Description
Choose a uniform toroidal origin cell from explicit positive grid dimensions; no payload resampling or coordinate wrap transformation is performed.
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 a uniform toroidal origin cell from explicit positive grid dimensions; no payload resampling or coordinate wrap transformation is performed.
When to use this tool
Use this tool to choose a uniform toroidal origin cell from explicit positive grid dimensions; no payload resampling or coordinate wrap transformation is performed.
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.row, result.column, using the stated boundary, ordering, sign and absence conventions.
Draw row uniformly in 0…rows−1 and column independently in 0…columns−1, returning one grid-cell origin.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.row | Zero-based selected grid row. |
| result.column | Zero-based selected grid column. |
{
"input": {
"rows": 3,
"columns": 4,
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"row": 1,
"column": 3
}
}
}Limitations and assumptions
- Dimensions are integers 1–128. The tool chooses an origin only; it does not translate a grid or model neighbor connectivity.
- 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
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