you can zoom into this huge image of a random walk based on the first 100 billion base-4 digits of pi 3.141... infinity: Rich Murray 2014.03.15
URL: http://friam.383.s1.nabble.com/you-can-zoom-into-this-huge-image-of-a-random-walk-based-on-the-first-100-billion-base-4-digits-of-p5-tp7585090.html
Sweet and gentle sensitive man/With an obsessive nature and deep fascination/For numbers/And a complete infatuation with the calculation/Of Pi.
Our slice of pi
A fruitful new approach is to display the digits of pi or other constants graphically, cast as a random walk.
The first plot below shows a walk based on one million base-4 pseudorandom digits generated by a computer, where at each step the graph moves one unit east, north, west or south, depending on the whether the pseudorandom base-4 digit at that position is 0, 1, 2 or 3.
The colour indicates the path followed by the walk, coloured by a standard hue-saturation-value scheme that produces a rainbow of colours.
The next figure shows a walk on the first 100 billion base-4 digits of pi. This may be viewed dynamically in more detail online at the Gigapan site, where the full-sized image has a resolution of 372,224 x 290,218 pixels (108.03 billion pixels in total).
This is one of the largest mathematical images ever produced and, needless to say, its production was by no means easy (see this paper for technical details).
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