new.db

query.sql

WITH consts AS (
  SELECT
    8 AS n,                      -- number of iterations
    500 AS l,                    -- width & height of image
    0.7265425280053609 AS tan36, -- tan(π/5)
    0.6180339887498948 AS d      -- 1/φ
), tiles (p, i, t, px, py, qx, qy, rx, ry, sx, sy, tx, ty) AS (
  SELECT 0, n, 1, -l/tan36, 0, 0, l, l/tan36, 0, 0, 0, 0, 0 FROM consts
  UNION ALL SELECT 1, i-1, t, px, py, qx, qy, rx, ry, (qx-px)*d+px, (qy-py)*d+py, (rx-px)*d+px, (ry-py)*d+py
    FROM tiles, consts WHERE p = 0 and i > 0
  UNION ALL SELECT 0, i, 0, rx, ry, sx, sy, qx, qy, 0, 0, 0, 0 FROM tiles, consts WHERE p = 1 and t = 0
  UNION ALL SELECT 0, i, 1, rx, ry, sx, sy, px, py, 0, 0, 0, 0 FROM tiles, consts WHERE p = 1 and t = 0
  UNION ALL SELECT 0, i, 1, tx, ty, sx, sy, px, py, 0, 0, 0, 0 FROM tiles, consts WHERE p = 1 and t = 1
  UNION ALL SELECT 0, i, 0, tx, ty, sx, sy, qx, qy, 0, 0, 0, 0 FROM tiles, consts WHERE p = 1 and t = 1
  UNION ALL SELECT 0, i, 1, rx, ry, tx, ty, qx, qy, 0, 0, 0, 0 FROM tiles, consts WHERE p = 1 and t = 1
)
SELECT (SELECT printf('<'||'svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="%d" height="%d" viewBox="%d %d %d %d"><'||'g id="t">', l, l, -l/2, -l/2, l, l) FROM consts)
||(SELECT group_concat(g, char(10)) FROM
  (SELECT printf('<'||'g stroke="#044a64" stroke-width="0.3" stroke-linejoin="bevel" fill="%s">%s<'||'/g>',
    CASE t WHEN 0 THEN '#044a64' ELSE '#fff' END,
    group_concat(printf('<'||'path d="M%f %fL%f %fL%f %fz"/>', px, py, qx, qy, rx, ry), char(10))
  ) as g
  FROM tiles WHERE p = 0 and i = 0 GROUP BY t)
)||'<'||'/g><'||'use xlink:href="#t" transform="scale(1 -1)"/><'||'/svg>'
as svg;

result.svg

schema.sql

BEGIN TRANSACTION;
PRAGMA writable_schema=ON;
PRAGMA writable_schema=OFF;
COMMIT;