Mandelbrot rendering implemented in SQL

mandelbrot.sql

WITH RECURSIVE
  -- First, we define the grid we are working on
  xaxis(x) AS (VALUES(-2.0) UNION ALL SELECT x+0.05 FROM xaxis WHERE x<0.5),
  yaxis(y) AS (VALUES(-1) UNION ALL SELECT y+0.1 FROM yaxis WHERE y<1),
  -- Then we compute the iterations of the mandelbrot function
  iterations(iter, cx, cy, x, y) AS ( -- one value per iteration step per point 
    SELECT 0, x, y, 0.0, 0.0 FROM xaxis, yaxis -- c = cx + i * cy
    UNION ALL
    SELECT iter+1, cx, cy, x*x-y*y + cx, 2.0*x*y + cy -- z(iter+1) = z(iter)^2 + c. x=Re(z(iter+1)), y=Im(z(iter+1)) 
    FROM iterations 
     WHERE (x*x + y*y) < 4 AND iter<50 -- if z(n)^2 >= 4, we diverged
  ),
  max_iter(iter, cx, cy) AS ( -- the number of iterations it takes to diverge for each point
    SELECT max(iter), cx, cy FROM iterations GROUP BY cx, cy
  ),
  lines(t) AS (
    -- For the values of c where the function does not diverge, we made 50 iterations
    SELECT group_concat(case iter when 50 then '*' else ' ' end, '')
    FROM max_iter GROUP BY cy
  )
SELECT group_concat(t,x'0a') as mandelbrot FROM lines;

-- source: https://sqlite.org/lang_with.html
-- changed the table names and added comments to make the code clearer