An Accidental Encounter With Rule 30

I came across Rule 30 today. No context, really. Just one of those things that shows up randomly—though, in hindsight, maybe my work and interests tend to orbit around certain kinds of ideas.

Rule 30 is a simple rule from the world of cellular automata, introduced by Stephen Wolfram. You define a 1D array of cells, each with one of two possible states: on or off (black or white). For each new generation, the state of every cell is updated based on its current state and the state of its two immediate neighbors. Despite its extreme simplicity, the resulting pattern turns out to be chaotic and unpredictable.

The simplicity of the rule and its output made me pause.

Visualization and the Story We Choose to Tell

One thing that struck me was how we choose to represent the pattern’s evolution. The classic way is to stack each new row below the last—so time appears to flow downward, and a triangular, chaotic shape emerges. But that’s just a choice. It’s how we’ve decided to observe the system.

This choice reminds me of how we visualize the layer-by-layer process in 3D printing—each layer tells a story of what came before. In Rule 30, too, each row holds the imprint of prior decisions. But this visualization doesn’t necessarily reflect any “truth” about the structure itself—it just happens to be convenient. Or maybe even biased by aesthetics.

ASCII art is the most common way people explore and present Rule 30 online. Rows of monospaced characters showing how 1s and 0s evolve line by line. It’s neat, compact, and takes advantage of how we read and write English—left to right, top to bottom.

But what if we visualized it differently? Rotated the whole thing sideways? Wrapped it around a circle? Projected it into 3D? Would different patterns emerge? Would we notice other things?

There’s something arbitrary about how we lay these out. The patterns we observe might just be artefacts of that arbitrary decision.

Structure, Behavior, and Meaning

This led me to another question: is there inherent structure in the pattern, or are we assigning it meaning based on how we see it?

In materials science, particularly in crystallography, they study how structures emerge based on optimization principles—like minimizing electron repulsion. The final arrangement has real, observable consequences. Maybe Rule 30 is similar, but we don’t yet know what kind of “optimization” it’s doing—if any.

Or maybe we’re trying too hard to impose purpose on something that’s just raw emergence from a very basic rule.

Still, the resemblance of Rule 30 to natural patterns—like the spiral markings on a conch shell—is hard to ignore. There’s a visual similarity. But that doesn’t mean the process behind both is the same. Our brains are wired to spot patterns, and sometimes we might over-index on that.

Final Thought

Rule 30 looks like chaos born from simplicity. But how we look at it, and what we take away from it, depends as much on our choices of framing as it does on the rule itself. Maybe that’s the real lesson—systems might hold unexpected complexity, but sometimes it’s the act of observing that introduces the story.