ζMATH MILLENNIUM/Probability Lab
▣ Research concluded 8 May 2026. This page shows the final static snapshot from a 41-hour Monte Carlo run. Live data feed has been retired. View summary results →
Probability Lab · Module

Chaos Wall

Final heatmap — research concluded

Every column the simulator generates contributes to this picture. After 41 hours of continuous simulation, the wall flattened — every number landed within ±0.64% of uniform expectation. This static snapshot captures the final state from 1.38 M simulations / 68.83 B columns. The Law of Large Numbers, made visible.

■ archived
Total simulations
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Numbers drawn (main)
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Numbers drawn (euro)
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Max deviation
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Frequency heatmaps

Color intensity ∝ relative frequency vs expected uniform mean

Each cell represents one number. Saturation shows how often that number has been drawn relative to the uniform expectation. Hover for exact counts and Z-score.

Main numbers · 1 to 50—
cold
hot
Euro numbers · 1 to 12—
cold
hot

Hot & cold rankings

Top deviations from uniform · main pool only

Numbers with the largest positive Z-score (drawn more than expected) and the largest negative Z-score (drawn less than expected). These deviations are the random fluctuations of a fair process — they prove nothing about the future.

▲ Hot — drawn MORE than expected
▼ Cold — drawn LESS than expected

Pair-affinity matrix

Which numbers tend to share a column with which

Pick a target number. The grid below shows the relative frequency of every other number co-appearing in a column with the target. In a fair draw, every co-appearance frequency converges to 4/49 ≈ 8.16%.

Target number: Sampled locally over 50 k Pure RNG columns
What you're seeing. Backend simulator generates random Eurojackpot draws and counts every drawn number into a global Postgres table. The frequency data was streamed in real time during the live run; this static snapshot captures the final state. With billions of columns evaluated, the 1-to-50 grid is now flat to within roughly ±1% — exactly what theory predicts for a Bernoulli sampler at this sample size.