Description
Choose independent fair binary values for each quarter-turn square-grid orbit, uniform over symmetry-compatible masks; orbit cells are tied, not independently sampled.
A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.
Choose independent fair binary values for each quarter-turn square-grid orbit, uniform over symmetry-compatible masks; orbit cells are tied, not independently sampled.
When to use this tool
Use this tool to choose independent fair binary values for each quarter-turn square-grid orbit, uniform over symmetry-compatible masks; orbit cells are tied, not independently sampled.
How to use the tool and how it works
- Enter rows, columns, seed using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.mask, result.orbitCount, using the stated boundary, ordering, sign and absence conventions.
Partition a square grid into quarter-turn rotation orbits. Draw one binary value per orbit in traversal order and assign it to every member cell, returning the mask and orbitCount.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| rows | Positive integer grid row count; bitmap generators allow 1–11, toroidal origin allows 1–128. | Finite safe integer satisfying the stated bounds. |
| columns | Positive integer grid column count under the same bounds; quarter-turn symmetry requires a square. | Finite safe integer satisfying the stated bounds. |
| seed | Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.seed | Original supplied seed string; injected-source replay additionally requires that source’s state. |
| result.mask | Row-major numeric binary bitmap, one list per row. |
| result.orbitCount | Number of independent symmetry orbits assigned binary values. |
{
"input": {
"rows": 2,
"columns": 2,
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"mask": [
[
1,
1
],
[
1,
1
]
],
"orbitCount": 1
}
}
}Limitations and assumptions
- Dimensions are equal integers 1–11. The sample space is quarter-turn-invariant bitmaps, not all bitmaps or connected shapes.
- A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.
Alternative or Complementary methods
Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.
References
Similar or alternative tools
- Random Mirror-Symmetric Bitmap
Choose independent fair binary values for each left/right mirror orbit, uniform over symmetry-compatible masks; orbit cells are tied, not independently sampled.
- Random Complementary Bitmap Pair
Sample one fair independent-cell binary bitmap and return its exact bitwise complement; pair assignments uniform over first masks, not independent paired images.