Random Spiral Packing Artwork Generator

Description

Place random-radius circles along an Archimedean spiral with explicit overlap traces and rejection; attempt count is not guaranteed accepted count or optimal packing.

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.

Place random-radius circles along an Archimedean spiral with explicit overlap traces and rejection; attempt count is not guaranteed accepted count or optimal packing.

When to use this tool

Use this generator to create reproducible spiral packing 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 attempts, startRadius, growthPerTurn, stepTurns, motifRadii, minimumGap, overlapPolicy 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 attempts, acceptedCount, bounds. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Place candidate motif centers along an Archimedean spiral, sampling each motif radius. Record overlap against previously accepted motifs using strict distance comparison with the requested gap. Either accept every candidate or reject blocked candidates, then bound accepted circle extents.^[1]

Input field	Meaning and units	Accepted input
attempts	Attempts	Required. Safe integer; minimum 1; maximum 64.
startRadius	Start Radius	Required. Finite number; strictly above 0.
growthPerTurn	Growth Per Turn	Required. Finite number; minimum 0.
stepTurns	Step Turns	Required. Finite number; strictly above 0.
motifRadii	Motif Radii	Required. Array of Finite number; strictly above 0.; minimum items 1; maximum items 16.
minimumGap	Minimum Gap	Required. Finite number; minimum 0.
overlapPolicy	Overlap Policy	Required. Text; one of "allow", "reject".
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
attempts	Attempts	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 64.
attempts[].center	Center	Required. Array of Finite number.; minimum items 2; maximum items 2.
attempts[].radius	Radius	Required. Finite number; strictly above 0.
attempts[].accepted	Accepted	Required. Boolean.
attempts[].blockedBy	Blocked By	Required. Array of Safe integer; minimum 0; maximum 63.; minimum items 0; maximum items 64.
acceptedCount	Accepted Count	Required. Safe integer; minimum 1; maximum 64.
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": {
    "attempts": 2,
    "startRadius": 2,
    "growthPerTurn": 0,
    "stepTurns": 0.25,
    "motifRadii": [
      0.5
    ],
    "minimumGap": 0,
    "overlapPolicy": "reject",
    "seed": 42
  },
  "output": {
    "attempts": [
      {
        "center": [
          2,
          0
        ],
        "radius": 0.5,
        "accepted": true,
        "blockedBy": []
      },
      {
        "center": [
          0,
          2
        ],
        "radius": 0.5,
        "accepted": true,
        "blockedBy": []
      }
    ],
    "acceptedCount": 2,
    "bounds": {
      "minX": -0.5,
      "minY": -0.5,
      "maxX": 2.5,
      "maxY": 2.5,
      "width": 3,
      "height": 3
    },
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Touching at the exact separation is allowed. This is sequential rejection artwork rather than optimal packing. Rejected motifs do not block later attempts, and reported bounds cover accepted motifs only.
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 Spiral Packing Artwork Generator — tool.io

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