I got something like the Sierpinski triangles too : http://wry.me/hacking/Turing-Drawings/#2,24,1,6,1,0,17,1,1,1...
even closer : http://www.wry.me/hacking/Turing-Drawings/#2,23,1,2,2,0,19,3...
even closer : http://www.wry.me/hacking/Turing-Drawings/#2,23,1,2,2,0,19,3...
Bonus animated brass rubbing: http://wry.me/hacking/Turing-Drawings/#4,3,1,1,2,2,1,1,3,1,0...