A T-SQL implementation of Sierpinski's Triangles, just to see if I could do it.

sierpinskis_tri.sql

/*
 Description: A T-SQL implementation of Sierpinski's Triangles, just to see if I could do it.
 Requires: SQL Server 2012
 Inspired by:  Alastair Aitchison SQLCLR implementation http://alastaira.wordpress.com/2012/03/06/drawing-fractals-with-sql-server-spatial/ 
 Author: Matthew Naul
*/
DECLARE 
 @itrations INT = 12,
 @seed geometry = geometry::STGeomFromText ('LINESTRING (9 12, 0 0, 18 0, 9 12)',0);
 
WITH SierpinskiTriangle(lvl,[Ax],[Ay],[Bx],[By],[Cx],[Cy], shape) AS (
 SELECT
  1 lvl,
  base.[Ax], base.[Ay],
  base.[Bx], base.[By],
  base.[Cx], base.[Cy],
  CONCAT('MULTIPOLYGON( (( ', [Ax],' ',[Ay],',',
         [Bx],' ',[By],',',
         [Cx],' ',[Cy],',',
         [Ax],' ',[Ay],')) )') as shape
 FROM (
  SELECT 
   @seed.STPointN(1).STX as [Ax], @seed.STPointN(1).STY as [Ay],
   @seed.STPointN(2).STX as [Bx], @seed.STPointN(2).STY as [By],
   @seed.STPointN(3).STX as [Cx], @seed.STPointN(3).STY as [Cy]
 ) AS base
UNION ALL
 SELECT
  itr.lvl+1 AS lvl,
  new.[Ax], new.[Ay],
  new.[Bx], new.[By],
  new.[Cx], new.[Cy],
  CONCAT('MULTIPOLYGON( (( ', new.[Ax],' ',new.[Ay],',',
         new.[Bx],' ',new.[By],',',
         new.[Cx],' ',new.[Cy],',',
         new.[Ax],' ',new.[Ay],')) )') as shape
 FROM SierpinskiTriangle AS itr
 CROSS APPLY(
  SELECT
   (itr.[Bx] + itr.[Cx]) * .5 as [A0x], (itr.[By] + itr.[Cy]) *.5 as [A0y],
   (itr.[Cx] + itr.[Ax]) * .5 as [B0x], (itr.[Cy] + itr.[Ay]) *.5 as [B0y],
   (itr.[Ax] + itr.[Bx]) * .5 as [C0x], (itr.[Ay] + itr.[By]) *.5 as [C0y]
 ) AS mid
 CROSS APPLY(
  SELECT 1, itr.[Ax] , itr.[Ay] , mid.[C0x], mid.[C0y], mid.[B0x], mid.[B0y] UNION ALL
  SELECT 2, mid.[C0x], mid.[C0y], itr.[Bx] , itr.[By] , mid.[A0x], mid.[A0y] UNION ALL
  SELECT 3, mid.[B0x], mid.[B0y], mid.[A0x], mid.[A0y], itr.[Cx] , itr.[Cy] 
 ) AS  new(number, [Ax], [Ay], [Bx], [By], [Cx], [Cy])
 
 WHERE
  ([A0x] > .00001 ) and --triagnel with inside geometry type error. Too small, bail
  itr.lvl < @itrations
)
 
SELECT
   sys.GeometryUnionAggregate(geometry::STMPolyFromText(shape,0))
FROM
 SierpinskiTriangle
WHERE
 lvl = @itrations