Random Paper Chain Color Order Plan Generator

Description

Construct an exact-length caller-color link sequence under run and undirected adjacency rules with bounded cyclic-order search and per-color counts.

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.

Construct an exact-length caller-color link sequence under run and undirected adjacency rules with bounded cyclic-order search and per-color counts.

When to use this tool

Use this generator to create reproducible paper chain color order 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 colors, linkCount, maximumRun, forbiddenNeighbors 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 links, colorCounts. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Build a color chain using bounded randomized backtracking. Reject a candidate when it exceeds maximumRun or forms a supplied forbidden neighbor pair in either direction; return the sequence and counts for every supplied color.^[1]

Input field	Meaning and units	Accepted input
colors	Colors	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 80.; minimum items 1; maximum items 16.
linkCount	Link Count	Required. Safe integer; minimum 1; maximum 64.
maximumRun	Maximum Run	Required. Safe integer; minimum 1; maximum 64.
forbiddenNeighbors	Forbidden Neighbors	Required. Array of Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 80.; minimum items 2; maximum items 2.; minimum items 0; maximum items 64.
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
links	Links	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 80.; minimum items 1; maximum items 64.
colorCounts	Color Counts	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 32.
colorCounts[].id	Literal identifier used to match records, independently of their display labels.	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 80.
colorCounts[].count	Requested count; the mechanics explain whether one draw expands into several returned records.	Required. Safe integer; minimum 0; maximum 128.
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": {
    "colors": [
      "red",
      "blue"
    ],
    "linkCount": 3,
    "maximumRun": 1,
    "forbiddenNeighbors": [],
    "seed": 42
  },
  "output": {
    "links": [
      "blue",
      "red",
      "blue"
    ],
    "colorCounts": [
      {
        "id": "red",
        "count": 1
      },
      {
        "id": "blue",
        "count": 2
      }
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The chain is open, so the last and first links are not checked as neighbors. Constraints can be infeasible and first-feasible search is not uniform over valid chains.
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 Paper Chain Color Order Plan Generator — tool.io

Similar or alternative tools

Random Mesh Color Pattern Generator
Generate random hex control nodes and a shared-edge bilinear encoded-sRGB color grid via the existing interpolator, retaining its numeric precision and byte quantization; this is a rectangular mesh approximation, not a perceptual or linear-light blend.
Random Origami Paper Selection Deck Generator
Match caller-reviewed size, weight and tag requirements to supplied paper stock and sample compatible model/paper pairs without inventing suitability facts.