Random Harmonograph Curve Artwork Generator

Description

Choose damped sinusoidal axis parameters and sample a bounded two-oscillator harmonograph in caller time units; this is illustrative geometry, not an apparatus design.

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.

Choose damped sinusoidal axis parameters and sample a bounded two-oscillator harmonograph in caller time units; this is illustrative geometry, not an apparatus design.

When to use this tool

Use this generator to create reproducible harmonograph curve art 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 xOscillators, yOscillators, duration, 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 xOscillator, yOscillator, points, bounds. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Choose one damped oscillator for each axis and sample amplitude times sine of two-pi times frequency-times-parameter plus phase, multiplied by exponential damping. Return both oscillator records, points, and sampled bounds.^[1]

Input field	Meaning and units	Accepted input
xOscillators	X Oscillators	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 16.
xOscillators[].amplitude	Amplitude	Required. Finite number; strictly above 0.
xOscillators[].frequency	Frequency	Required. Finite number; minimum 0.
xOscillators[].phaseTurns	Phase Turns	Required. Finite number.
xOscillators[].damping	Damping	Required. Finite number; minimum 0.
yOscillators	Y Oscillators	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 16.
yOscillators[].amplitude	Amplitude	Required. Finite number; strictly above 0.
yOscillators[].frequency	Frequency	Required. Finite number; minimum 0.
yOscillators[].phaseTurns	Phase Turns	Required. Finite number.
yOscillators[].damping	Damping	Required. Finite number; minimum 0.
duration	Duration	Required. Finite number; strictly above 0.
intervals	Intervals	Required. Safe integer; minimum 2; 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
xOscillator	X Oscillator	Required. Object; no unknown keys.
xOscillator.amplitude	Amplitude	Required. Finite number; strictly above 0.
xOscillator.frequency	Frequency	Required. Finite number; minimum 0.
xOscillator.phaseTurns	Phase Turns	Required. Finite number.
xOscillator.damping	Damping	Required. Finite number; minimum 0.
yOscillator	Y Oscillator	Required. Object; no unknown keys.
yOscillator.amplitude	Amplitude	Required. Finite number; strictly above 0.
yOscillator.frequency	Frequency	Required. Finite number; minimum 0.
yOscillator.phaseTurns	Phase Turns	Required. Finite number.
yOscillator.damping	Damping	Required. Finite number; minimum 0.
points	Points	Required. Array of Array of Finite number.; minimum items 2; maximum items 2.; minimum items 1; maximum items 128.
bounds	Bounds	Required. Object; no unknown keys.
bounds.minX	Min X	Required. Finite number.
bounds.minY	Min Y	Required. Finite number.
bounds.maxX	Max X	Required. Finite number.
bounds.maxY	Max Y	Required. Finite number.
bounds.width	Width	Required. Finite number.
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.

json

{
  "input": {
    "xOscillators": [
      {
        "amplitude": 2,
        "frequency": 1,
        "phaseTurns": 0,
        "damping": 0
      }
    ],
    "yOscillators": [
      {
        "amplitude": 3,
        "frequency": 1,
        "phaseTurns": 0,
        "damping": 0
      }
    ],
    "duration": 1,
    "intervals": 4,
    "seed": 42
  },
  "output": {
    "xOscillator": {
      "amplitude": 2,
      "frequency": 1,
      "phaseTurns": 0,
      "damping": 0
    },
    "yOscillator": {
      "amplitude": 3,
      "frequency": 1,
      "phaseTurns": 0,
      "damping": 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

Frequency and damping use reciprocal units of the supplied duration parameter and phase is in turns. This is parametric artwork rather than calibrated mechanical motion; bounds are sampled extrema.
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

Tool behavior and example: Random Harmonograph Curve Artwork Generator — tool.io

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