随 means “follow along, at will”

ずい · zui

Also: follow, though, notwithstanding, while

Kun'yomi (Japanese reading)
まにまに, したがう
On'yomi (Chinese reading)
ズイ

JLPT N1 · Taught in secondary school · 12 strokes

The story

A mound (阝) and a road (辶) with 有, have, traveling it: picture going wherever the road leads. 随時 is "at any time", 随筆 an essay that follows the pen, like The Pillow Book, and 随分 means quite a lot.

Used in 随分 (zuibun, considerably), 随時 (zuiji, at any time), and 随筆 (zuihitsu, essay)

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Readings from KANJIDIC2, © EDRDG, CC BY-SA.