Description
Arrange supplied square motifs on an explicit lattice with legal transforms and optional exact matrix-border continuity across neighbors and repeat seams.
A repeat pattern builds a larger design from a smaller set of cells or motifs. The repeat boundary, orientation, and adjacency rules determine whether the returned structure joins as intended.
Arrange supplied square motifs on an explicit lattice with legal transforms and optional exact matrix-border continuity across neighbors and repeat seams.
When to use this tool
Use this generator to create reproducible wallpaper motif repeat cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.
How to use the tool and how it works
- Supply rows, columns, motifs, origin, columnVector, rowVector, boundaryPolicy in the field shapes below. Set seed when you need an explicit replay.
- Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
- Read placements, repetitionCounts, latticeDeterminant, seamless. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Expand supplied square motifs into their permitted quarter-turn/reflection variants. Search row-major placements on a nondegenerate lattice, optionally matching matrix borders at neighbors and both repeat seams, then return transformed motifs, coordinates and repetition counts.1
Delegated operations used for this result: rotate 90; flip vertical. Their calculation or parsing conventions apply to the corresponding result fields.2, 3
| Input field | Meaning and units | Accepted input |
|---|---|---|
| rows | Rows | Required. Safe integer; minimum 1; maximum 16. |
| columns | Columns | Required. Safe integer; minimum 1; maximum 16. |
| motifs | Motifs | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 16. |
| motifs[].id | Literal identifier used to match records, independently of their display labels. | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64. |
| motifs[].matrix | Matrix | Required. Array of Array of Finite number.; minimum items 1; maximum items 8.; minimum items 1; maximum items 8. |
| motifs[].quarterTurns | Quarter Turns | Required. Array of Safe integer; minimum 0; maximum 3.; minimum items 1; maximum items 4. |
| motifs[].allowReflection | Allow Reflection | Required. Boolean. |
| origin | Origin | Required. Object; no unknown keys. |
| origin.x | X | Required. Finite number. |
| origin.y | Y | Required. Finite number. |
| columnVector | Column Vector | Required. Object; no unknown keys. |
| columnVector.x | X | Required. Finite number. |
| columnVector.y | Y | Required. Finite number. |
| rowVector | Row Vector | Required. Object; no unknown keys. |
| rowVector.x | X | Required. Finite number. |
| rowVector.y | Y | Required. Finite number. |
| boundaryPolicy | Seamless requires exact transformed matrix-border equality between neighbors and across both repeat seams. | Required. Text; one of "free", "seamless". |
| seed | Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed. | Optional. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| placements | Placements | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 256. |
| placements[].row | Row | Required. Safe integer; minimum 0; maximum 15. |
| placements[].column | Column | Required. Safe integer; minimum 0; maximum 15. |
| placements[].motifId | Motif Id | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64. |
| placements[].quarterTurns | Quarter Turns | Required. Safe integer; minimum 0; maximum 3. |
| placements[].reflected | Reflected | Required. Boolean. |
| placements[].x | X | Required. Finite number. |
| placements[].y | Y | Required. Finite number. |
| placements[].matrix | Matrix | Required. Array of Array of Finite number.; minimum items 1; maximum items 8.; minimum items 1; maximum items 8. |
| repetitionCounts | Repetition Counts | Required. Array of Object; no unknown keys.; minimum items 0; maximum items 128. |
| repetitionCounts[].id | Literal identifier used to match records, independently of their display labels. | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 64. |
| repetitionCounts[].count | Requested count; the mechanics explain whether one draw expands into several returned records. | Required. Safe integer; minimum 0; maximum 9007199254740991. |
| latticeDeterminant | Lattice Determinant | Required. Finite number. |
| seamless | Seamless | Required. Boolean. |
| randomness | Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional numeric replay seed; normalization and precedence are explained below. | Required. Safe integer. or Null. |
| randomness.source | Source | Required. Text; one of "context", "seed". |
An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.
{
"input": {
"rows": 2,
"columns": 2,
"motifs": [
{
"id": "checker",
"matrix": [
[
1,
2
],
[
2,
1
]
],
"quarterTurns": [
0,
1
],
"allowReflection": false
}
],
"origin": {
"x": 10,
"y": 20
},
"columnVector": {
"x": 3,
"y": 1
},
"rowVector": {
"x": 1,
"y": 2
},
"boundaryPolicy": "seamless",
"seed": 42
},
"output": {
"placements": [
{
"motifId": "checker",
"quarterTurns": 1,
"reflected": false,
"matrix": [
[
2,
1
],
[
1,
2
]
],
"row": 0,
"column": 0,
"x": 10,
"y": 20
},
{
"motifId": "checker",
"quarterTurns": 0,
"reflected": false,
"matrix": [
[
1,
2
],
[
2,
1
]
],
"row": 0,
"column": 1,
"x": 13,
"y": 21
},
{
"motifId": "checker",
"quarterTurns": 0,
"reflected": false,
"matrix": [
[
1,
2
],
[
2,
1
]
],
"row": 1,
"column": 0,
"x": 11,
"y": 22
},
{
"motifId": "checker",
"quarterTurns": 1,
"reflected": false,
"matrix": [
[
2,
1
],
[
1,
2
]
],
"row": 1,
"column": 1,
"x": 14,
"y": 23
}
],
"repetitionCounts": [
{
"id": "checker",
"count": 4
}
],
"latticeDeterminant": 5,
"seamless": true,
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Seamless means exact supplied matrix-border equality, not a continuous optical or manufactured surface. The search is bounded and nonuniform, and coordinate units follow the explicit lattice.
- A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
- The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.
Alternative or Complementary methods
For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.
References
Similar or alternative tools
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