Triangles Everywhere

After seeing the Mandelbrot fractal implemented in SQL and drawn as ASCII art. I wanted to see if anyone had implemented any fractals with the Geometry datatype. The closest that I found was Drawing Fractals with SQL Server Spatial by Alastair Aitchison. Which is a nice example Sierpinski triangle fractal as a CLR function, but I wanted to see if I could I could do it in pure SQL.
Let me know if you have suggestions for making it go faster