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Wolfram's Rule 30 contest

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In case anyone wants to discuss the contest for Wolfram's rule 30 on Community, please respond on this thread.

It's about the center column of rule 30. There are three questions. The answer is a mathematical proof. There are cash prizes.

ArrayPlot[CellularAutomaton[30, {{1},0},100]]
POSTED BY: Todd Rowland
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POSTED BY: Tigran Nersissian

Hi everyone, I submitted a solution paper to the Wolfram Rule 30 Prize around January 17, 2026 using the official “Submit a Solution” form, but I didn’t receive any confirmation email.

For those who have submitted before: do you typically get an automatic acknowledgment, or is it normal to hear nothing unless the committee needs clarification? Also, what kind of response timeline should I expect?

Thanks in advance!
POSTED BY: Tigran Nersissian
David Gallimore
David Gallimore
Posted 2 months ago

Hi Tigran, I am still working on my rule 30 solution, I am not sure if the prize is still running as I dont see any activity there. want to meet up and chat about your ideas?
POSTED BY: David Gallimore

Hi David, thanks for the reply!

Good luck with your Rule 30 work, it’s definitely a deep and fascinating problem. I’m also not entirely sure about the current status of the prize, which is part of why I asked.

I’d be happy to chat and exchange ideas. Feel free to reach out and we can find a time that works.

Tigran.nersissian@hotmail.com
POSTED BY: Tigran Nersissian
POSTED BY: David Gallimore

Wolfram's Elementary Cellular Automata

(Left) rule30 using my new equation ( can be done on a four function calculator )

(Middle) 4th order Z transform of occupancy matrix.

(Right) Power spectra of the 4th order co-effecients WOW! really exciting find :-)
RULE30 iterated using my new recurrence relation.

POSTED BY: graham medland

Graham this looks neat. Can you explain a little more?

I understand that it's not in Mathematica. If it's one or two lines of math, we can translate it.
POSTED BY: Todd Rowland

Hi Todd, please email me, gmail.com@graham.medland

Graham

POSTED BY: graham medland

Hi, I have an algebraic equation for RULE30, it runs on octave but would be great to see it iterated on Mathematica, https://www.linkedin.com/feed/update/urn:li:activity:6609546528723877889/

I also have a turmite equation (based on my langtons ant wave equation) which would be nice to see in Mathematica, could someone please help me ?
POSTED BY: graham medland

Hi Graham,

it seems that one needs a LinkedIn account to access that document. I suggest to change that.

Michael
POSTED BY: Michael Brunnbauer

I wanted to play with cellular automata for a while. When I saw the post about the contest, it finally got me into gear and I had some fun with rule 30:

https://brunni.de/findings30/

From the abstract:

The usual pattern starting from a single cell with state 1 / black is examined. It is contructed from a richer structure which yields a progression of polynomials for diagonals from the right. It is shown that each diagonal from the left can be expressed by the progression of polynomials for diagonals from the right and how the connection between left and right diagonals forces the diagonals from the left to eventually become periodic.

The necessary and sufficient condition for period doubling of diagonals from the right is established. It is also shown that periods cannot decrease. The result suggests that predicting period doubling is computationally expensive.

I suppose there is nothing new in there?
POSTED BY: Michael Brunnbauer
POSTED BY: Todd Rowland
POSTED BY: Michael Brunnbauer

Thanks, yes, that sounds familiar from a talk Eric Rowland gave. It is pretty neat though, and yeah, a little hard to explain in words.
POSTED BY: Todd Rowland
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