Suggested Credit Francisco J. Aragón Artacho, Jonathan M. Borwein, The University of Newcastle
Use plain language to answer the questions below.
Describe your entry. This picture shows a walk drawn using the first 100 billion digits of pi in base 4. At each step the path moves one unit east, north, west or south, depending on whether the corresponding digit of pi is 0, 1, 2 or 3. The color indicates the path followed by the walk: it starts at red and moves up the spectrum (red-orange-yellow-green-cyan-blue-purple-red) as the walk progresses. After 100 billion steps it is close to where it started.
The image is a 15% reduction of the original, which has a resolution of 108 gigapixels (see http://gigapan.com/gigapans/106803/), and probably is the largest mathematical picture ever plotted. It is unknown whether the digits of pi are random, although it is generally believed that they are. The picture clearly supports this conjecture: it shows a seemingly 'random' walk.
Who is the intended audience for your entry? Anyone at all interested in mathematics, or at least in pi, and certainly every mathematician.
Describe the purpose or intended use of your entry. Our objective is to show the behaviour of the first billions of digits of pi in just one picture. The walk drawn from the first 100 billion digits looks quite random, and one can easily observe some of the characteristic features of a random walk: it returns to the origin, it is space-filling, and it has a fractal-like structure.
Use plain language to explain how your entry fulfills each criterion below.
Visual Impact The picture clearly shows that the first 100 billion (10^12) digits of pi are seemingly random. The colors permit the viewer to follow easily the path made by the walk. The use of an HSV (hue, saturation and value) model with S and V equal to one yields a beautiful rainbow-like range of colors which are completely highlighted by the black background.
Effective Communication Visual tools are extremely important in this case. It is really difficult to spot any characteristic of a number just by looking at its digits. Our picture is extremely effective in showing billions of digits of pi, and just with a quick glance anyone can capture its main features.
Freshness/Originality This is probably the largest mathematical picture ever drawn, and surely the largest one made out the digits of pi—this many digits were first computed fairly recently. The research paper which contains a thumbnail of the picture was recently featured both in Wired (http://goo.gl/kOjDH) and Wired Japan (http://goo.gl/QEfZv). The computations for creating this image took roughly a month, where several parts of the algorithm were run in parallel with 20 threads on our Centre’s MacPro cluster.
Wadim Zudilin wrote:
Even in base 4, it is the true Life of Pi.
11-03-2012 11:04:34 AM
FRomo JF- wrote:
Otro pa la saca.
Un abrazo muy fuerte
11-06-2012 09:02:52 AM
Melanie James wrote:
11-07-2012 04:50:56 AM
Damara Hernandez wrote:
Cool!!! I cant wait to see how you represent an infinity dimensional hilbert space related to my dear friend Laplace!!!
11-07-2012 06:15:56 AM
Barrie Stokes wrote:
As a follower of Edward Tufte's ideas on good scientific graphics, particularly the idea of containing and contrasting a lot of information in a single image, I think this graphic must surely be an outstanding example, compressing 10^11 base 4 digits into something the eye/brain can perceive as a gestalt. Bravo!