Projects / rule-30-explorer

Rule 30 explorer

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A small browser demonstration: one seed, one local rule and a finite picture of its evolution.

Watch a local rule unfold

Choose a number of generations and draw Rule 30 from a single centered seed. Each new row applies left XOR (center OR right) to the row above it. The center readout follows the original seed position.

The demonstration supports up to 128 generations and runs in your browser. Its text output provides another way to inspect the finite sequence.

What the picture tells you

The picture shows the evolution for the selected finite interval. Changing the displayed depth changes the amount of data, not the mathematical status of the center-column problem. An irregular-looking pattern is not a proof of nonperiodicity.

The research project page explains the open question and the distinction between experiments and arguments. This demonstration is separate from a reviewed research release.

Rule 30, one row at a time

Start with one black cell. Each new cell depends on the three cells immediately above it.

The eight neighborhoods
Previous row111110101100011010001000
New cell00011110

Contributions & AI assistance

Contributions

Jordi Gartner directs this personal research archive and decides what is released. Publication-specific authorship and contributions are recorded with each work; the website alone does not establish independent scientific review.

AI assistance

This archive is prepared with AI assistance. Research records include AI-assisted exploration, programming, proof drafting and internal checks. A check by another AI agent is an internal check, not independent external review or peer review. Each released work must identify its contributors, checks and limitations.

Related releases

No releases have been published for this project yet.

Version history

VersionPublishedChange note
v4Updated publication information.
v3Editorial revision of English, German and Chinese copy; mathematical claims and evidence unchanged.
v2Wording revised for clarity; comment guidance updated where relevant.
v1Initial editorial overview; no research files released.

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