Patterns that appear. Patterns that persist. Follow ten examples from 100 to 100,000 positions. Count their digits, reveal their structure, and inspect what changes when the scale grows.
All values use the full digit stream. Dense traces retain within-bin extrema for display. Drag to zoom; use the position inspector for exact values.
Open any of the 40 signature views.
Construction, numerical verification, and display conventions.
Position 1 is the first digit after the point; the integer part is never counted. Eight views use base 10, Thue–Morse uses base 2, and the BBP view of π uses base 16. These are different digit systems, not interchangeable sequences.
Counts and frequencies are computed from all digits, not a sampled subset. Dense plots retain first, last, minimum, and maximum values within display bins. Zooming recalculates the display from the full data. The inspector and CSV export retain exact positions.
Fractions use integer long division; constructed streams use their defining rules. Numerical constants were evaluated at two high precisions with 80 and 140 extra decimal digits beyond the precision required for 100,000 hexadecimal positions. All retained prefixes agree. This is a numerical stability check, not a formal interval proof of every decimal digit.
For window width w, the value at x counts the selected digit in positions max(1, x−w+1)…x and divides by min(w, x). The window width does not silently change with the selected range.
The uniform stream is reproducible pseudorandom data with seed 20261003. A shuffled prefix preserves the exact histogram of the selected number at the selected range. No confidence bands or significance claims are implied; choosing a striking pattern after looking at many patterns needs separate statistical treatment.
The bulk hexadecimal stream comes from high-precision π. The probe directly evaluates the BBP sums at the requested position using exact modular arithmetic and fixed-point integer error bounds. A result is accepted only when both bounds produce the same extracted block; that block is then compared with the stored stream.