Monday, May 17, 2010

Mathematical Ambigrams


On the site QED Cat, you can find a very nice article written by Burkard Polster on the subject of mathematical ambigrams.  One of my favorites from the article is a 2x2 determinant written using Roman numerals:




As you see it written here you get the equation:  X·I-II·IV=II (10x1-2x4=2).  If you flip it as a mirror image you get the equation:  II=VI·II-I·X (2=6x2-1x10).

What other mathematical ambigrams do you know of?



Be sure to check out some of B. Polster's books on mathematics:

Monday, May 10, 2010

Cairo - Part 2

In an earlier post I showed a very rough pencil sketch of an ambigram of the word Cairo.  Here is a preliminary model done in Inkscape.  The 'C' and 'O' are rough and need to be modified to be parts of a circle rather than sections of a path, and the outlines of the 'god' glyph inside the 'A' and 'R' need have more detail added around the head and other general cleanup done but you can see how the idea is transitioning from the pencil sketch to a more refined image.

Tuesday, May 4, 2010

Miscellaneous City Names

Yet another post in support of Ambigram Magazine's 'Where in the World' city name ambigram contest...  ...you'd think they were sponsoring this blog space.

In the two images below you'll find a number of different city names with a little bit of exploration work done on a few.

I'm sure I've seen the mirror-image version of 'Baghdad' before, so I doubt I can take credit for it. 

'Alexandria' feels like it wants to be a mirror-image ambigram but that 'N' in the middle might be a challenge.

To me 'Rome' feels like it wants to be rendered as a vertical mirror-image, but with the top half of the letters 'completed' and the bottom half reflecting the top.  You'll see that the tops of the letters are missing so that the closed loop at the top of the 'R' isn't completely closed allowing the bottom to also remain open.  This might work out better in the native Italian spelling 'ROMA'.

The 'Paris' idea has some merit and deserves to be pursued further.  I'm not sure that the 'A' and 'I' can both be convincingly rendered as the Eiffel tower without causing confusion over which is the 'A' and which is the 'I', but as with most ambigrams, our minds create what we expect to see so it would probably work.

'Cape Town' was explored only briefly.

'Baranagar' might not fit the Ambigram Magazine contest criteria if the judges are very strict (they state that the city name must be considered a major city), but all those 'A's are begging to be mirrored.

'Pune' was so obvious it almost hurt when it smacked me in the face.

'Bally' should be easy enough to complete as a rotational ambigram.

'Pasay' almost writes itself as a rotational ambigram, but again it might not meet the contest criteria if the judges are strict.

I only played with 'Manila' briefly to see what I could do with the starting 'M' and ending 'A'.  It should be fairly easy to manipulate the 'L' and interior 'A' to be legible in more than one position.

'Beijing' surprised me a bit.  I wasn't sure what to do with the 'E'-'N' combination and the current representation looks rather Art Nouveau.  I'm also not completely thrilled with the way the 'J' jumps out in the middle; it looks too much like a violin f-hole or an integral sign.  Perhaps if I made each of the 'J's the same height as the other interior letters it would be less obtrusive.  The glyphs should also be rendered to look a bit more like Chinese characters for emphasis.

Last, but not least, the second image shows something workable for 'London'.  I'm not too terribly surprised that it has ended up looking a lot like John Langdon's anagram of his own name.



Cairo - City of the Gods

In an earlier blog I mentioned that Ambigram Magazine had posted a new design contest.  This contest is all about cities.  To get me started (ignore the fact that I had already started in the first posting) I visited Wikipedia to get a list of cities so I could get a look at a whole bunch of names all at once.

Almost immediately, the name Cairo jumped off the page and into my lap.  In mixed case lettering it's not much, but look what happens when you apply all caps:  CAIRO  It's as if RA himself had decreed that a mirror-image ambigram would one day be summoned to proclaim to greatness of that city.

In the three renditions below you'll find a progression of ideas.  In the first image the 'A' and 'R' were altered a bit to find a glyph that could represent either letter.  The letters AIR prompted an image of a pyramid so in the second line I puposefully straightened out the leading edge of the 'A' and trailing edge of the 'R' to give a more definate pyramidal shape to the three middle letters.

In the third rendition I started by thickening up the letters using an outline block font and flattening the tops of the 'A' and 'R' so a more definite pyramid could be placed on top.  As soon as that had been done, the negative spaces of the 'A' and 'R' created a rough outline of an Egyptian hieroglyphic, so I quickly searched for some images that might fill that space.  As providence would have it, the hieroglyph for 'god' fit almost perfectly, and I was lucky enough to stumble upon the hieroglyph for 'town', which is an 'x' inside a circle.

In the next few weeks I'll be refining the image of the 'City of the Gods' a bit more before submitting it to the contest.

AMBIGRAMBIGRAM - What's in a Name?

Obviously the word 'ambigram' is heavily used by people creating websites and blogs devoted to the subject, so when I had to pick a name for this blog space it was no surprise when Google reported that the website ambigram.blogspot.com was already taken.  What to do?

Since ambigrams are essentially a graphical way of playing with words I thought it would be fitting to choose a name that played with the word 'ambigram'.  Two obvious plays on the word that were begging to be employed were 'ambigram·a·rama' and 'ambigrambirama'.  They roll off the tongue like the name of your favorite bowling alley or laudromat but they didn't quite suit my taste.

The next name that came to mind was the one I decided to adopt: ambigrambigram.  The word 'ambigram' already starts and ends with the 'am' letter combination and the popular form of ambigrams repeat the same word twice (overlapped) so it wasn't a stretch to take two of the word, overlap the 'am's, and come up with the result.

I hadn't really thought about what kind of logo could be done with the word when I started the blog, but here are some very rough sketches of where I'll probably end up.

The Ambigram Magazine 'Where in the World' Challenge

Ambigram Magazine has announced their latest ambigram design challenge:  Where in the World.  The idea for this challenge is to design ambigrams for the names of major world cities.  With that in mind, here are some quick doodles I sketched this morning for the cities of Chicago, Los Angeles, and Amsterdam.  They are obviously rough, but should show each concept as a 'work in progress'.