cuneiform, Hieroglyphics, Proto-sinaitic/Phoenician/Greek/Etruscan/Latin alphabets, as well as various typographic styles & period. He then shifts into formal analysis of letterforms and letter anatomy, discussing various structural elements & topics such as the Golden Rectangle, colors and their connection to alphabet.

This is where the content becomes relevant to ambigrammists. The third section of the book examines each letter in excruciating detail (I only say excruciating because I can’t imagine how much work went into each letter’s section, let alone the whole book!) Laurent starts by tracing the origins of each letter and its evolution, going back as far as 800BC.

He discusses various uses of each letter, while making connections to each of the alphabets discussed in the previous chapter. Then, he talks about various aspects of each letter, such as shapes/interpretations, meaning & different abbreviations. In every section devoted to a letter, a timeline is included; this timeline traces the origin of each letter from its earliest known record to present day, and shows its evolution within various alphabets & typographic periods.

So after reading all this, aren’t you asking yourself ‘how the heck does this book help me become an ambigrammist’? This book helps you become more flexible when examining a word and understanding its potential to be an ambigram. If you are used to seeing a letter in one way, this book will help you see that letter in a completely different light.

If you’ve taken a typography course, various topics such as letterform structure, proportion & consistency have been hammered into your head. After reading this book, as well as examining various ambigram examples, you will be able to get out of your own (restricted) way of seeing letterforms and will be able to maintain a more open mind, which is essential when attempting to create ambigrams.

So what are you waiting for? Go buy the book (or sit at Borders & read it), and get to work!

The only way to understand the true essence of an ambigram is to read Ambigram.com, twenty-four hours a day, seven days a week, nonstop, ignoring any other commitments and responsibilities in your life. Sounds like a good idea, right?