DNA can be expressed as a number, if say you wanted to upload yourself to your Tableau public account. Would you fit? There are 4 base pair possibilities, so this could be encoded in 2 bits; so with 8 bits in a byte you could store 4. There are about 3 billion base pairs in human DNA, 3 billion/4 = 750 million bytes or about 750 megabytes. So even in an uncompressed format you would fit well under the current 1GB storage limit of Tableau public! So future generations of data enthusiasts could download you as a packaged workbook, then using their advanced technology they could bring you back.
Hang on a second… can that be right? Windows 8 is at least 10GB, and it sucks; how is it I can be stored in less than 1GB? Well, there is more to you than written in your DNA, and I don’t just mean your experiences. Identical twins have the same DNA, yet they are different people. Our experiences shape who we are, but any parents of twins will tell you it is more than that. Even at birth, twins have different personalities. That could be hard to prove objectively, but they also have different fingerprints. So your DNA doesn’t dictate your fingerprints, at least not entirely. So where do they come from?
Math. DNA is already compressed pretty efficiently. Computing the number of cells in the human body isn’t strait forward but a recent journal article estimates it at 37.2 trillion. Also, that is just a count. Consider all the types of cells, their location, and connections to one another. Now that is a lot of data! Expressing this complexity as a number would be a lot trickier, and likely a lot larger (no, I’m not calling you fat).
Fractals exhibit a property that would be very useful in this type of compression. Fractals are remarkably complex structures that can result from a relatively simple set of instructions. The magic is in the process, not the underlying data, and the process can be expressed very compactly, often in a single equation.
When simple instructions create fractals or life, one byproduct seems to be similarity across different scales. Think of the branching in your blood vessels, or in a tree, smaller and smaller scale but with similar rules. If you cut off a piece of most fractals you end up with a structure that is no less complex than the original. If you zoom in, you can often see a very similar picture to the whole. There are a couple areas of math whose significance didn’t sink in for years after I studied them; fractal geometry is one such example.
Right. So how is this about Tableau? The dashboard below is driven by a dataset with only 2 rows. I guess building life might be a stretch, but it sure does look like it. For more of the details on how I’m pulling this off, as well as some other pretty images in Tableau, have a look at my post Creating data, multi-step recurrence relations, fractals and 3D imaging… without leaving Tableau. Feel free to skip to the pictures, but I do recommend 3D glasses for the last ones.
Noah, As always, wonderful work here. One question, from your Tableau Public workbook, how did you generate the image in the header?
Thanks for the question Joe, and the compliment.
The secret sauce in the header image is transparency. That image contains 2 million points with a transparency (technically opacity) of just 6%. I liked those settings for a static image, but they don’t scale very well because points get sparse as you zoom in.
Without getting tangled in the underlying math, there are two ways I envision playing with this viz. One is to zoom, increasing the number of points as needed; to investigate the similarity at different scales. The other is to tinker with the big picture by changing the number of points, transparency, point size and color to get the best looking overall image.
I went with the scalable version for the public workbook, since self-similarity was mentioned in the text; to get the best image I’d suggest downloading the workbook and relaxing the size constraints on the dashboard.
Pingback: Rise of Tableau – by Noah Salvaterra | Drawing with Numbers
Pingback: Random Adventures in Tableau - The Information Lab