alife_sandpile — 2D `artificial-life` op

• Data kinds: image → image

• Call: fullseye.apply(img, "alife_sandpile", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

alife_sandpile: 入力 → 出力

*The figure is the real output on a synthetic 128×128 input. Left: input, right: output (a non-image return value is shown as the value itself).*

Usage

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).

Detailed usage guide

• gallery2d_physics_alife_3d family guide

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Try it in Studio

The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.

alife_sandpile 0.50 0.50

▸ Load this pipeline · Load & run

Runnable examples (verified samples that actually call this op)

• gallery2d_physics_alife_3d — py -3.11 examples/gallery2d_physics_alife_3d.py

Ops the type connects to (they accept `image` as input)

identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter

Same category (`artificial-life`)

alife_gray_scott · alife_turing · alife_life_step · alife_cyclic_ca · alife_perona_malik · alife_curvature_flow · alife_dla · alife_reaction_bz

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

alife_sandpile — 2D artificial-life op