A 256-bit ARX-based pseudorandom number generator with rotation constants derived from Recursive Division Tree entropy analysis.
Starting point for random sequence (0xC0FFEE in decimal)
More rounds = better diffusion, slower generation
Triangle entropy constant (default: 1.585)
Menger-like entropy constant (default: 1.926)
Tetrahedral entropy constant (default: 1.262)
Optional: Different domains produce different sequences
Number Generation
💡 For good visualizations: use 1,000+ numbers. For statistical tests: use 10,000+
💡 For true continuous floats (0.0-1.0), use 32-bit Unsigned then switch to Floats tab
Click "Generate Numbers" to begin...
Statistical Analysis
Numbers Generated
0
Mean Value
-
Min / Max
- / -
Std Deviation
-
Entropy
-
Ideal = 100%
Current: -
Chi-Square Statistic
-
Lower is better
Expected ≈ -
KS Statistic
-
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Distribution Visualization
📊 What am I seeing?
Generate numbers to see distribution analysis.
Performance & Benchmarks
Generation Speed
-
numbers per second
Last Generation Time
-
milliseconds
Total Generated
0
all time
Generator Status
Not Initialized
🎮 Interactive Demos & Games
See RGE-256 in action with classic probability applications!
🎲 Dice Roller
Roll virtual dice using RGE-256
🎲
Click "Roll Dice" to start!
Rolls: 0Average: -
🪙 Coin Flipper
Flip coins and track statistics
🪙
Click "Flip Coins" to start!
Heads: 0 (0%)Tails: 0 (0%)
🃏 Card Drawer
Draw random playing cards from a deck
🃏
Click "Draw Cards" to start!
Cards drawn: 0 / 52
🎰 Lottery Numbers
Generate lottery-style numbers
🎰
Click "Generate Numbers" to start!
📚 RGE-256 Help & Guide
🎲 What is RGE-256?
RGE-256 is a 256-bit ARX-based pseudorandom number generator (Add-Rotate-XOR) with rotation constants derived from Recursive Division Tree (RDT) entropy analysis. It's designed for:
Simulations: Monte Carlo methods, statistical modeling
Education: Understanding PRNGs and statistical tests
⚠️ Not for cryptography! This generator has not been cryptographically analyzed and should NOT be used for security-critical applications like key generation, encryption, or authentication.
📊 Understanding Statistics
Mean Value
Average of all generated numbers. Should be near the midpoint of your range.
✓ Good: Within 1-2% of midpoint ⚠ Warning: 2-5% off ✗ Bad: More than 5% off
Standard Deviation
Measures spread of values. Higher = more spread out.
For uniform distribution:
σ ≈ (max - min) / √12
Shannon Entropy
Measures information content and randomness. Higher = more random.
Tests if distribution is uniform. Statistic should be close to expected value.
✓ Good: Within 20% of expected ⚠ Acceptable: 20-40% off ✗ Failed: More than 40% off
Kolmogorov-Smirnov Test
Tests uniformity by measuring maximum deviation from expected distribution.
✓ PASS: D < critical value ⚠ WEAK: D ≥ critical value
Critical value: 1.36/√n
Runs Test
Checks for patterns in sequences (runs above/below median).
Tests independence of consecutive values
📈 Visualizations Explained
Histogram
Shows distribution of generated values across bins.
Green bars: Within 20% of expected count
Yellow bars: 20-40% deviation
Red bars: More than 40% deviation
Red line: Expected average per bin for uniform distribution
Tip: Use 1,000+ numbers for clear histograms
Bit Pattern Analysis
Shows percentage of 1s at each bit position (0-31).
Green bars: Within 2% of 50%
Yellow bars: 2-5% off from 50%
Red bars: More than 5% off
Red line: 50% (ideal balance)
Tip: Works best with 32-bit range, use 10,000+ numbers
Scatter Plot
Plots numbers in sequence. Should look random with no visible patterns.
Warning signs: Lines, clusters, or obvious structure
Bit Transition Heatmap
Shows frequency of bit changes between consecutive numbers.
All transition types (0→1, 1→0, 0→0, 1→1) should occur with similar frequency.
Good: Uniform color across all cells
⚙️ Configuration Parameters
Seed
Starting value for the sequence. Same seed = same sequence (reproducible).
Range: 0 to 253-1
Rounds
Number of mixing rounds per generation.
3 rounds: Fast, good quality (default)
4 rounds: Better mixing
5 rounds: Maximum quality, slower
ζ Parameters
Rotation constants derived from RDT entropy:
ζ₁ (1.585): Triangle entropy
ζ₂ (1.926): Menger-like entropy
ζ₃ (1.262): Tetrahedral entropy
Tip: Use defaults unless experimenting
Domain Separation
Optional string mixed into initialization.
Same seed + different domain = different independent sequences.
Use case: Multiple independent random streams
💡 Tips for Best Results
Sample size matters: Use 1,000+ for visualizations, 10,000+ for statistical tests
Histogram: Best with custom ranges (1-100, 1-1000)
Bit patterns: Best with 32-bit unsigned range
Reproducibility: Save your session or record seed/configuration
Comparison: Generate same count with different seeds to compare quality
📤 Export Options
Download TXT
Simple text file with one number per line.
Export CSV
Spreadsheet format with Index and Value columns.
Export JSON
Complete data with configuration, statistics, and all numbers.
Export PDF Report
Professional report with all statistics, visualizations, and interpretations.
📚 Citation
If you use RGE-256 in your research:
Paper: "RGE-256: A New ARX-Based Pseudorandom Number Generator With Structured Entropy and Empirical Validation" Author: Steven Reid ORCID: 0009-0003-9132-3410 Related Work: Recursive Division Tree entropy analysis (DOI: 10.5281/zenodo.17682287)