Conquest Algorithm for Stochastic Filling of Two-Dimensional Discrete Grids with Connected Regions
Bibliographic record
Abstract
The object of research is the process of procedural coloring of a two-dimensional discrete space with topological constraints. A new algorithm is proposed that solves the widespread problem of generating meaningful stochastic connected regions on two-dimensional discrete fields. A study was conducted in which a clear formulation of the task was given and illustrated by constructing a game board for a modified version of the classical N-Queens problem. The task is to implement an algorithm able to create an arbitrary N x N board (for any manually specified N > 0). The board must then be filled procedurally with connected regions. An analysis of existing algorithms commonly used in procedural generation for related industries was carried out. The following methods were examined: Gradient Perlin Noise, Cellular Automata, Wave-Based Flood Fill and Random Walk. It was concluded that, in their classical form, these algorithms are not suitable for procedural construction of a game board for the chosen task, so a new method derived from the random-walk approach was proposed. The proposed algorithm introduces a set of agents, which – in this context – are the queens on a chessboard. Each agent moves in turn, but both the possibility of making a move and the choice of orthogonal direction is driven by additional criteria, as such: turn skip formula, empty cells bias against controlled ones, borderline cells bias against inner and prohibition of stepping onto the cells owned by other agents. The algorithm was implemented in the C# programming language. The program includes the ability to run several consecutive generations and to compute metrics for the shapes obtained on the grids. To evaluate the success of the proposed algorithm the following metrics were used: average elongation, average rectangularity, average roughness, maximum elongation, maximum rectangularity and minimum roughness. In addition, an efficiency metric was calculated from the complexity standpoint – namely, the total number of agents steps divided by the grid area. To measure efficiency and collect the metrics, one thousand experiments were carried out for the board sizes of N x N, where N = 8, 12 and 20. The results show that the algorithm operates correctly, fulfils the stated task, and is efficient.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".