Wolfram Rule 90 Computer

  • Mur
    27th Apr 2015 Member 6 Permalink

    During the past few days I've made a machine that computes Wolfram's Rule 90 elementary cellular automaton:

    I chose Rule 90 mainly because of it's simplicity: it is possible to implement it with only one XOR gate per cell, and wires coming from only two cells. This also makes it possible to fit a large number of cells (50x40 in this version) within TPT's screen. Here's a schematic diagram showing how it works:

     

    Schematic

     

    The inputs of each XOR gate are connected to the upper-left and upper-right cell outputs, and the cell right above it is ignored. When one presses the "start" button, the first row, i.e. the "seed" row, is read and sent to the lower row. Each cell then XOR's the coming inputs, thus setting the state to 1 or 0:

    Left Right Result
    0 0 0
    0 1 1
    1 0 1
    1 1

    0

     

    ...the result is also sent to next lower row of cells, and the process repeats itself, until the calculation is complete (i.e. no more cells can be changed, or the screen limit has been reached).

     

    Okay, but where's the fun? Well, the main interest of Rule-90 is the neat Sierpinski triangle it produces when fed only one "on" cell in the seed:

     

    Sierpi?ski

     

    You may note that if you try to make a Sierpinski triangle in the center of the display, this happens:

     

    broken

     

    After the edges of the triangle hit the borders of the screen, it becomes "broken". That is perfectly normal, because the borders of the screen are always "0"s and cannot be set to a different state, unlike "real" cellular automata programs, in which the borders can (theoretically) grow endlessly, according to need.

     

    Usage:

    - Press the yellow buttons on the top to set the initial pattern (seed);

    - Press the "start" button to begin calculation;

    - ???;

    - Profit!

     

    The other buttons do exactly what they say: "random seed" randomizes the seed, "reset seed" resets the initial pattern and "clear display" explodes the whole thing clears the display. That's all.

     

    Also, I suggest you to try the following seed: 110110...11011

     

    More info about Wolfram's Rule 90: http://en.wikipedia.org/wiki/Rule_90

     

    Thanks to:

    @mniip 's deco style in their 1-D celullar automaton, and the machine itself, which inspired me;

    @mecha-man for their WireWorld ultra-compact XOR gate, without which, the realization of this machine would not have been entirely possible.

    Edited 5 times by Mur. Last: 27th Apr 2015
  • NF
    27th Apr 2015 Member 2 Permalink

    @Mur (View Post)

     I thought you died from cancer ... *FACEPALMS* 

    Edited once by NUCLEAR_FOX. Last: 27th Apr 2015
  • Mur
    27th Apr 2015 Member 1 Permalink

    @NUCLEAR_FOX (View Post)

     Seriously? It was Merbo who died...

    Edited once by Mur. Last: 27th Apr 2015
  • CeeJayBee
    27th Apr 2015 Member 2 Permalink
  • NF
    27th Apr 2015 Member 0 Permalink

    @Mur (View Post)

     *FACEPALMS again.* My mistake no need to flip out. Great save though +1 for greatness!

    @CeeJayBee (View Post)

     ...

    Edited 2 times by NUCLEAR_FOX. Last: 27th Apr 2015
  • mniip
    28th Apr 2015 Developer 1 Permalink
    @Mur (View Post)
    Inspired by this, I made my own, more compact and robust :P


    Bonus: rule 150:
  • Mur
    28th Apr 2015 Member 0 Permalink

    @mniip (View Post)

     Nice =o it has less than half particles as mine...and the cells are toggleable...make Rule 110 NAO

    ...and I should learn how to use the magic of CRAY, DTEC, etc.

    Edited 3 times by Mur. Last: 28th Apr 2015