Description
Generate a seeded bounded integer walk with fair unit-step proposals and absorbing endpoints, retaining every proposal after absorption.
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.
Generate a seeded bounded integer walk with fair unit-step proposals and absorbing endpoints, retaining every proposal after absorption.
When to use this tool
Use this generator to create replayable examples of a process that stops changing after reaching either boundary, while retaining its unused driving proposals.
How to use the tool and how it works
- Enter initial, minimum, maximum, steps, seed using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.seed, result.states, result.proposals, using the stated boundary, ordering, sign and absence conventions.
Generate exactly steps independent signed ±1 proposals from one advancing source. Begin states with initial. If the current state already equals minimum or maximum, append that same state; otherwise add the next proposal. Proposals continue to be generated and reported after absorption.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| initial | Initial integer state within the explicitly supplied counter/walk bounds. | Finite safe integer satisfying the stated bounds. |
| minimum | Inclusive integer lower state bound within ±1,000,000; minimum<maximum. | Finite safe integer satisfying the stated bounds. |
| maximum | Inclusive integer upper state bound within ±1,000,000; minimum<maximum. | Finite safe integer satisfying the stated bounds. |
| steps | Number of transitions, integer 1–127; the states output includes the initial state as well. | 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.states | State sequence including the initial coordinate followed by every transition. |
| result.proposals | Independent signed ±1 proposals before reflection. |
{
"input": {
"initial": 1,
"minimum": 0,
"maximum": 2,
"steps": 3,
"seed": "batch56"
},
"output": {
"result": {
"seed": "batch56",
"states": [
1,
2,
2,
2
],
"proposals": [
1,
1,
1
]
}
}
}Limitations and assumptions
- The endpoints are absorbing, so visible state paths are not uniformly distributed. Bounds and initial are integers within ±1,000,000 with minimum<maximum and initial inside; steps is 1–127. Starting at an endpoint yields a constant state path.
- 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.
- Numeric outputs must remain finite and within safe-integer magnitude. Original record indexes and cell coordinates are zero-based; stated half-open ranges exclude their end.
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
Similar or alternative tools
- Reflecting integer walk
Reflect signed proposals at the supplied state boundaries instead of absorbing there.
- Saturating counter input trace
Clamp generated integer increments to explicit counter bounds.