First, a quick overview of some technical bits. The user can select a range of dates from the map interface, and a new set of markers is rendered after an AJAX query to the backend PHP code, which requests the data from our database and aggregates it at the zip code and state level. The decision to do this two level aggregation was based on the performance hit that would be taken in trying to render on the order of 7000 icons for a year’s worth of data on a nationwide map. The MarkerManager class (which used to be part of the core Google Maps API) is used to display one set of icons when zoomed inside of what might be called “state level” and another set when zoomed out further. This adds a bit of extra complexity to our colormap choice.

There are a number of ways that this data could have been mapped into visual symbols. The size or shape of the glyphs could be related to the number of admissions, for example. The method that we are using maps the number of admissions to color (when this mapping is stored, it is called a colormap). The particular mapping that we use is important, because some mappings are better than others for certain tasks. For the markers on the map, we use a colormap that smoothly transitions from a blue at the low end to a red at the high end. The particular choice of blue to red leverages our cultural understanding of blue as “cold” and red as “hot” (note that sometimes colormap choice depends on cultural interpretation), a metaphor which works well as a representation of low vs. high admission rates. The combination of these two choices allows us to understand the general trends in the data without needing to refer back to the legend frequently. The drawback is that it is a bit more difficult to compare the value of two individual markers than it would be if we had picked a colormap of more distinct hues such as {red, orange, yellow, green, blue, purple}. We tried to make it easier for the viewer to make comparisons by limiting the number of colors in our legend.

The next important choice is how exactly to map the number of admissions to a particular color. To do this well, an understanding of the distribution of the data is necessary. Intuitively, we would expect that there will be high admissions numbers for the zip codes closest to the museum, and the trend will be toward increasingly lower admissions from more distant zip codes, and likely there will be many zip codes with very low, but non-zero admissions numbers. The best way to look at this objectively is with a histogram. I will take a number of approaches with the data from the year 2008, for which the highest raw admission count for a zip code was 12,375 (during the aggregation, 9 digit zip codes are merged into 5 digit zip codes, resulting in slightly higher numbers in some instances), out of 6806 zip codes.

This first histogram segments the zip codes into buckets in a linear fashion, with each bucket representing 10% of 12,375. As you can see, the vast majority of the zip codes end up in the first bucket. If we used 10 colors with this linear mapping, almost all of the glyphs would be blue. It would be great for identifying and comparing the few zip codes that have very high admission, but a lot of subtlety in the big picture would be lost.

This histogram also uses a linear segmentation, but with an upper limit (or clamp). Any zip code with 10 admissions or more are put into the red bucket. This would be fine for comparing admissions from distant zip codes, but we wouldn’t be able to distinguish visually between admissions from zip codes around Indianapolis.

This is where the beauty of logarithms comes to the rescue. Let’s use our example to walk through the process. First we determine the logarithm of our maximum number, 12375, in base 2 (working in base 2 is very efficient for computers). The result is 13.59. The highest bucket represents 12375 in the real world, and 13.59 in exponent-land. Each bucket represents a tenth of 13.57 in exponent-land, just as in our first histogram each bucket represented a tenth of 12375. We then simply derive the numbers that each bucket represents in the real world; 2 to the 1.359th power equals 3 (when represented as a whole number), for example. These whole numbers in the real world are then used to put the zip codes in the proper bins.

The result is that we have teased out more meaning to bestow upon our colors. There are still thousands of zip codes in those blue buckets, but they are the ones that are scattered across the nation on our map, so here we are aided by spatial distribution. In the red zone, there are dozens of zip codes in each bucket, and this is just what we want to be able to analyze the subtleties around Indianapolis where the icons are more spatially dense. It also turns out that this trend is pretty much independent of the date range, and the colormap still works out well at the state level.

On the actual map we use eight icons rather than ten to reduce clutter in the legend, but the algorithm is the same.

You might notice that we use a different type of colormap in the demographic windows. We actually tried using a smooth colormap for this data for the more linear demographics (Income, Age, etc.). The problem was that it was then very difficult to visually relate a particular shade of blue or green to a particular age or income level, which would almost certainly lead to eye strain and headaches. So here we used a more rainbow-like colormap to make that analysis easier.

In summary, colormap selection is a complex process involving aspects of mathematics, design, and the nature of the dataset. It’s one of those areas where art and science come together and the best practices of each can lead to successful communication of concepts and beautiful representations of data.

(stay tuned for a great way to experience the IMA grounds before the end of this post!)

A friend told me about how they went letterboxing on a recent vacation and was surprised that I’d never heard of it before. Letterboxing is similar to its more recent cousin, GeoCaching, and involves hiding small boxes with journals and stamps inside them. The idea being to bring your own stamp and journal with you to collect a log of all the treasures you have found! Letterboxers leave clues to the locations of boxes they have planted online for others to find. Experienced letterboxers can collect hundreds of stamps from around the country and individual boxes can stay alive for many years! As I began to learn a bit more about it… I was hooked!

A Brief History of Letterboxing

Apparently, letterboxing has been around for a long time. Wikipedia’s article on letterboxing says that it originated in England around 150 years ago! Letterboxing seems to have gained popularity in North America in the late 1990’s. In exploring this a bit more online, I was stunned to find out how many boxes exist right around the corner! One popular letterboxing website lists over 46,000 registered letterboxes in the United States and over 1000 in the state of Indiana. There are even 2 letterboxes close by for our blog readers in Zimbabwe… What… am I living in a cave? How could I have missed this one? The thought of all these stealthy hidden little boxes brings out the pirate in me… Arggh!

(A Google Map of Letterbox locations around Indianapolis)

Letterboxing Resources

I’ve found a few great sites to fuel your burning letterboxing habit! Lately, I’ve been looking these sites up on my phone as we sail around with the top down on the Jeep looking for stamps to fill our journal. A good primer on what you need to start letterboxing can be found on this “Getting Started” page.

When you’re ready to find some boxes to search for these are some great links to start with:

• Search Letterboxes on AtlasQuest.com
• Search for Letterboxes on Letterboxing.org

Letterboxing @ IMA

So, why talk about a crazy hobby like letterboxing on the IMA’s blog? Well besides the obvious craft involved in creating some of the stamps I’ve seen… I was stunned to find out that there are two, count ‘em, two letterboxes already hidden on the grounds of the IMA. I’d be breaking the secret code of letterboxers if I gave away their exact locations… but here are the links to the clues so you can find them yourself. We’ve found both of them in the last two weeks, so I know their both still safe and sound. I wonder if our grounds keeping staff knows about these?

• IMA – planted by “Trail Mail Junkie”
• Robert Indiana – planted by “Dream a Dream”

I’m thinking that we’ll have to take it upon ourselves as proud IMA-staffers to plant a few more of these puppies out in the Art and Nature Park before it opens! Any ideas of some good hiding spots?