[JimJames]

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...

[to3m]

Here are some stable ones: http://wry.me/hacking/Turing-Drawings/#4,3,0,1,3,0,2,1,3,1,2...

Bonus animated brass rubbing: http://wry.me/hacking/Turing-Drawings/#4,3,1,1,2,2,1,1,3,1,0...

[abecedarius]

The second one really looks like Rule 30 (which someone else linked to here).