[seqfan] An integer-cellular automata (in French) + PHP page

Eric Angelini Eric.Angelini at kntv.be
Tue Jan 19 14:29:44 CET 2010


Hello SeqFans (Douglas McNeil and Maximilian Hasler),
... a friend of mine, Gilles Esposito-Farèse, has build
an on-line dynamic page here:
Have fun !
(Douglas has found several gliders and this one is neat;
just copy and paste in Gilles' page, then click "engendrer")


> And my personal new favourite, with the shortest period, *and* the
only glider I've found yet which travels at faster than 1 step/period:

period 4 shift -7 glider:

<                                                   2 1247  9       >


(translation in very short):
- start generation zero with an integer, put somewhere on a single
  line of squares, one digit per square
- now (generation n+1) all digits start to move simultaneously:
  * an odd digit k moves k squares to the the left -- then is
    turned into k+1
  * an even digit j moves j squares to the the right -- then is
    turned into j+1
- a single square shows at generation n+1 the sum of the digits
  that land there -- but:
  * if a single square has to host a quantity > 9, than the 
    "special addition/carry" rule applies:

    Say that the cumulative effect of generation n produces at
    the next generation (n+1) a local situation where square
    'a' is 31, square 'b' is 28, 'c' is 5 and 'd' is empty:
    We have thus [generation n+1] : ....abcd....
    1) write on three parallel lines the 'influence' of each
       integer a, b and c
    2) give two squares to a 2-digit integer a, b or c -else only
       one- aligned on the letter's position
    According to (1) et (2), the 'influences' of a, b, c and d

    generation n+1 : ....abcd....
    image of 'a' :   ....31......
    image of 'b' :   .....28.....
    image of 'c' :   ......5.....
    Proceed to "special addition/carry" (from left to right):

    generation n+1 : ....abcd....
    image of 'a' :   ....31......
    image of 'b' :   .....28.....
    image of 'c' :   ......5.....
    SPECIAL ADDn :   ....3313....

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