drawing dragon curve in SQL

dc.svg

dc1s.svg

dragon-curve-one-stroke.sql

/*
**requires SQLite version 3.44.0 or higher**

make db:
$ sqlite3 dc1s.db < dragon-curve-one-stroke.sql

usage:
$ echo 'update param set n=15; select * from dragon_curve;' | sqlite3 dc1s.db > dc1s.svg
 */

create table param as select 12 as n;
create view dragon_curve as
with r(i, o, sx, sy, ex, ey) as (
  select n, 0, 0.0, 0.0, 1.0, 0.0 from param
  union all select i-1, o*2, sx, sy, (sx+ex+(sy-ey)*(1-o%2*2))/2, ((ex-sx)*(1-o%2*2)+sy+ey)/2 from r where i > 0
  union all select i-1, o*2+1, (sx+ex+(sy-ey)*(1-o%2*2))/2, ((ex-sx)*(1-o%2*2)+sy+ey)/2, ex, ey from r where i > 0
)
select
  '<svg xmlns="http://www.w3.org/2000/svg" width="960" height="640" viewBox="-100 -100 450 300">'
  || '<path stroke="#093" stroke-width="0.25" fill="none" d="M 0 0'
  || group_concat(printf(' L %s %s', ex*256, ey*256), '' order by o)
  || '"/></svg>'
from r where i = 0;

dragon-curve.sql

/*
make db:
$ sqlite3 dc.db < dragon-curve.sql

usage:
$ echo 'update param set n=15; select * from dragon_curve' | sqlite3 dc.db > dc.svg
 */

create table param as select 12 as n;
create view dragon_curve as
with r(i, sx, sy, ex, ey) as (
  select n, 0.0, 0.0, 1.0, 0.0 from param
  union all select i-1, (sx-sy)/2, (sx+sy)/2, (ex-ey)/2, (ex+ey)/2 from r where i > 0
  union all select i-1, 1-(sx+sy)/2, (sx-sy)/2, 1-(ex+ey)/2, (ex-ey)/2 from r where i > 0
)
select '<svg xmlns="http://www.w3.org/2000/svg" width="960" height="640" viewBox="-100 -100 450 300">'
union all select '<g stroke="#093" stroke-width="0.25">'
union all select printf('<path d="M %s %s L %s %s"/>', sx*256, sy*256, ex*256, ey*256)
from r where i = 0
union all select '</g></svg>';