Highlights highly divisible row/column numbers such as 60.
Shows coprime density φ(n)/n on the axes.
Marks the smallest prime shared by numerator and denominator.
Shading follows the length of the reduced ratio's continued fraction.
Base-sensitive: highlights fractions whose expansion terminates in this base.
Click a ratio. Families satisfying |ad−bc|=1 are highlighted.
BASE-DEPENDENT COLOR MODES
• terminating vs repeating: whether the reduced denominator eventually divides a power of the base.
• period length: length of the repeating cycle after non-repeating digits are removed.
• first repeating digit: colors by the first digit of the eventual cycle.
• multiplicative order: the order of the base modulo the denominator after removing factors shared with the base.
• full repeating cycle signature: colors the whole cycle, not merely its first digit; rotations of the same repeating block share a color.
• cycle digit entropy: measures how evenly the base digits are used inside the repeating block.
• cycle rotational symmetry: detects repeated substructure inside the cycle.
• cycle barcode: at close zoom, draws the whole repeating cycle as a tiny strip inside each cell.
Digits above base 36: 0–9, A–Z, then a–n for values 36–49.
Base 12: digits A=ten, B=eleven. These modes genuinely reorganize when the base changes.
drag to pan · wheel to zoom · click a cell to isolate a ratio family · zoom range 0.18–160 px/cell
BASE EXPLORER 2–50
click a tile to jump into that base · same arithmetic window in every tile