Growth from one seed
Free-range and GCTS use the same growing frontier. GCTS adds the learned marking.
Measured comparison
Choose a tile, then run all four methods.
| Method | Total | Branches | Backtracks | Forced | Proved cuts | Marking cuts | Clusters | Result |
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Inside the selected method
Run a comparison to inspect costs, elimination reasons and learned cluster expansions.
Learned cluster library
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Measured cold runs · fixed window
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| Tile / seed | Free-range | GCTS | RL clusters | GCTS + RL |
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Protocol and full results · Timings include learning. Your device may differ.
Historical v2.0 experiment · original 3D model
Original 3D windows with half-weight prism caps. These results do not describe the v2.1 single-slab hat and turtle. Five cases × three seeds; 27 points.
| Tile | Free-range | GCTS | RL clusters | GCTS + RL | Small periodic / isohedral probe |
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Counts are verified windows out of three seeds. These recorded runs are separate from your live experiment.
What is being compared?
The main comparison follows GCTS-I’s seed-based point growth. Both free-range and GCTS start with the same tile at the origin. Adding a tile exposes new frontier points. Every allowed positive-support alignment is enumerated; global dead ends precede forced moves, then branching uses the earliest generation. Candidate ordering uses fill, frontier incidence, existing support and new points, with seeded random ties.
Free-range has no marking. GCTS first learns and validates a marking from unmarked pair-corona checks, then runs the same growth search with overlapping assigned marking values required to agree. RL lanes propose short validated clusters within the same scheduler.
Certified exclusions first checks unmarked pairs for local impossibility, then encodes only proved failures in sparse point components. Rotations permute components. Unresolved connections remain allowed; positive examples are not required. Preparation uses at most forty percent of the lane budget, capped at thirty seconds. If it finds no exclusions, the lane continues unmarked and reports that fallback. These exclusions preserve infinite exact tilings, but can remove finite patches that cannot extend indefinitely.
GCTS enumerates neighboring pairs, attempts an unmarked one-corona with viable frontier, and updates point markings after every label. Only a complete qualifying marking starts the marked search. Hover over the learning preview to inspect current values and *. RL learns returns for irregular three-placement cluster proposals and uses them to order the complete base list. Every proposed step passes the base scheduler. No periodic motif or catalog identity guides either lane. The cluster lane combines rollout lookahead with online returns; its advantage cannot automatically be attributed to learning.
Comparison lanes start fresh. Use Learn new marking for a standalone run, Continue learning to retain resolved samples and retry unfinished checks, or Tile with marking to replay a compatible marking saved in this browser. These are online experiments, not a pretrained or held-out generalization claim. The export includes proposal expansions, costs, point data and independently replayed results.
What would count as evidence?
Measured slab demonstrations record the earlier fixed-window experiment; those timings do not measure this growth comparison. The full catalogue audit records the broader research cases. Slab speedups do not establish a benefit for the non-layered polycubes or a new aperiodic monotile. The geometric follow-up checks voxel overlap and introduces an explicit center-and-corner research model.
A separate checked pair-corona proof now excludes catalogue tile p9-48258 from integer-grid tiling under cubic rotations. Unrestricted Euclidean tiling remains outside that result. The browser lanes still learn fresh from their selected point model.
The main result is a consistent finite growth patch with independently verified frontier viability. A separate fixed-window control retains the old finite-target experiment. Hat and turtle use one slab on the index-3 A₂ sublattice: both caps have planar weights, and translations stay within the slab. Research polycubes use explicit voxel centers and corners, with independent voxel replay. Other catalog tiles use their declared three-dimensional point support. Growth has no preselected boundary: every exposed positive-support point remains an obligation. It does not certify a geometric solid tiling or infinite extension. A budget limit means unknown. Exhausting the seed search concerns only that seed, point model and growth target. Exhausting a learned marking does not exclude unmarked solutions.
Research tiles and nonconvex stress tests are separate from known periodic controls. A missed bounded periodic probe does not establish aperiodicity. All geometric pictures illustrate the point data; geometric overlap is not a base legality test.
Compare multiple seeds and larger growth targets. Total time includes model construction, complete graph construction, marking synthesis, learning and verification. Runs are sequential to avoid four workers competing for CPU. Memory is an estimated data footprint, not browser process memory.