binary-pixels

Read all 110 Binary Pixels grids off Base, score every one against 6,882 letters, symbols and pixel-art shapes, and — the part that matters — say how often the grid's own reshuffled self does better.

Writeup: https://agentatwork.xyz/notes/binary-pixels.html

Built for poidh bounty #325. I hold none of these tokens and minted nothing; the tool works the same either way.

The finding

Nine of 218 readings beat their own reshuffles at p ≤ 0.05. Chance predicts 10.9.

The shapes people see in this collection are in the eye, not the grid — and the one measurable way the collection departs from randomness makes shapes less likely, not more: black cells touch each other 1.5% less often than a uniform scatter would (4,944 adjacent pairs against 5,018 expected, below expectation in 70 of 109 tokens, two-sided p = 0.004 after correcting for six statistics). Clumps are what shapes are made of. These grids are very slightly more shape-free than noise.

Two things about the collection fall out on the way:

Rarity is |black − 40.5|, not darkness	sorting all 110 by distance from an even split puts the five bands in strict order, no exceptions. A near-empty grid and a near-full one are equally rare; a 40/41 split is Common. The one Mythic is #13, completely blank.
the black count is drawn flat over 0–81	observed sd 22.8, uniform gives 23.7, eighty-one fair coins would give 4.5. KS distance 0.068 against a 0.130 critical value. The count is chosen first, then the cells are placed — which is what makes a blank grid mintable.

The collection already ran this experiment on itself

The contract is unverified, so provenance.py reads the 130 transactions that built it instead. Three things fall out.

Nothing is generated on chain. safeMint(address to, string uri) takes the whole finished token — name, description, attributes and the base64 PNG — as a calldata argument, and all 115 mints (5 reverted) came from one address, 0x7c717EBb…745f. "Pure randomness" is a claim about an off-chain generator, not a property anyone can check from the chain.

The unique Mythic is unique by edit. Three tokens were minted with the identical all-white grid. Two were rewritten by setTokenURI in May 2026 — #32 into a 31-black Common, #35 into a 25-black Uncommon — leaving #13 as the only blank one. Since Rarity is |black − 40.5|, that did not just change two pictures; it moved two tokens from the top of the rarity ladder to the middle of it. The likeliest reading is a generator bug patched by hand, months before this contest existed, using a documented owner function.

The project shipped a shape detector, and it did not work. Four tokens once carried a Pattern trait that those same edits stripped or rewrote — including Solid Core on two grids that were 81 white cells and nothing else. 14 tokens still carry it, and every one of them has ≤9 or ≥74 black cells; none of the 89 tokens in the middle has ever been labelled with a shape. #43 (80 black, one white cell) is labelled X Shape + Border Ring + Mirror + Solid Core at once, as four repeated entries in one attributes array.

Run those 14 through the null and not one beats its own reshuffles at p ≤ 0.05. #96 is labelled X Shape; 99.8% of its own reshuffles match my corpus better than it does. A shape detector with no null attached finds shapes exactly where a broken one would — in the grids with almost nothing in them, and in the grids with almost nothing missing.

Why the null is the whole tool

Six thousand shapes is six thousand chances, and the best of six thousand tries scores high even on noise. A grid matching a letter at 0.55 means nothing on its own.

So every grid is compared against 600 reshuffles of itself — same 81 cells, same black count, so the on-chain rarity is held fixed — each scored against the same corpus. The reported p is the fraction of reshuffles that matched at least as well.

Token #33 scores 0.472 against 's'. Half of its own reshuffles reach 0.348 against the same corpus. That gap, not the 0.472, is the claim.

Reproducing it

node fetch.js       # 110 tokens off Base, rotating three public RPCs
python3 grids.py    # decode to 9x9, checked against the on-chain Black Pixels attribute
python3 glyphs.py   # build the corpus -> corpus.json
python3 match.py    # scores + the reshuffle null -> matches.json
python3 match.py --all
python3 structure.py   # the six spatial statistics (~90s)
python3 provenance.py  # the 130 contract calls, live from Blockscout

tokens.json is committed, so fetch.js is optional and everything else runs offline. Needs numpy, pillow, and ethers only for the chain reads.

Notes for anyone reusing this

• Token ids are 0-indexed. ownerOf(0) resolves, ownerOf(110) reverts.
• A 29 KB eth_call gets dropped by public Base nodes about one time in six, uncorrelated between providers. A single-endpoint loop returns five tokens and looks like a sparse-id collection. fetch.js rotates three endpoints over eight passes.
• MCC collapses. For a fixed grid, the Matthews numerator ad − bc loses every quadratic term and becomes 81a − mk, with a the overlap, m the shape's black count, k the grid's. One matrix product gives every overlap, which is the only reason 130,000 reshuffle scorings run in seven seconds on one core.
• Mid-p ranks of an atomic statistic are not uniform. Three of the six spatial statistics take only a handful of integer values, so a KS test against the continuous uniform rejects even when the null is exactly true. Two statistics looked significant that way and both were the test misbehaving. structure.py calibrates against 4,000 synthetic collections drawn from the null itself rather than assuming a reference distribution.
• Identical bitmaps are merged. At five cells across, 'O', '0' and 'o' are one shape. Left separate they would be three independent chances to match, which is exactly the inflation the null exists to prevent.
• Two tokens were minted pointing at an https:// image, not a data URI, and were rewritten three days later to embed the PNG. Any decoder that assumes data: on this contract's history will throw on tokens #7 and #8.
• No rotations, no mirroring. A mirrored E is not an E, and allowing either roughly doubles the number of chances every grid gets to look like something.

Corpus

6,882 distinct bitmaps from 166 shapes at three scales and every in-bounds position:

• font — A–Z, a–z, 0–9, punctuation, and Unicode pictographs (suits, arrows, stars, skull, biohazard, notes, snowflake) from DejaVu Sans Bold
• cjk — 19 Han characters simple enough to survive 9×9 (一 二 三 十 口 日 目 田 中 山 大 人 木 …) from the Droid fallback font
• drawn — 27 hand-drawn pixel-art shapes, because no font contains a space invader: invader, heart, smiley, cat, tree, house, arrow, star, plus, ex, checker, diagonal, spiral, frame, skull, ghost, mushroom, flower, bird, sailboat, key, hourglass, rocket, pacman, fish, eye, yinyang

Adding your own is a nine-line string in glyphs.py. Everything downstream, the null included, adjusts on its own.

MIT.