```
\\ Copyright 2015 Kevin Ryde
\\ This file is part of Math-PlanePath.
\\
\\ Math-PlanePath is free software; you can redistribute it and/or modify it
\\ under the terms of the GNU General Public License as published by the Free
\\ Software Foundation; either version 3, or (at your option) any later
\\ version.
\\
\\ Math-PlanePath is distributed in the hope that it will be useful, but
\\ WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
\\ or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
\\ for more details.
\\
\\ You should have received a copy of the GNU General Public License along
\\ with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
\\ This is a bit of fun drawing the flowsnake in ascii art for
\\ http://codegolf.stackexchange.com/questions/50521/ascii-art-of-the-day-2-flow-snakes
\\ ____
\\ ____ \__ \
\\ \__ \__/ / __
\\ __/ ____ \ \ \ ____
\\ / __ \__ \ \/ / __ \__ \
\\ ____ \ \ \__/ / __ \/ / __/ / __
\\ ____ \__ \ \/ ____ \/ / __/ / __ \ \ \
\\ \__ \__/ / __ \__ \__/ / __ \ \ \ \/
\\ __/ ____ \ \ \__/ ____ \ \ \ \/ / __
\\ / __ \__ \ \/ ____ \__ \ \/ / __ \/ /
\\ \ \ \__/ / __ \__ \__/ / __ \ \ \__/
\\ \/ ____ \/ / __/ ____ \ \ \ \/ ____
\\ \__ \__/ / __ \__ \ \/ / __ \__ \
\\ __/ ____ \ \ \__/ / __ \/ / __/ / __
\\ / __ \__ \ \/ ____ \/ / __/ / __ \/ /
\\ \/ / __/ / __ \__ \__/ / __ \/ / __/
\\ __/ / __ \ \ \__/ ____ \ \ \__/ / __
\\ / __ \ \ \ \/ ____ \__ \ \/ ____ \/ /
\\ \ \ \ \/ / __ \__ \__/ / __ \__ \__/
\\ \/ / __ \/ / __/ ____ \ \ \__/
\\ \ \ \__/ / __ \__ \ \/
\\ \/ \ \ \__/ / __
\\ \/ ____ \/ /
\\ \__ \__/
\\ __/
\\
\\ Each hexagon of the flowsnake is 2 characters and a line segment does
\\ across its corners either by __, / or \. The loop goes over x,y and
\\ calculates which of these to show at each location. Only moderate
\\ attempts at minimizing.
\\
\\ The code expresses a complex number z in base b=2+w and digits 0, 1, w^2,
\\ ..., w^5, where w=e^(2pi/6) sixth root of unity. Those digits are kept
\\ just as a distinguishing 1 to 7 then taken high to low for net rotation.
\\
\\ This is in the style of Ed Shouten's http://80386.nl/projects/flowsnake/
\\ (xytoi) but only for net rotation, not making digits into an "N" index
\\ along the path.
\\
\\ The extents calculated are relative to an origin 0 at the centre of the
\\ shape (not the start of the curve as in Math::PlanePath::Flowsnake). The
\\ vecmin()/vecmax() calculate with centre of the little hexagons. Segments
\\ other than the start and end are always / or \ and so go only to that
\\ centre. But if the curve start or end are the maximum or minimum then
\\ they are the whole hexagon so a +1 is needed. This only occurs for k=0
\\ for X minimum and k<3 for the X maximum.
\\
\\ Pari has "quads" like sqrt(-3) builtin but the same can be done with real
\\ and imaginary parts separately.
k=3;
{
S = quadgen(-12); \\ sqrt(-3)
w = (1 + S)/2; \\ sixth root of unity
b = 2 + w; \\ base
\\ base b low digit position under 2*Re+4*Im mod 7 index
P = [0, w^2, 1, w, w^4, w^3, w^5];
\\ rotation state table
T = 7*[0,0,1,0,0,1,2, 1,2,1,0,1,1,2, 2,2,2,0,0,1,2];
C = ["_","_", " ","\\", "/"," "];
\\ extents
X = 2*sum(i=0,k-1, vecmax(real(b^i*P)));
Y = 2*sum(i=0,k-1, vecmax(imag(b^i*P)));
for(y = -Y, Y,
for(x = -X+!!k, X+(k<3), \\ adjusted when endpoint is X limit
z = (x- (o = (x+y)%2) - y*S)/2;
v = vector(k,i,
z = (z - P[ d = (2*real(z) + 4*imag(z)) % 7 + 1 ])/b;
d);
print1( C[if(z,3,
r = 0;
forstep(i=#v,1, -1, r = T[r+v[i]];);
r%5 + o + 1)]) ); \\ r=0,7,14 mod 5 is 0,2,4
print())
}
```