There is a better reason why one-dimensional automata are interesting than the Sierpinski triangle and the Rule-90 (90 is the decimal representation of 01011010) responsible for its creation. This reason is the Rule-110 (01101110). In the 1990's Matthew Cook, a research assistant of Stephen Wolfram proved that Rule-110 is (drumroll, please!) Turing-complete. That's right, folks, these eight extremely simple rules, combined with an infinite one-dimensional strip, form a universal Turing machine, capable of answering any answerable question and simulating the whole Universe, including every one of us with arbitrary precision, given the right input.

Before Rule-110 was found, the simpliest universal Turing machine required not 8, but 28 rules. It is possible, though, that an even simplier machine with 6 rules is possible.

Now behold the beauty, greatness and simplicity of the Rule-110.

```Values at t:      111 110 101 100 011 010 001 000
--- --- --- --- --- --- --- ---
Value at t + 1:    0   1   1   0   1   1   1   0

t = 1:                                         *
**
***
** *
*****
**   *
***  **
** * ***
******* *
t = 10:                               **     ***
***    ** *
** *   *****
*****  **   *
**   * ***  **
***  **** * ***
** * **  ***** *
******** **   ***
**      ****  ** *
***     **  * *****
t = 20:                     ** *    *** ****   *
*****   ** ***  *  **
**   *  ***** * ** ***
***  ** **   ******** *
** * ******  **      ***
*******    * ***     ** *
**     *   **** *    *****
***    **  **  ***   **   *
** *   *** *** ** *  ***  **
*****  ** *** ****** ** * ***
t = 30:           **   * ***** ***    ******** *
***  ****   *** *   **      ***
** * **  *  ** ***  ***     ** *
******** ** ***** * ** *    *****
**      ******   ********   **   *
***     **    *  **      *  ***  **
** *    ***   ** ***     ** ** * ***
*****   ** *  ***** *    ********** *
**   *  ***** **   ***   **        ***
***  ** **   ****  ** *  ***       ** *
t = 40: ** * ******  **  * ***** ** *      *****
```

I can go on an on, but if you really want to see a lot of generations, like a few billions, get Mathematica and try it yourself with different inputs.

Further watching: a MIT lecture by Stephen Wolfram, available for download at http://mitworld.mit.edu/video/149/ (fast forward to 46th minute for the discussion of Rule-110)