ENTROPY
32 bits4,294,967,296
doubling proof2 × 2^31 = 2^32
LIVE ×2 MODEL

Every bit doubles the world.

Left is one bit ago. Watch the right grow to exactly twice its width as a second identical world appears.

PHYSICAL DOUBLING MODEL0.1 mm × 2^32

≈ 48.5 Mount Everests

429 km4.9 more bits reaches Earth's diameter.

Imagine 0.1 mm doubling with every bit. The distance is a scale model, not a physical keyspace.
LEFT · ONE BIT AGO · 1×31 BITS215 km
RIGHT · NOW · 2× THE LEFT32 BITS429 km
PASSED · Mount EverestNEXT · Earth
↓ Cross a whole-bit gate
ENTROPY / FIELD NOTES

How to read this instrument

01

Entropy counts possible states

H bits describes an ideal space of 2^H possibilities under stated assumptions. It does not say that a human-chosen string is random.

02

Every bit creates another complete world

Adding one independent uniform bit multiplies the search space by two. The left block stays fixed as the one-bit-ago reference. The right starts at the same width, then reveals a second identical copy and lands exactly twice as wide.

+1 bit
03

The paper ruler makes ×2 physical

The central ruler imagines a 0.1 mm sheet thickness doubling once per bit. It passes familiar distances from a hand to Earth, the Moon, a light-year, and the observable universe. This is a distance model of the same exponential rule, not a claim that a keyspace has physical size.

04

The possibility field is adaptive

Up to 12 whole bits, every current state is drawn. Above that, the current right field uses 4,096 logarithmic buckets. The left reuses one of its two copies as a comparison reference; the legend always states what a current-field cell means.

05

Uniform randomness is an assumption

Character, dice, and word formulas apply when each choice is uniform and genuinely random. Human patterns can reduce entropy dramatically.

06

Independent components can add

Independent source entropies add. If two components depend on each other, Entropy excludes the dependent part from its guaranteed total.

07

Compromise removes a component

If an attacker already knows one component, that component contributes no remaining search. Build mode shows both all-unknown and selected-compromise totals.

08

Guess rate is a model

The slider is deliberately abstract. Real rates vary with algorithms, hardware, memory cost, and the verification process.

09

Entropy is not the whole cryptosystem

Algorithm-specific security strength may be lower than source entropy and depends on the construction and attack.

10

Read the precision labels

Exact values are mathematical. Modeled comparisons expose their inputs. Order-of-magnitude analogies carry visible uncertainty.

11

Privacy by construction

No secrets, accounts, analytics, or network calculation. Parameters stay in your browser; share links contain generation settings only.

12

Sources