Description
Draw integer-frequency Lissajous parameters and sample a complete turn with exact closure and sampled bounds, without audio synthesis.
Procedural artwork expresses a visual idea through coordinates, repeated motifs, colors, or explicit placement constraints. A coordinate plan can be checked and reproduced before rendering, while physical material behavior and fabrication require separate information.
Draw integer-frequency Lissajous parameters and sample a complete turn with exact closure and sampled bounds, without audio synthesis.
When to use this tool
Use this generator to create reproducible lissajous curve set 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 count, minimumFrequency, maximumFrequency, phaseTurns, amplitudeX, amplitudeY, intervals 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 curves. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw integer x and y frequencies and a supplied phase in turns, then sample the corresponding sinusoidal Lissajous curve over one turn. Repeat the starting point exactly and return point bounds per curve.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Requested count; the mechanics explain whether one draw expands into several returned records. | Required. Safe integer; minimum 1; maximum 16. |
| minimumFrequency | Minimum Frequency | Required. Safe integer; minimum 1; maximum 32. |
| maximumFrequency | Maximum Frequency | Required. Safe integer; minimum 1; maximum 32. |
| phaseTurns | Phase Turns | Required. Array of Finite number.; minimum items 1; maximum items 16. |
| amplitudeX | Amplitude X | Required. Finite number; strictly above 0. |
| amplitudeY | Amplitude Y | Required. Finite number; strictly above 0. |
| intervals | Intervals | Required. Safe integer; minimum 4; maximum 127. |
| 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 |
|---|---|---|
| curves | Curves | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 16. |
| curves[].frequencyX | Frequency X | Required. Safe integer; minimum 1; maximum 32. |
| curves[].frequencyY | Frequency Y | Required. Safe integer; minimum 1; maximum 32. |
| curves[].phaseTurns | Phase Turns | Required. Finite number. |
| curves[].points | Points | Required. Array of Array of Finite number.; minimum items 2; maximum items 2.; minimum items 1; maximum items 128. |
| curves[].bounds | Bounds | Required. Object; no unknown keys. |
| curves[].bounds.minX | Min X | Required. Finite number. |
| curves[].bounds.minY | Min Y | Required. Finite number. |
| curves[].bounds.maxX | Max X | Required. Finite number. |
| curves[].bounds.maxY | Max Y | Required. Finite number. |
| curves[].bounds.width | Width | Required. Finite number. |
| curves[].bounds.height | Height | Required. Finite number. |
| 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": {
"count": 1,
"minimumFrequency": 1,
"maximumFrequency": 1,
"phaseTurns": [
0
],
"amplitudeX": 2,
"amplitudeY": 3,
"intervals": 4,
"seed": 42
},
"output": {
"curves": [
{
"frequencyX": 1,
"frequencyY": 1,
"phaseTurns": 0,
"points": [
[
0,
0
],
[
2,
3
],
[
0,
0
],
[
-2,
-3
],
[
0,
0
]
],
"bounds": {
"minX": -2,
"minY": -3,
"maxX": 2,
"maxY": 3,
"width": 4,
"height": 6
}
}
],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Bounds describe sampled points rather than guaranteed continuous extrema. Frequencies are dimensionless counts over the parameter period; this is artwork rather than a time-calibrated signal measurement.
- 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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Sample integer-radius hypotrochoids through r/gcd(R,r) turns with exact copied endpoints and sampled bounds.