Greetings from The On-Line Encyclopedia of Integer Sequences
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Displaying 1-1 of 1 results found. page 1 short internal text references ... off L1 ('city-block') distances from the origin to a 2D random walk based on the digits of pi.
list graph listen OFFSET COMMENT The distance from the starting point has physical applications, eg, in aggregation models. All distance metrics generate sequences which coincide at the zero points. The L1 (city-block) metric is the simplest and is intrinsically integer valued on integer-spaced lattices (as used here). The r sequence is not affected by the dimension ordering (i.e. whether each pair of values taken from the digits of pi represents [x,y] or [y,x]). LINKS Hemphill, Scott, Pi (gives 1.25 million digits of pi) Eric Weisstein's World of Mathematics, Pi Digits. FORMULA r(n) = abs(cx(n)) + abs(cy(n)), where cx = cum_sum([odd digits of pi] - 4.5) and cy = cum_sum([even digits of pi] - 4.5). EXAMPLE The first 10 digits of pi are: 3 1 4 1 5 9 2 6 5 3 This gives five 2-tuples (x,y pairs): [3 1], [4 1], [5 9], [2 6], [5 3] | |
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