wolframscience.com

A New Kind of Science: The NKS Forum : Powered by vBulletin version 2.3.0 A New Kind of Science: The NKS Forum > Pure NKS > How to solve a CA with algebra
  Last Thread   Next Thread
Author
Thread Post New Thread    Post A Reply
alan2here


Registered: Oct 2007
Posts: 12

How to solve a CA with algebra

I'm not sure if this is my method or an obvious algebraic method or even if it definitely works but here goes.

It's based on something similar I did for Minesweeper that did work, inspired by something I read online about suprisingly long distance behaviour in certain Minesweeper configuations.

Start with a simple example from WireWorld.
http://mathworld.wolfram.com/WireWorld.html
An amazing CA, LifeLike and Generations CA's should work in a simerlar way though.

Lets say for simplicity:

000
133
000

According to the rules of WireWorld this will progress as so.

000
213
000

000
321
000

000
332
000

000
333
000

As the signal travels down the wire

First create (a map?) for each state that changes.

All
000
133
000

State 1
000
100
000

State 2
000
000
000

And assign letters to each cell in each map.

All
abc
def
ghi

State 1
rst
uvw
xyz

State 2
ABC
DEF
GHI

Construct the formuli

(I'm using square brackets here to represent subscript as I don't know how to do that formatting in the forum)

a[0] = 0
...
I[0] = 0

Skip a to i for this next part.

r[n] = (0 < s[n-1] + u[n-1] + v[n-1] < 3)
...
I...

Now you can rearange the equation to ask questions like for example, does this cell EVER become state 1 or what are all the possiblilites for the previous generation that could lead to this one.

Report this post to a moderator | IP: Logged

Old Post 05-27-2009 09:02 PM
alan2here is offline Click Here to See the Profile for alan2here Visit alan2here's homepage! Edit/Delete Message Reply w/Quote
Post New Thread    Post A Reply
  Last Thread   Next Thread
Show Printable Version | Email this Page | Subscribe to this Thread


 

wolframscience.com  |  wolfram atlas  |  NKS online  |  web resources  |  contact us

Forum Sponsored by Wolfram Research

© 2004-14 Wolfram Research, Inc. | Powered by vBulletin 2.3.0 © 2000-2002 Jelsoft Enterprises, Ltd. | Disclaimer | Archives