Collatz Conjecture (3n+1)

COLLATZ · 3n+1

n even → n/2 · n odd → 3n+1.
Conjecture: every positive integer reaches 1.
Verified to ~2⁶⁸. Unproven in general.

① SINGLE TRAJECTORY · n

The ONE starting integer plotted in the center. Drives the ● charts on the right (parity, tree, coordinate, etc.).

Famous record-holders for stopping time.

② POPULATION · all integers [1..N]

Computes stats for EVERY integer from 1 to N. Drives the ▦ charts (chaos curve, peak, glide histogram) and the optional stack-mode overlay below. Higher N = richer scatter, slower compute.

Center plot

Log y-axis

Dots at each step

Color by parity

Stack mode

Show all trajectories [1..N]

Color mode (when stacked)

Alpha 0.10

Range uses the [1..N] above. Bigger N = denser spaghetti (slower).

① Stats — single trajectory (n)

starting n27

stopping time—

peak (max)—

peak ÷ start—

odd steps—

even steps—

current value—

② Stats — population [1..N]

range[1..1000]

avg stopping—

max stopping—

record holder—

Space play/pause R reset
← → step ±1 Shift+← → ±10
B build now L log y
Type any positive integer in the n field.

TRAJECTORY · n → ... → 1

step 0 / 0

paused

Speed 40ms

Step

0 / 0

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