Dendrite
Watch frost climb a window, then move one dial and the same growth thins into a lightning bolt. Every arm shadows the ground behind it, and that shadowing is the whole reason any of it branches.
Growth goes where the electric field is strongest, and eta says how strongly it prefers the strongest point. At zero it is a fat blob, at one it is frost, and past three it is a single bolt. Moving this switches to the field and regrows the picture.
A particle that touches only sticks this often. Turn it down and particles slide deep into the gaps before they settle, so the arms thicken and fill in.
Boxes of each size are laid over the cluster and the full ones counted. A solid shape doubles its count four times over when the boxes halve, a line doubles it twice. This one lands in between, and the number is measured here rather than quoted.
Pointer, size and pace
Anything you paint is cluster from that moment on, so you can drop a wall in front of a growing arm and watch it lose the race.