A terminal program that computes Pi digits in real time and visualizes the frequency distribution of each digit (0-9) to experimentally test whether Pi is a Normal Number.
Normal Number: A number whose digits are uniformly distributed in every base. Whether Pi is a Normal Number remains an open problem in mathematics, but empirical evidence strongly supports it.
- Chudnovsky Binary Splitting Algorithm — the same algorithm used to set Pi world records
- Real-time bar chart — color-coded visualization of digit counts, percentages, and deviation from 10%
- Statistical tests
- Chi-squared (χ²) — goodness-of-fit test for uniform distribution (df=9, α=0.05)
- Shannon Entropy — convergence toward the theoretical maximum log₂(10) ≈ 3.3219 bits
- Max |deviation| — largest deviation from the expected 10%
- Convergence sparklines — visual trace of how each metric converges to uniformity as more digits are computed
- Flicker-free rendering — in-place cursor overwrite with clear-to-EOL, no full-screen redraw
# Build
cargo build --release
# Run
cargo run --releasePress Ctrl+C or ESC to stop.
Implements the Chudnovsky formula with Binary Splitting:
- Each term yields ~14.18 decimal digits of precision
- Batch size grows progressively: 1,000 → 2,000 → 4,000 → ... → 2,000,000
- Computation runs on a background thread; the main thread handles visualization
| Metric | Threshold | Interpretation |
|---|---|---|
| χ² < 16.919 | df=9, p=0.05 | Cannot reject uniform distribution → UNIFORM |
| Entropy → 3.3219 | log₂(10) bits | Digit probabilities are equal |
| |dev|max → 0 | Deviation from 10% | All digits converge to exactly 10% |
χ² = 6.574 UNIFORM
Entropy: 3.3219/3.3219 bits (100.00%)
|dev|max: 0.047%
At one million digits, each digit 0-9 appears at almost exactly 10%, passing all uniformity tests.
num-bigint— Arbitrary-precision integer arithmeticnum-traits— Numeric traitscrossterm— Cross-platform terminal manipulation
MIT