Overview
Hammersley sequences are useful when the final sample count is known, giving evenly distributed quasi-random points.
CoreSource checked
Hammersley Sequence
Generates low-discrepancy points using an index coordinate and radical inverse coordinates.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Randomness & Sampling
- Difficulty
- Intermediate
- Family
- Low-Discrepancy Sequence
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
radical inversefixed sample countlow discrepancyunit domain
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(dimensions log n)
Average
O(samples * dimensions log n)
Worst
O(samples * dimensions log n)
Space
O(1)
When to Use
- Use when monte Carlo simulation needs radical inverse.
- Use when the input matches the assumptions behind low-Discrepancy Sequence.
When Not to Use
- Avoid when independence, reproducibility, or distribution quality cannot be checked.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Generates low-discrepancy points using an index coordinate and radical inverse coordinates
- Uses radical inverse and fixed sample count to guide the work.
- Produces samples.
Use Cases
- Monte Carlo simulation
- Randomized algorithms
- Sampling distributions
Inputs
- Random source
- Distribution or weights
- Sample count
Outputs
- Samples
- Estimated statistic
- Randomized selection
Key Formulas (1)
Hammersley point
pi = (i / N, radicalinverse(i))
p_i = (i / N, radical_inverse(i))Uses normalized index as one coordinate and radical inverse for another.
Pseudocode
- 1.Prepare the inputs and state needed for Hammersley Sequence.
- 2.Apply the radical inverse step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return samples.
Canonical Example
- Input
- Hammersley Sequence input with a small representative case
- Output
- Samples
- Explanation
- Hammersley Sequence applies radical inverse to produce samples.
Implementation Notes
- Expose seed handling when reproducibility is important.
- Keep the radical inverse step separate enough to test independently.
Common Pitfalls
- Using a biased random source can quietly invalidate downstream estimates.
- Forgetting to check edge cases can make Hammersley Sequence look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryPlot generated samples against the target distribution or domain.
Step 1 of 4: Prepare the inputs and state needed for Hammersley Sequence.
randomness-sampling-mechanismNotes
Hammersley Sequence should be used with the assumptions and tradeoffs of low-Discrepancy Sequence in mind.
Sources (1)
What each reference supports for this entry.
Monte Carlo Statistical Methods
BookMonte Carlo reference for Hammersley Sequence low-discrepancy point sets and quasi-Monte Carlo sampling.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborHalton Sequence
Hammersley sequences use radical inverse structure like Halton sequences.
Alternative toSobol Sequence
Both are deterministic low-discrepancy sample sets.
Tags
Randomness & SamplingLow-DiscrepancyQuasi Monte CarloSampling