The following problems concern the infinite sequence of center-cell values in the pattern (shown above) generated by rule 30 evolving from a single nonzero cell:

Problem 1
Does the center column always remain non-periodic?

Problem 2
Does each color of cell occur on average equally often in the center column?

Problem 3
Does computing the nth cell of the center column require at least O(n) computational effort?

Details

Prize Committee

The Prize Committee will oversee the review and validation of candidate correct solutions. Since it is not known what methods may be successful, the Prize Committee includes experts in a wide variety of areas.

Note: The Prize Committee has an advisory role; submissions should not be directed to its members. (Submissions sent directly to Prize Committee members may be disqualified from further consideration.)

(more to be announced)

Prize Guidelines

The Wolfram Foundation ("Wolfram") is offering $30,000 (US) in prize money ("Prize"/"Prizes") for correct solutions ("Solution"/"Solutions") to the three Wolfram Rule 30 Prize Problems ("the Problems"). The three separate $10,000 Prizes, one for each Problem, shall go to the first individual or group to successfully submit a Solution for that Problem, providing a full proof of such Solution to the satisfaction of the Prize Committee in accordance with these Guidelines.

The invitation to participate, and eligibility to win these Prizes, is extended to everyone. Each submitter agrees to be bound and abide by the rules, decisions and interpretations of the Prize Committee.

For each of the Problems, submissions will be accepted until a satisfactory Solution has been achieved.

All submissions must be the original work of the submitter(s) and include the names of all relevant contributors. Anonymous submissions will not be accepted.

Submissions remain the property of their submitter(s), but the submitter grants Wolfram the non-exclusive royalty-free right to publish the submission.

Submissions will be judged by the Prize Committee, and all decisions will be final and binding upon all participants. In the event of unexpected circumstances (such as proofs with different axiomatic foundations), the Prize Committee will make a discretionary decision consistent with the goals and purpose of the Prize.

Wolfram may request additional or clarifying information in connection with submissions. Submitters will be contacted at the email addresses they provide.

Winners may be required to provide proof of identity, address and birth date, as well as to execute and return tax acknowledgment forms, a liability release and a publicity release prior to claiming a Prize.

By making a submission for a Prize, submitters hereby release and agree to indemnify and hold harmless Wolfram and the Prize Committee from and against any and all costs, claims or damages, whether due to negligence or otherwise, due in whole or in part, directly or indirectly, for their participation therein.

Submit a Solution

Note: the Wolfram Rule 30 Prize Problems are definite, precise problems. Submissions that do not provide definite, precise results and arguments will not be considered.

The Solution should be submitted in the form of a technical research paper, suitable for publication. If successful, the submission will be published.

By uploading a submission, you are agreeing to the Prize Guidelines.

Submit a Solution