Brad, Thanks for answering (on April 26) my questions about the period length of rule 30, etc. I've just created sequences A334496, A334497, and A334501-A334515 as a result of your reply. If we start with a single ON cell, with any of the 256 rules, in a cyclic universe of width n, many of the resulting sequences are uninteresting, many others are duplicates, many more were already in the OEIS, which left A33449 and A334501-A334515. They all just have the 10 terms that you calculated, so all 16 of them need more terms, in case anyone would like to extend them. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sun, Apr 26, 2020 at 4:52 PM Brad Klee <bradklee@gmail.com> wrote:
Bill mentioned this last year Oct. 1 in a thread "The Rule 30 Prizes are Launched!"
I did the following search of OEIS:
https://oeis.org/search?q=rule+period+cellular+automaton&sort=&language=engl... "
and found: https://oeis.org/A180001, probably the closest entry to what you are looking for. The code can be generalized to Rule 30 by adding one variable:
a[rule_, n_] := -Subtract @@ Flatten[Map[ Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[rule], Prepend[Table[0, {n - 1}], 1], Unequal, All], {0}]]
In[36]:= a[30, #] & /@ Range[10] Out[36]= {1, 1, 1, 8, 5, 1, 4, 40, 72, 15}
This sequence does not appear to be in OEIS.
It is also possible to map over all 255 rules: In[40]:= Outer[a[#1, #2] &, Range[0, 255], Range[10]] Out[40]= https://0x0.st/ijnD.txt
To get the true max period, you need to search over initial conditions:
a[rule_, init_] := -Subtract @@ Flatten[Map[ Position[#, #[[-1]]] &, NestWhileList[CellularAutomaton[rule], init, Unequal, All], {0}]] tri[n_] := a[30, #] & /@ Tuples[{0, 1}, n];
In[61]:= tri /@ Range[7] Max /@ %
Out[61]= {{1, 1}, {1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1}, {1, 8, 8, 8, 8, 1, 8, 8, 8, 8, 1, 8, 8, 8, 8, 1}, {1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 4, 4, 63, 4, 63, 63, 4, 4, 4, 63, 63, 63, 63, 4, 63, 4, 4, 4, 4, 63, 63, 63, 63, 63, 4, 63, 63, 4, 63, 63, 4, 4, 63, 4, 63, 4, 63, 4, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 4, 63, 63, 63, 63, 4, 4, 63, 63, 4, 63, 63, 4, 4, 4, 63, 63, 4, 4, 63, 63, 63, 4, 4, 63, 63, 4, 63, 63, 4, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 4, 63, 4, 63, 4, 63, 4, 63, 63, 4, 63, 63, 4, 63, 63, 63, 63, 63, 4, 4, 4, 4, 63, 63, 4, 63, 63, 4, 4, 63, 4, 63, 4, 4, 4, 4, 1}}
Out[62]= {1, 1, 1, 8, 5, 1, 63}
It looks like n=7 is the first time that the max period disagrees with the period of the usual one-ON initial condition. Too easy.
--Brad
On Sun, Apr 26, 2020 at 1:04 PM Neil Sloane <njasloane@gmail.com> wrote:
Bill Gosper's link led me eventually to Stephen Wolfram's web age about the "Rule 30" prizes.
https://writings.stephenwolfram.com/2019/10/announcing-the-rule-30-prizes/
In that page there is a section that begins like this:
"Here’s something else, that may be confusing, or may be helpful. The
Rule
30 Prize Problems all concern rule 30 running in an infinite array of cells. But what if one considers just *n* cells <
https://www.wolframscience.com/nks/p255--systems-of-limited-size-and-class-2...
, say with the periodic boundary conditions (i.e. taking the right neighbor of the rightmost cell to be the leftmost cell, and vice versa)? There are 2^ *n* possible total states of the system—and one can draw a state transition diagram <
https://www.wolframscience.com/nks/notes-6-7--state-networks-for-systems-of-...
that shows which state evolves to which other. Here’s the diagram for *n* = 5: ..."
Me: So take a cylinder of perimeter n, say Z/nZ X N, turn some cells ON in the top ring, and run Rule 30. What is the max period? Is this in the OEIS?
On Sun, Apr 26, 2020 at 9:36 AM Brad Klee <bradklee@gmail.com> wrote:
I tried to ctrl-f for "virial theorem", but didn't find anything. --Brad
On Sat, Apr 25, 2020 at 9:20 PM Bill Gosper <billgosper@gmail.com> wrote:
It turns out General Relativity was a mistake.
https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-th...
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