alife_sandpile — 2D `artificial-life` op

• データ種: image → image

• 呼び出し: fullseye.apply(img, "alife_sandpile", a=0.5, b=0.5) (2-D は 1 画像 + 2 スカラつまみ a,b∈[0,1] のモデル)

Abelian sandpile / self-organised criticality (Bak-Tang-Wiesenfeld 1987).

The image is quantised to integer grain heights h = round(K * image) with

K = 4 + int(12a), then relaxed by the BTW toppling rule: a cell with 4 or

more grains gives one grain to each orthogonal neighbour and keeps the rest.

The boundary is dissipative (grains leaving the grid are lost), which is what

lets the pile settle into the self-organised critical state where every cell

holds at most 3 grains.

`a` sets the initial grain scale K (how supercritical the pile starts);

`b` sets the number of parallel relaxation sweeps 1 + int(50b). For

b >= 0.9 the pile relaxes *toward* stability with early termination, but the

sweep count is bounded by a total-work budget (`_SANDPILE_BUDGET` grain-

updates) so the op stays fast on any image size: a small or varied pile

reaches the stable critical state (every cell <= 3), while a very large

maximally-supercritical pile is only partially relaxed (full BTW

stabilisation is O(L^2) sweeps). Returns h / max(h) in [0, 1]; a fully

relaxed pile (max 3) takes values in {0, 1/3, 2/3, 1} (or {0, 1/2, 1} when

the stable maximum is 2).

• サンプルデータカタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。

• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。

• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

• gallery2d_physics_alife_3d — py -3.11 examples/gallery2d_physics_alife_3d.py

*Provenance: ops.py — 2D operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*

alife_sandpile — 2D artificial-life op