Loose Ends

The rule, exactly as read: the first segment is unit length. The second gets a random angle and touches an endpoint of the first somewhere along its own length — a T, not a joint. Every segment after that must touch the still-untouched endpoints of two other segments, and touch nothing else at all.

How that's built here, spelled out because the request left it to be resolved: the first two segments are placed by the tool, not by you — "a random angle" reads as the tool's choice, so segment 2's angle, length and where along it the contact falls are all randomised. From segment 3 on there is no random angle left to give: the direction is forced by whichever two open endpoints you weld together, so the only freedom is which pair to pick and how far the new piece runs past each of them (0 uses that end up too). The tool refuses any placement that crosses or touches anything besides the two endpoints you chose.

Dots that glow are untouched and tappable. Dim dots are already used. A small perpendicular tick marks a T-junction, same idea as segment 2's contact.

Run automatically does the same thing the tapping does, just picked by the tool: it repeatedly searches for a random valid pair of untouched endpoints and a random pair of extensions, and places whichever one it finds first. It's a search, not a proof — if it stops early saying it couldn't find a move, that means it tried hundreds of random combinations and failed, not that none exist. Stop it any time and keep going by hand.