A visual proof of a result of Knuth on spanning trees of Aztec diamonds in the case of odd order

The even Aztec diamond image is known to have precisely four times more spanning trees than the odd Aztec diamond image—this was conjectured by Stanley and first proved by Knuth. We present a short combinatorial proof of this fact in the case of odd image. Our proof works also for the more general case of odd-by-odd Aztec rectangles.