Random Concentric Rectangle Insets

Description

Choose a uniform distinct subset of feasible integer concentric inset distances then sort outward-to-inward; rectangles have positive interior dimensions, not arbitrary recursive cuts.

A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.

Choose a uniform distinct subset of feasible integer concentric inset distances then sort outward-to-inward; rectangles have positive interior dimensions, not arbitrary recursive cuts.

When to use this tool

Use this tool to choose a uniform distinct subset of feasible integer concentric inset distances then sort outward-to-inward; rectangles have positive interior dimensions, not arbitrary recursive cuts.

How to use the tool and how it works

Enter width, height, count, seed using the definitions below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.seed, result.insets, result.rectangles, using the stated boundary, ordering, sign and absence conventions.

Enumerate integer insets d from zero through floor((min(width,height)−1)/2). Choose count distinct insets uniformly, sort them and return [d,d,width−d,height−d] for each.^[1]

Input field	Meaning and units	Accepted input
width	Integer width, 1–256, in the positions/cells described above.	Finite safe integer satisfying the stated bounds.
height	Positive integer rectangle height, bounded to 128 for cuts or 256 for concentric insets.	Finite safe integer satisfying the stated bounds.
count	Positive number of samples/items to request, within the generator’s eligible-support bounds.	Finite safe integer satisfying the stated bounds.
seed	Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws.	Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply.

Output field	Interpretation
result	Object containing the fields below.
result.seed	Original supplied seed string; injected-source replay additionally requires that source’s state.
result.insets	Sorted distinct integer distances applied equally to all rectangle sides.
result.rectangles	Generated [minX,minY,maxX,maxY] bounds under the stated partition/inset rule.

json

{
  "input": {
    "width": 10,
    "height": 8,
    "count": 2,
    "seed": "batch56"
  },
  "output": {
    "result": {
      "seed": "batch56",
      "insets": [
        2,
        3
      ],
      "rectangles": [
        [
          2,
          2,
          8,
          6
        ],
        [
          3,
          3,
          7,
          5
        ]
      ]
    }
  }
}

Limitations and assumptions

Dimensions are 1–256 and count cannot exceed available insets. Every rectangle has positive dimensions; outputs are concentric axis-aligned bounds.
A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.

Alternative or Complementary methods

Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.

References

Tool behavior and example: Random Concentric Rectangle Insets — tool.io

Similar or alternative tools

Random Guillotine Rectangle Cut Trace
At each step choose a uniform splittable current rectangle, then a uniform legal axis and integer interior cut; local-choice process, not uniform over final partitions.
Random Block Order Permutation
Uniform whole-block position permutation preserving internal order and duplicate display labels.