  We provide a simple and natural solution to the problem of generating all
$2^n \cdot n!$ signed permutations of $[n] = \{1,2,\ldots,n\}$. Our solution
provides a pleasing generalization of the most famous ordering of permutations:
plain changes (Steinhaus-Johnson-Trotter algorithm). In plain changes, the $n!$
permutations of $[n]$ are ordered so that successive permutations differ by
swapping a pair of adjacent symbols, and the order is often visualized as a
weaving pattern involving $n$ ropes. Here we model a signed permutation using
$n$ ribbons with two distinct sides, and each successive configuration is
created by twisting (i.e., swapping and turning over) two neighboring ribbons
or a single ribbon. By greedily prioritizing $2$-twists of the largest symbol
before $1$-twists of the largest symbol, we create a signed version of plain
change's memorable zig-zag pattern. We provide a loopless algorithm (i.e.,
worst-case $\mathcal{O}(1)$-time per object) by extending the well-known
mixed-radix Gray code algorithm.
