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A332246 a(n) is the X-coordinate of the n-th point of the Minkowski sausage (or Minkowski curve). Sequence A332247 gives Y-coordinates.

%I A332246 #24 Feb 12 2020 16:17:43
%S A332246 0,1,1,2,2,2,3,3,4,4,3,3,4,5,5,4,4,5,5,6,6,6,7,7,8,8,9,9,8,7,7,8,8,8,
%T A332246 9,9,8,7,7,8,8,9,9,10,10,10,11,11,12,12,11,11,12,13,13,12,12,13,13,14,
%U A332246 14,14,15,15,16,16,15,15,16,17,17,16,16,15,15,14
%N A332246 a(n) is the X-coordinate of the n-th point of the Minkowski sausage (or Minkowski curve). Sequence A332247 gives Y-coordinates.
%C A332246 This sequence is the real part of {f(n)} defined as:
%C A332246 - f(0) = 0,
%C A332246 - f(n+1) = f(n) + i^t(n)
%C A332246   where t(n) is the number of 1's and 6's minus the number of 3's and 4's
%C A332246              in the base 8 representation of n
%C A332246     and i denotes the imaginary unit.
%C A332246 We can also build the curve by successively applying the following substitution to an initial vector (1, 0):
%C A332246                         .--->.
%C A332246                         ^    |
%C A332246                         |    v
%C A332246                    .--->.    .    .--->.
%C A332246                              |    ^
%C A332246                              v    |
%C A332246                              .--->.
%H A332246 Rémy Sigrist, <a href="/A332246/b332246.txt">Table of n, a(n) for n = 0..4096</a>
%H A332246 Robert Ferréol (MathCurve), <a href="https://www.mathcurve.com/fractals/minkowski/minkowski.shtml">Saucisse de Minkowski</a> [in French]
%H A332246 Rémy Sigrist, <a href="/A332246/a332246.png">Representation of the first 1+8^4 points of the Minkowski sausage</a>
%H A332246 Wikipedia, <a href="https://en.wikipedia.org/wiki/Minkowski_Sausage">Minkowski sausage</a>
%H A332246 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A332246 a(8^k-m) + a(m) = 4^k for any k >= 0 and m = 0..8^k.
%o A332246 (PARI) { dd = [0,1,0,-1,-1,0,1,0]; z=0; for (n=0, 75, print1 (real(z)", "); z += I^vecsum(apply(d -> dd[1+d], digits(n, #dd)))) }
%Y A332246 See A163528, A323258 and A332204 for similar sequences.
%Y A332246 Cf. A332247 (Y-coordinates).
%K A332246 nonn,base
%O A332246 0,4
%A A332246 _Rémy Sigrist_, Feb 08 2020