Random Within-Block Permutation

Description

Independently uniformly permute positions within each fixed block, preserving block order and source indexes.

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.

Independently uniformly permute positions within each fixed block, preserving block order and source indexes.

When to use this tool

Use this tool to independently uniformly permute positions within each fixed block, preserving block order and source indexes.

How to use the tool and how it works

Enter blocksJson, seed using the definitions below. Serialize JSON text fields in the decoded shape shown below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.seed, result.blocks, using the stated boundary, ordering, sign and absence conventions.

For each fixed block separately, Fisher–Yates shuffle its {value,index} positions, preserving block order and original within-block indexes. Use one advancing source across all blocks.^[1]

Input field	Meaning and units	Accepted input
blocksJson	JSON array of arrays of literal strings, preserving the distinction between block and member positions.	Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply.
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.

These decoded structures show the examples inside JSON text fields. Supply their serialized JSON strings as input.

json

{
  "blocksJson": [
    [
      "a",
      "b"
    ],
    [
      "c",
      "d"
    ]
  ]
}

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.blocks	Whole blocks in selected order or within-block permuted position records, as stated above.

json

{
  "input": {
    "blocksJson": "[[\"a\",\"b\"],[\"c\",\"d\"]]",
    "seed": "batch56"
  },
  "output": {
    "result": {
      "seed": "batch56",
      "blocks": [
        [
          {
            "value": "a",
            "index": 0
          },
          {
            "value": "b",
            "index": 1
          }
        ],
        [
          {
            "value": "c",
            "index": 0
          },
          {
            "value": "d",
            "index": 1
          }
        ]
      ]
    }
  }
}

Limitations and assumptions

At least one block must have more than one element. Equal text values remain distinct positions; the complete flattened list is not shuffled across blocks.
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 Within-Block Permutation — tool.io

Similar or alternative tools

Random Block Order Permutation
Uniform whole-block position permutation preserving internal order and duplicate display labels.
Random Contiguous Block Start
Choose one uniform legal contiguous block start in a finite index domain; positive block length cannot exceed domain size.