⋮ A 3X − 1 NOTEBOOK

Odd lines 3x−1.

First children to the left.
Follow the Tracks to the right.

Show 1-doubling first children 2-doubling first children Tracks · 4x − 1 Red circles & same-value links Horizontal red-pair links Green circles & same-value links Horizontal green-pair links Blue circles & same-value links Horizontal blue-pair links Horizontal blue–red links Horizontal blue–green links Horizontal green → red links Horizontal red → green links

Track members per click

Click a right-hand number to reveal this many following members. Enter 1–256.

Space between rows 48

Drawing

Turn on Draw to mark the notebook. Turn it off to click numbers again.

↳

Click any middle or left-side odd number to isolate its Blue-to-Vine left-side path (click again to show all).

Set the extension above, then click the right-hand number whose Track you want to follow.

The arithmetic

Remainder 2 after division by 3:
(2x − 1) / 3

Remainder 1, except at 1:
(4x − 1) / 3

At 1, the self-return is skipped. Its first proper child is 5, after four doublings, marked *.

Track links join siblings, except the initial 1 → 5 Trunk birth. These are local arithmetic relations; the display does not test connection to 1.

CHILDREN & TRACKS (3X − 1)1–99 · 50 odd rows

Click any odd for Blue → Vine path · Click Track to extend →