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PostGIS Mandelbrot
with recursive
dims (r1, r2, i1, i2, s, it, p) as (values (-2::float, 1::float, -1.5::float, 1.5::float, 0.01::float, 100, 256.0::float)),
sprites (s) as (values (st_makepolygon(st_geomfromtext('linestring (0 0, 0 1, 1 1, 1 0, 0 0)')))),
n1 (r, i) as (select r, i from dims, generate_series((r1 / s)::int, (r2 / s)::int) r, generate_series((i1 / s)::int, (i2 / s)::int) i),
n2 (r, i) as (select r::float * s::float, i::float * s::float from dims, n1),
l (cr, ci, zr, zi, g, it, p) as (
select r, i, 0::float, 0::float, 0, it, p from n2, dims
union all
select cr, ci, zr*zr - zi*zi + cr, 2 * zr * zi + ci, g + 1, it, p from l where g < it and zr*zr + zi*zi < p
x (cr, ci, zr, zi, g) as (
select distinct on (cr, ci) cr, ci, zr, zi, g
from l
order by cr, ci, g desc
select st_union(st_translate(sprites.s, round(cr / dims.s), round(ci / dims.s)))
from x, sprites, dims
where zr*zr + zi*zi > p
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