Random Mirror Kaleidoscope Layout Generator

Description

Reflect a supplied wedge polyline through alternating sectors and clip every transformed segment to a centered square.

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.

Reflect a supplied wedge polyline through alternating sectors and clip every transformed segment to a centered square.

When to use this tool

Use this generator to create reproducible mirror kaleidoscope layout 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 motif, sectorOptions, clipHalfSize 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 sectorCount, segments, bounds. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Choose an even sector count, alternately reflect and rotate a supplied motif around the origin, then clip consecutive motif segments to the centered square. Return visible sector-labeled segments and their bounds.^[1]

Input field	Meaning and units	Accepted input
motif	Motif	Required. Array of Array of Finite number.; minimum items 2; maximum items 2.; minimum items 2; maximum items 32.
sectorOptions	Sector Options	Required. Array of Safe integer; one of 2, 4, 6, 8, 10, 12, 14, 16.; minimum items 1; maximum items 8.
clipHalfSize	Clip Half Size	Required. Finite number; strictly above 0.
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
sectorCount	Sector Count	Required. Safe integer; minimum 2; maximum 16.
segments	Segments	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 128.
segments[].sector	Sector	Required. Safe integer; minimum 0; maximum 15.
segments[].from	From	Required. Array of Finite number.; minimum items 2; maximum items 2.
segments[].to	To	Required. Array of Finite number.; minimum items 2; maximum items 2.
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": {
    "motif": [
      [
        1,
        0
      ],
      [
        1,
        1
      ]
    ],
    "sectorOptions": [
      2
    ],
    "clipHalfSize": 2,
    "seed": 42
  },
  "output": {
    "sectorCount": 2,
    "segments": [
      {
        "from": [
          1,
          0
        ],
        "to": [
          1,
          1
        ],
        "sector": 0
      },
      {
        "from": [
          1,
          0
        ],
        "to": [
          1,
          -1
        ],
        "sector": 1
      }
    ],
    "bounds": {
      "minX": 1,
      "minY": -1,
      "maxX": 1,
      "maxY": 1,
      "width": 0,
      "height": 2
    },
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The motif must fit the narrowest allowed initial angular wedge and at least one clipped segment must remain. This constructs line symmetry rather than a physical mirror or light-path simulation.
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 Mirror Kaleidoscope Layout Generator — tool.io

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