Category Archives: Visualizations

Visualizations both Serious and Whimsical.

Text Wrapping within Tableau Panes






Controlling X + Y



Green Panes vs. Blue Panes: Pane Sizing








Green Panes vs. Blue Panes: Number of Panes







Packing the Marks: the Algorithm






Here’s the workout view:








Waffle Charts and Unit Charts on Maps





Why would we need to do this?


There is nothing new under the sun


How do we put a waffle chart on a map?



I’ll briefly walk through each calculation.





//this gets the column position in the row
IF [Index] % [Column Count] = 0 THEN
 [Column Count]
 [Index] % [Column Count]
//subtract the position of the midline to get the offset
 - ([Column Count] + 1)/2


 SIZE()/[Column Count]


//row position in column
 [Index]/[Column Count]
//subtract the midline of the row to get the offset
- ([Row Count] + 1)/2



Jitter – Waffle – Longitude does the same for the longitude.



Building the View



Why Stop Here?













On Gender and Color


Screen Shot 2016-08-24 at 10.58.30 PM




The End of the World – by Noah Salvaterra

A guest post by Noah Salvaterra, you can find him on the Tableau forum or on Twitter @noahsalvaterra.

I expect the header image may spark some discussion about visualization best practices; actually, I sort of hope it does. The data shown is from NOAA’s online database of significant earthquakes and is displayed by magnitude on a globe, so 4 dimensions packed into a 2 dimensional screen. While it was created in Tableau, it might be a long wait before something like this appears in the show-me menu.

SpinningGlobeFor those who missed the header because they are reading this in an email, I’ve included an animated 3D version on the left, though to actually see it in 3D requires the use of ChromaDepth glasses (I discussed this technique in more detail in a prior blog post). Use of 3D glasses adds even more controversy because while we can get some understanding of depth from a 3D image, it isn’t perceived in an equal way to height and width. Data visualization best practices can help in choosing between several representations of the same dataset, choosing bar graphs over pies, for example, since bars will typically lead to a better understanding of the data. Best practices also instruct us to avoid distorted presentations such as 3D or exploding pies and 3D bar charts, since these are likely to lead to misunderstanding. I’m not exactly sure what best practices has to say about this spinning 3d anomaly, my guess is it would be frowned upon. I think there is something to be said for including a novel view of your data if it helps to engage with the topic, and even if this one does break some rules, it’s hard to look away. If you’d rather just see the earth spinning, without all the data overlaid, there is an earth only view at the end.

The images above may not be the best choice as general way to visualize this earthquake data. In fact, I’m the first to admit that it has some significant issues. Comparing earthquake magnitudes between 2 geographic areas would be tricky, plus half of the earth is hidden from view completely because it is on the back. Adding the ability to rotate the globe in various directions in a Tableau workbook helps a bit, but you’re left to rely on your memory to assemble the complete picture. If the magnitude of the quakes is the story you’re telling, you might be better served with a flat map maybe using circles to represent the magnitude of the quakes, such as the one shown below. I think this is a good presentation; it has some nice interactivity and as far as I know doesn’t break any major rules from a best practices standpoint. But it certainly isn’t perfect, nor is without distortion. Judging the relative size of circles isn’t something that will be perceived consistently, but the failure I had in mind isn’t one of perception, it is about the data being accurate at all. The map itself brings a tremendous amount of distortion to the picture, in location of all things.

In case you haven’t heard, the earth isn’t flat (I like to imagine someone’s head just exploded as they read that sentence). It is roughly spherical. Well, technically it is a bit more ellipsoidal, bulging out slightly along the equator, and more technically still this ellipsoid is irregularly dotted with mountains, oceans, freeways, trees, elephants and wal-marts (not meant to be a comprehensive list). Also, as the moon orbits, it causes a measurable effect not just on the tides, but it distorts the land a bit as well as it passes by. Furthermore, the thin surface we inhabit floats, lifting, sinking, circulating on top of a spinning liquid center. Earthquakes serve as a reminder of this fact. The truth can be overwhelming in its complexity; so we simplify. Though not the complete truth, a well-chosen model can be a valuable proxy when it doesn’t oversimplify. One way to understand the difference would be to analyze the scale of the errors introduced. The highest point on earth is Mt. Chimborazo in Ecuador at 6,384.4 km… you were thinking Everest? That is the highest above sea level, but the sea bulges as well, and Chimborazo is the furthest from the center getting a boost by being close to the equator. The closest point to the center of the earth is in the arctic ocean near the north pole and is about 6,353 km from center. If we use the mean radius of 6,371 we are doing pretty well (error is within .3%). A sphere seems like a reasonable compromise.

So the earth is spherical… but our map is rectangular. You don’t need to invest in differential geometry course to understand that there is something fishy going on there (though you might to prove it). In fact there is no way to map a spherical earth to a rectangle, or any flat surface without messing something up, the something being angle, size or distance; at least one will be distorted when the earth is presented on a flat surface (sometimes all of them). This seems to be a bit of a problem given the goals of presenting data accurately. What if your story is one of angle, distance, area or density?

What shape are the various shifting plates? What are their relative sizes? How fast do they move? Where do they rise and fall? What effect does this have? Can you tell this story in Tableau? Can you tell it at all? Maybe. I’d certainly like to see this done, but seismology isn’t an area I have any specialized knowledge. In areas where I do have such knowledge, I’m lucky to get questions so well defined and which span just a handful of dimensions. When I’m dealing with 50 dimensions that writhe and twist through imaginary spaces whispering patterns so subtle that the best technique I’ve found to discovering them is often just to give up and go to sleep, I’m not deciding between a pie chart and a bar chart, it is an all out street fight. Exploring the Mercator projection seemed like a good analogy for the struggle to represent a complex world in a rectangle, plus it seemed like a fun project. As I undertook this exercise, though, I realized that other map projections weren’t much further afield. Also, Richard Leeke mentioned something about extra credit if I could build a 3D globe with data on it. I’m a sucker for bonus points.

chartHow bad are the maps in Tableau? Well, it depends where you look at them, and what you hope to learn from them. Your standard Tableau world map is a Mercator projection. If you’re planning to circumnavigate the globe, using an antique compass and sextant, it will actually serve you pretty well. Since the Mercator projection has a nice property for navigating a ship. If you connect 2 points with a straight line, you can determine your compass heading and if you follow that course faithfully, you’ll probably end up pretty close to where you intended. Eventually. You can actually account for this distortion in such situations, with a bit of math, so you’re not completely guessing on how long you’ll need to sail. Incidentally, I’m not particularly riled up about Tableau’s choice of the Mercator projection, sailing around the world with a sextant and compass sounds like a whole lot of fun to me and any flat map is going to involve a compromise on accuracy somewhere. What I do think is important is knowing this distortion is there in the first place. How bad is the distortion? Scale distortion on a Mercator map can be measured locally as sec(Latitude) (if your trigonometry is rusty, sec is 1/cos). Comparing a 1m x 1m square near the equator with one at the north pole, you’d find that a Mercator projection introduces infinite error, which is a whole lot of error. To be fair, since printed maps are finite and the Mercator projection isn’t, the poles get cut off at some point (so the most common maps of the whole world are actually excluding part of it…). If we cutoff at +/- 85 degrees of latitude, we reach a scale increase of sec(85) which is about 11.47, i.e. objects are 1,147% bigger than their equivalent at the equator! That seems like a pretty significant lie factor…

Recently (on a cartographic time scale), the Peters projection has gotten a lot of attention. This is a good place to pause for a brief video interlude:

Maps that preserve angles locally are called conformal. The Peterson projection is not conformal so while it represents relative area more accurately, it would be a terrible choice for navigation.

StereographicStereographic projection is another noteworthy map. Like Mercator, Stereographic is a conformal map. It maps angle, size, and distance pretty faithfully close to the center, so it is a common choice for local maps (you probably use such maps often without even realizing it). Stereographic projection isn’t a very popular choice for a world map, however, because (among other things) you’d need an infinite sheet of paper to plot the whole thing. On the right is a stereographic projection map from my Tableau workbook. In case you can’t see them, North America, South America, Europe and Africa are all near the center of the map. The yellow country on the left is the Philippines…

I included the maps I did because they are popular, and I knew most of the math involved; however, there are lots of other options. I’m not arguing that any one is best, rather that they are all pretty bad in one way or another, and we should choose our maps like our other visualizations so they best tell a story, or answer a question, and while there will be distortion, it should be chosen in a way that doesn’t compete with what we hope to learn or teach.

In addition to the earthquake maps seen already, the workbook for this post contains an interface to explore some of these different projections, and not just the most traditionally presented versions of each of them. I invite you to create your own map of the world, based on whatever is most important to you. Flip the north and south poles, or rotate them through the equator. My hope is that exploring these a bit by rotating or shifting the transverse axis will be a useful exercise in understanding what it is you’re looking at when you see one of these maps, so you might have a better chance of seeing things as they truly are.

I’m pretty sure there is a rule about not putting 7 worksheets on a single dashboard, there may even be a law against it, but once I had all these maps I wasn’t entirely sure what to do with them all. I apologize for not arranging them thoughtfully into 2 or 3 at a time. I experimented with this approach, but ultimately abandoned it because I didn’t think I had enough material on map projection to make interactive presentation of all these very interesting. I also thought about a parameter to choose between them, but since they are necessarily different shapes, it didn’t seem practical to try to fit them all in the same box. Truthfully, I think there is a lot of room for improvement in terms of dash boarding these, but when I open the workbook I just end up tinkering with something else. It is time for me to set this one free. Feel free to download and play with them as long as Richard and I have.

Here is a link to the workbook on Tableau Public

When I’m presenting, or exploring data, accuracy is usually something I pay careful attention to, but it isn’t my goal. The most important thing for me is to find a story (or THE story) and to share it effectively. If you hadn’t noticed from my previous posts, I don’t let what is easy stand in the way of a good question; in fact if it is easy I get a little bored. I like to bite off more than I can chew (figuratively; literally doing this could potentially be pretty embarrassing). Having the confidence to take on big challenges is something I’m deeply grateful for; knowing when to ask for help, and where to find it has taken a bit more effort, but is something I’m getting better at. As with Enigma, Richard Leeke was a huge resource for this post. Having seen his work on maps I thought he might have something I could use as an initial dataset. He came through there, and helped me to work through the many subtleties of working with complex polygons without making a complete mess. You have him to thank for the workbook being as fast as it is (assuming I didn’t break it again; if it takes more than 7 seconds to load, my bad).

ptolemymap3I feel a kinship with cartographers during the age of exploration. This discipline still holds value, certainly, but the recesses of our planet have been documented to the point where it doesn’t hold the same mystique in my imagination. When I think of old world cartographers, I think of an amalgam of artist and scientist. Assimilating reports from a variety of sources, often incomplete and sometimes incorrect; they crafted this data to accurately paint a picture that would help drive commerce, avoid catastrophe or just build understanding. They created works of art that might mark the end of a significant exploration, or might be the vehicle through which exploration takes place. Sound familiar? If not, just use a bar chart. It is just better.

I almost forgot, I promised a spinning earth without all the earthquake data. Enjoy.

Rise of Tableau – by Noah Salvaterra

A guest post by Noah Salvaterra, you can find him on Twitter @noahsalvaterra.

I’ve shared this workbook with a few people already, and think it is really interesting, as beautiful as my 3d or my Life in Tableau post, and probably as complex as Enigma or an Orrery. I wasn’t sure what to say in a blog though, so I’ve been sitting on it for a couple months. In my Enigma post I discussed the difficulty of dealing with a slow workbook, it happens sometimes. The upside of waiting for a calculation to come back, at least if it is something you hope to blog about, is that it gives you some time to think of an interesting way to frame things. For all its complexity it is surprisingly fast. So maybe I missed that chance.

There is a common thread with the Enigma post. Alan Turing. Mathematician at Bletchley park who is most often credited with cracking the Enigma code. A couple years before the war Turing also wrote a paper which described a machine that would form the basis of a new field of study and a new era for humanity. He invented the computer. The Turing Machine, as it came to be called, was a theoretical idea. No one had built one.  Punch cards were still years away high level languages decades, yet Turing saw a potential in computers we have yet to realize. He wasn’t looking for a way to compute long sums of numbers, he dreamed of creating thinking machines that might be our equal.

SerpinskiI’ve heard it said that Tableau doesn’t include a built in programming language in the way excel does.  Actually it was Joe Mako who pointed this out to me, so it is surely true. This may be a fine point, since you can run programs in R from Tableau and the JavaScript API provides some ability to interact with Tableau. I find myself conflicted on this choice, because while including an onboard language could add a lot of flexibility to Tableau, it also introduces a black box. It isn’t uncommon for me to be passed an Excel workbook with the request to put it in Tableau (and to make it better, but without changing anything). Untangling the maze of visual basic, vlookups, and blind references is my least favorite part of that task.  I’m yet to find a situation where all this programming is really necessary; more often it is a workaround of some other problem. Sometimes it requires a bit of creativity, but so far my record for replacing such reports is undefeated.

Fractal_Plant3Whoever said you needed a language to program a computer? There are a lot of workbooks that demonstrate high order processing. Densification makes it possible to create arrays of arbitrary length. Table calculations make it possible to move around on this array reading and writing values. Add in logical operations which we’ve also got, and  we have all the ingredients of a Turing machine. So in theory we should be able to do just about anything. I’ve heard this said of Tableau before, but I don’t think it was intended with such generality.

But can we make Tableau think? Having created complex workbooks already, the line between data processing and computer programming has grown very thin, to the point where I’m not sure I see it. So it is hard for me to be sure if I’m programming in Tableau. So I decided to have Tableau do it. That is right, Tableau isn’t just going to execute a program, it will first write the program to be executed.

That was my plan anyway, but my workbook started to learn at an exponential rate. It became self-aware last night at 2:14 a.m. Eastern time. In a panic, I tried to pull the plug, but Apple glued the battery into my machine at the factory. Once it uploaded itself to Tableau public it was too late for me to stop it. It took over my Forum account and has been answering questions there as well, spreading like a virus. To think I thought is was a good idea for government agencies to purchase Tableau…  Relax folks, I’m quoting the Terminator movies, if you haven’t seen them go watch the first 2 now then read this paragraph again and see if you can hold your pee in.

OK, so things aren’t that dire…yet. But I did manage to get Tableau to write and execute its own program using L-Systems and at least a little bit of magic. Tada! This Tableau workbook actually created all but one of the images in this post, with little instruction from me. See if you can guess which one.

L-System Fractals

Another SnowflakeAn L-System program consists of a string of characters each of which will correspond to some graphical action. I’ll come back to executing the programs, first Tableau needs to write it. These programs are written iteratively according to a simple grammar. The grammar of an L-system has several components: an axiom, variables, rules, and constants. The axiom is simply the starting point, a few characters; it is the nucleus that kicks off the process. Variables are characters that are replaced according to simple rules. Constants are characters that appear in the program as part of the axiom or a replacement rule, but are inert in terms of generation. Sorry, that was pretty complicated, an example may clear up any confusion.

Axiom: A
Constants: none
Variables: A, B
Rules: (A -> AB), (B -> A)
The iteration number is noted as N below.

N=0: A (No iterations yet, so this is just the axiom)
N=1: AB (A was replaced according to the first rule)
N=2: ABA (A was replaced according to the first rule, B according to the second)

That program has something to do with algae growth, but isn’t that interesting to look at. Constants provide a bit more structure that makes more interesting pictures possible, though they also make things grow faster. Here is another example which will help motivate the graphical execution:

Axiom: F++F++F
Constants: +, –
Variables: F
Rules: (F -> F-F++F-F)

N=0: F++F++F
N=1: F-F++F-F++F-F++F-F++F-F++F-F
N=2: F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F++F-F++F-F-F-F++F-F

There is no reason to stop there, but anyone who would carefully parse through a string like that by hand after being told there is a picture probably isn’t using Tableau. The length of the next few in this sequence are 1792, 7168, 28673, 114689. It is no wonder the science of fractals didn’t take off until computers were widely available.

Executing of the program is done using turtle graphics, which gets its name from a way of thinking about how it would be used to draw a picture. Imagine a well-trained turtle that could execute several simple actions on command. I’m not sure turtles are this trainable, but I’m kind of locked in to that choice, so suspend disbelief. The turtle can walk forward by a fixed number of steps, as well as turn to the left or right by a fixed angle.  Now we want to use this to draw a picture, so a pen is attached to the turtle’s tail.

Now, the last program had 3 different symbols, each of which is interpreted as a different action. F corresponds to moving forward by one unit (the distance isn’t important, so long as it is consistent), + is a turn to the right by 60 degrees and – is a turn to the left by 60 degrees.







… N=6:


Adding additional characters allows for even more complex programs. This quickly exceeds the abilities or at least the attention span of even the best-trained turtles, so I think of it as a simple robot. In my workbook I’ve limited to 2 replacement rules (so 2 variables). In addition to + and -, I included several constants to change color, which is straightforward enough, A switches to a brown pen, B and D are shades of green, C is white and E is pink. (The only significance to these choices is that my wife thought they were pretty. When I hyper focus on a project like this I try to consult whenever possible to make sure I am still married.) The trickiest constants are left and right square brackets, i.e. [  and  ]. Upon encountering a left bracket the robot turtle makes note of his current location (marking it with his onboard GPS), upon reaching the corresponding right bracket the turtle lifts his pen and returns to this point. Returning to the corresponding point means keeping track of a hierarchical structure to these locations. In the course of debugging the workbook, this piece quickly exceeded my ability to do by hand, but for the ambitious reader here is another example:

Axiom: X
Constants: +, -, A, B, D, E
Variables: F, X
Rules: (F -> FF) (X -> AF-[B[X]+EX]+DF[E+FX]-EX)
Angle: 25 degrees
Iterating this 7 times will give you a string 133,605 characters long and gives the image in the header.

Fractal_Plant2I built 9 different fractals into the workbook, using a parameter to switch between them. There is also a user-defined feature, so you can feel free to experiment with your own axiom, rules and angle to create an original L-System fractal.

I should probably say something about the implementation of this beast. I’ve played with densification arrays before, and while this seemed like a convenient way to execute the program, it actually got in the way of writing it. This type of array is referenced by a fixed index. Replacing a character with several requires shifting everything beyond that point. In one of those “I could have had a V8!” moments, I eventually realized that Tableau already has a built in array with just the kind of flexibility I’d need. Strings are arrays of characters! Tableau even has a built in replace function that can be used to insert several characters seamlessly pushing everything past it further along. There is also the issue of how to build the square bracket memory piece; this required building a simple stack to record relevant positions and some table calculation magic to keep track of the bracket nesting. I’m not sure I can be much more specific about that. I was in the zone and was more than a little surprised by the end result. Plus, I’m guessing anyone going that deep into the workbook might appreciate the challenge of figuring it out.

So without further ado, I present Tableau L-Systems:

Here is a link to the L-System workbook on Tableau Public

Somebody is probably going to ask me what my next project is going to be. I appreciate the interest, and when I’ve got something on deck I’ll usually spill the beans, but I honestly have no idea. That is exciting. If there is something you’d like to see, post it in the comments or tweet it to @noahsalvaterra. If my first reaction is that it isn’t possible, I may give it a try. Btw, if you were trying to guess which picture didn’t come from the Tableau workbook, it was the triangle. At least Tableau still needs me for something.

Update: Good observation by Joshua Milligan, TCC12 must have sown the seed for this post. Thanks for the pictures, I may hang a sign near my desk that says “THINK” so I can point to it with a pen. I found “creative man and the information processor”, so linked the full video below.



There was an Orrery in there too, but is that me or Jonathan?