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Random Complementary Bitmap Pair

Replay seed or one advancing injected source, uniform over the explicitly stated finite support, not cryptographically secure. Sample one fair independent-cell binary bitmap and return its exact bitwise complement; pair assignments uniform over first masks, not independent paired images.

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Description

Sample one fair independent-cell binary bitmap and return its exact bitwise complement; pair assignments uniform over first masks, not independent paired images.

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.

Sample one fair independent-cell binary bitmap and return its exact bitwise complement; pair assignments uniform over first masks, not independent paired images.

When to use this tool

Use this tool to sample one fair independent-cell binary bitmap and return its exact bitwise complement; pair assignments uniform over first masks, not independent paired images.

How to use the tool and how it works

  1. Enter rows, columns, seed using the definitions below.
  2. Run the operation. Resolve input-format errors before interpreting an output.
  3. Read result.seed, result.first, result.complement, using the stated boundary, ordering, sign and absence conventions.

Draw an independent binary value for every cell, then calculate the second bitmap deterministically as 1−first at each position.1

Input fieldMeaning and unitsAccepted input
rowsPositive integer grid row count; bitmap generators allow 1–11, toroidal origin allows 1–128.Finite safe integer satisfying the stated bounds.
columnsPositive integer grid column count under the same bounds; quarter-turn symmetry requires a square.Finite safe integer satisfying the stated bounds.
seedNonblank 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 fieldInterpretation
resultObject containing the fields below.
result.seedOriginal supplied seed string; injected-source replay additionally requires that source’s state.
result.firstFirst independently sampled row-major binary bitmap.
result.complementDeterministic cellwise 1−first bitmap.
json
{
  "input": {
    "rows": 2,
    "columns": 2,
    "seed": "batch56"
  },
  "output": {
    "result": {
      "seed": "batch56",
      "first": [
        [
          1,
          1
        ],
        [
          1,
          1
        ]
      ],
      "complement": [
        [
          0,
          0
        ],
        [
          0,
          0
        ]
      ]
    }
  }
}

Limitations and assumptions

  • Dimensions are 1–11. The second bitmap is fully dependent on the first rather than an independent random bitmap.
  • 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

  1. Tool behavior and example: Random Complementary Bitmap Pair — tool.io

Similar or alternative tools

  • Random Fixed-Pair Dyck Word

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  • Random Mirror-Symmetric Bitmap

    Choose independent fair binary values for each left/right mirror orbit, uniform over symmetry-compatible masks; orbit cells are tied, not independently sampled.

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