This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309384 #19 Dec 13 2021 23:34:30 %S A309384 0,1,2,3,4,5,6,7,8,7,8,9,10,11,12,11,10,11,12,13,14,15,14,13,14,15,16, %T A309384 17,18,19,20,21,20,21,22,23,24,25,24,23,24,25,26,25,24,25,26,27,28,29, %U A309384 28,29,30,29,30,31,30,31,32,33,34,35,34,35,36,37,36,37 %N A309384 Number of black squares after n moves of a variant of Langton's ant with turns of 45 degrees. %C A309384 Initially, all squares are white, and the ant is at the origin and oriented towards the east. The ant can travel horizontally or vertically (in any of the four cardinal directions) and diagonally (in any of the four intercardinal directions). %C A309384 At a white square, the ant turns 45 degrees left, flips the color of the square and moves forward. %C A309384 At a black square, the ant turns 45 degrees right, flips the color of the square and moves forward. %C A309384 As in the original variant, the ant eventually builds a recurrent highway pattern, in the present case of 196 steps. %H A309384 Rémy Sigrist, <a href="/A309384/b309384.txt">Table of n, a(n) for n = 0..10000</a> %H A309384 Rémy Sigrist, <a href="/A309384/a309384.png">Representation of the squares visited during the first 100000000 moves</a> (the dark squares are the most visited) %H A309384 Rémy Sigrist, <a href="/A309384/a309384_1.png">Representation of the grid after 1021259426 steps</a> %H A309384 Rémy Sigrist, <a href="/A309384/a309384.gp.txt">PARI program for A309384</a> %H A309384 Wikipedia, <a href="https://en.wikipedia.org/wiki/Langton's_ant">Langton's ant</a> %F A309384 a(n + 196) = a(n) + 72 for n >= 1021254426. %e A309384 The first positions of the ant are: %e A309384 . . 4 3 . . . . %e A309384 . 5 . . 2 . . . %e A309384 . 6 . . 1 . . . %e A309384 . . 7 0,8 . . 11 . %e A309384 . . . . 9 10 . . %o A309384 (PARI) See Links section. %Y A309384 Cf. A255938. %K A309384 nonn %O A309384 0,3 %A A309384 _Rémy Sigrist_, Jul 27 2019