Binary Runs

 I was recently digging through some papers that were about a year old and rediscovered this puzzle idea. I'm pretty sure it was meant to be another take on the idea of Romantic Spot (see elsewhere in blog), but the ruleset ended up feeling a lot more cohesive and less arbitrary. The first two puzzles (one of which is solved for you as an example) were taken directly from the paper and the larger one was made on 8/5/24.

Place a 0 or 1 in some cells so that all the digits are orthogonally connected and every horizontal/vertical run of digits forms a binary number that describes its length.

It might not be obvious from just these puzzles, but this puzzle type does have the capability to get really explosive. For example, using proper placement, only three digits are needed to force a single solution in a 9x9 grid! And yet, somehow, this ruleset does have the means to slow down its expansion given enough space and care.