[pleion]

I designed a system of cellular automata based around this idea of colliding lines. You can play with it at http://sciencevsmagic.net/logicgrid

The XOR Sierpinksi's triangle is at http://sciencevsmagic.net/logicgrid/#282800 but there are other ways make it too. For example XNOR makes an inverse http://sciencevsmagic.net/logicgrid/#828200

If you keep hitting random you'll find plenty of surprising analogues to Sierpinksi's.