%I #23 Feb 07 2021 09:49:03
%S 0,1,1,0,-1,0,1,2,3,3,3,2,2,1,1,0,-1,-2,-1,0,0,-1,-2,-3,-2,-2,-3,-4,
%T -4,-3,-3,-4,-5,-4,-3,-2,-1,-1,-2,-3,-2,-1,0,0,1,2,2,1,2,3,4,4,3,2,3,
%U 4,5,6,6,6,5,5,4,4,5,5,5,4,4,3,3,2,1,0,1,2,2,1,1
%N a(n) is the X-coordinate of the n-th point of Gosper's flowsnake curve; sequence A334486 gives Y-coordinates.
%C Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:
%C Y
%C /
%C /
%C 0 ---- X
%C The Gosper curve can be represented using an L-system.
%H Rémy Sigrist, <a href="/A334485/b334485.txt">Table of n, a(n) for n = 0..2401</a>
%H Rémy Sigrist, <a href="/A334485/a334485.png">Colored scatterplot of the first 7^7+1 points of the Gosper curve</a> (where the hue is function of the number of steps from the origin; the origin is located on the right side, at the black mark)
%H Rémy Sigrist, <a href="/A334485/a334485.gp.txt">PARI program for A334485</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gosper_curve">Gosper curve</a>
%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%e The Gosper curve starts (on a hexagonal lattice) as follows:
%e . . . . . +---+---+ . . . .
%e \ \
%e . . +---+---+ +---+ + . . . .
%e \ \ / /
%e . . . +---+ +---+ + +---+ . .
%e / \ \ \
%e . . +---+ +---+---+ + + + . .
%e / \ \ \ / 49
%e . . + +---+ +---+ + + . . .
%e \ \ \ / /
%e . . + + +---+ + +---+ . . .
%e \ / \ / /10
%e . . . + +---+---+ + + . . .
%e 25 \ \ /9
%e . . . . +---+ +---+ . . . .
%e / 7 8
%e . . . . +---+ . . . . . .
%e 0 1
%e - hence a(8) = a(9) = a(10) = a(50) = 3.
%o (PARI) See Links section.
%Y Cf. A334486 (Y coordinate), A229214 (directions +-1,2,3), A261180 (directions 0..5).
%K sign,look
%O 0,8
%A _Rémy Sigrist_, May 03 2020