computer week · 28 September 2026

Does the Picture Have Physics?

… rule 30

the world

its picture

the picture run by its own rule

picture's own rule–exact

invented per bit–bits the picture cannot supply

predictable–of each picture bit's entropy

cells right–own rule against the picture

choose a world · frame: does it have a picture with physics at some mesh up to 4?

rule

mesh: cells per block

the camera: which blocks it reports as black · tap to change

1 0 the picture's own rule is wrong here has a picture with physics only pictures that go blank no closed picture

What this is

A picture π of a world F has physics of its own exactly when some rule G on pictures commutes with the world:

π ∘ F^N = G ∘ π

Here π reports one bit per block of N cells and one picture step is N world steps, so a picture cell's future can depend only on its two neighbours. The page checks the equation exactly, for every arrangement of three blocks. When it holds, the third panel matches the second forever. When it fails, the best any rule on pictures can do is guess, and the "invented" figure is how many bits per cell per step it must guess (the conditional entropy of the next picture bit).

Wittgenstein, Tractatus 6.342: what characterises a picture of the world "is that it can be described completely by a particular net with a particular size of mesh." Rule 90 is described completely by meshes of 2 and 4 cells and hardly at all by a mesh of 3.

Across all 256 worlds, meshes up to 4
a picture with physics of its own	112
only pictures that go blank	90
no closed picture at all (Rule 30 and Rule 110 among them)	54
Rule 30, most predictable 3-cell camera, with 6 frames of history	12% predictable
Rule 110, the same	93% predictable