Random Spirograph Trochoid Set Generator

Description

Sample integer-radius hypotrochoids through r/gcd(R,r) turns with exact copied endpoints and sampled bounds.

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.

Sample integer-radius hypotrochoids through r/gcd(R,r) turns with exact copied endpoints and sampled bounds.

When to use this tool

Use this generator to create reproducible spirograph trochoid 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, minimumFixedRadius, maximumFixedRadius, minimumRollingRadius, maximumRollingRadius, penOffset, 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 fixed and rolling radii with rolling radius strictly smaller. Use their greatest common divisor to choose the closed hypotrochoid period, sample the curve with the supplied pen offset, and return sampled bounds with an exactly repeated starting endpoint.^[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.
minimumFixedRadius	Minimum Fixed Radius	Required. Safe integer; minimum 2; maximum 128.
maximumFixedRadius	Maximum Fixed Radius	Required. Safe integer; minimum 2; maximum 128.
minimumRollingRadius	Minimum Rolling Radius	Required. Safe integer; minimum 1; maximum 127.
maximumRollingRadius	Maximum Rolling Radius	Required. Safe integer; minimum 1; maximum 127.
penOffset	Pen Offset	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[].fixedRadius	Fixed Radius	Required. Safe integer; minimum 2; maximum 128.
curves[].rollingRadius	Rolling Radius	Required. Safe integer; minimum 1; maximum 127.
curves[].closureTurns	Closure 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.

json

{
  "input": {
    "count": 1,
    "minimumFixedRadius": 4,
    "maximumFixedRadius": 4,
    "minimumRollingRadius": 2,
    "maximumRollingRadius": 2,
    "penOffset": 1,
    "intervals": 4,
    "seed": 42
  },
  "output": {
    "curves": [
      {
        "fixedRadius": 4,
        "rollingRadius": 2,
        "closureTurns": 1,
        "points": [
          [
            3,
            0
          ],
          [
            0,
            1
          ],
          [
            -3,
            0
          ],
          [
            0,
            -1
          ],
          [
            3,
            0
          ]
        ],
        "bounds": {
          "minX": -3,
          "minY": -1,
          "maxX": 3,
          "maxY": 1,
          "width": 6,
          "height": 2
        }
      }
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Bounds cover sampled points, not guaranteed continuous extrema. Radii use a common arbitrary length unit; finite intervals approximate the smooth curve and do not model mechanical tolerances.
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 Spirograph Trochoid Set Generator — tool.io

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