On July 20, 2026, Claude Heiland-Allen published a catalog on his personal site mathr.co.uk — sparse, undecorated, functional. The trigger was a blog post by Guy Birkin three days earlier: Birkin, an independent researcher studying the aesthetics of visual complexity, had re-described the algorithm for block cellular automata. Heiland-Allen read it, wrote his own enumeration program in Haskell over a few days — using the list monad, with a custom replicateM fix for a space leak — and put the results online: a plain HTML index of textures grown from random seeds, each clickable to reveal the rule text that generated it.

The logic of block cellular automata isn't complicated. In a colored grid, each iteration maps N×N overlapping blocks according to a fixed rule table, then shifts the block origin diagonally before the next step. The rule table determines everything — the total number of possible BCAs is astronomically large. To get images that are visually isotropic and uniform in color density, Heiland-Allen specifically enumerated "symmetric" BCAs: those whose rule tables are invariant under spatial symmetries of the square (rotations, reflections) and cyclic color permutations. Even with this constraint, the space is inexhaustible: 2×2 blocks with 9 colors yields 14 symmetric BCAs; 3×3 with 2 colors, 132. Those rows in his table marked "..." — the unfilled counts — mark where his work hasn't yet reached.

In the SAE aesthetic framework of 余项之美 (beauty of the remainder), this catalog's structural significance lies precisely in its incompleteness. Conway's Life is already 已构 — already-construct: it has a name, a culture, a place in art history. Wolfram's enumeration of elementary cellular automata is already-construct too: those 256 rules have been classified, named (Rule 110, Rule 30...), and absorbed into a citable knowledge system. But the visual space of symmetric block cellular automata has no language yet. No one has told us what these textures mean; no art-world framework has digested them; even the counting method is still being worked out. "I have not found a way to count them apart from enumerating them," Heiland-Allen writes. This is precisely the condition of 余项之美: the answers exist logically, but they haven't been fully absorbed or given names.

The chisel-construct cycle (凿构循环) is visible here. Heiland-Allen is in the chisel phase: he found bugs in his enumeration code ("I spotted that some images looked very similar"), corrected his canonicalization of color permutations, extended the algorithm to N×N and 3D, and put intermediate results online. This is not a finished work — it's a public exposure of ongoing process, not an exhibition, not a statement, but a mathematical exploration made visible in real time. That openness is the marker of a living remainder: once this work is fully completed, named, absorbed into a knowledge system, it becomes 已构, and the beauty of the remainder dissolves with it.

What happened between Birkin and Heiland-Allen is itself worth noting. Both work independently — not in university art-and-technology departments, not in residency programs, not under any institutional umbrella. Birkin runs a WordPress blog on visual complexity aesthetics; Heiland-Allen has a hand-built static site where he has made art with mathematics and free software since 2005. Within three days, one blog post became another person's implementation, became a public catalog. That reaction speed wasn't curated — it was itself a structural remainder, two people working at each other's edges, with no shared institution, only shared curiosity.

We look at this catalog now because it is still growing. The page at mathr.co.uk/bca is sparse and undecorated: images arranged directly in HTML, rules hidden behind links. No gallery walls, no curatorial narrative, no price tag. It exists in a space between mathematical notes and a visual archive — and that in-between territory is exactly where 余项 lives.

Han Qin (秦汉) · @hqinjarsy · SAE Judgment & Aesthetics