Ginkgo Combination Puzzle

cults3d

This is a little puzzle I invented (or at least I'm ignorant of other versions). The object is to rotate the pieces to produce a given pattern. Mathematically, it’s in the class of “2 dimensional combination puzzles”. I called it a ginkgo puzzle because the pieces remind me of ginkgo leaves. A relatively easy challenge is to place all the pieces pointing in one direction, then rotate pieces until all the pieces are pointing in the other direction. A more complex challenge, which I haven’t done yet, is to place all the pieces pointing in one direction, then rotate pieces until half the pieces point in a direction at right angles to the original pieces. Even though it can be a very simple puzzle, I find it fun to just turn the pieces. I've posted a video of me playing with an earlier version of this puzzle at https://youtu.be/yhvrXx4ZLu4 There are 3,625,093,120 unique, valid (non-overlapping pieces, no mutually-dependent loops) board layouts in this puzzle. I've posted a program that calculates that number, at https://github.com/bneedhamia/GinkgoPuzzleEnumeration The next question: how many of those 5.4 thousand million layouts can be achieved by starting with all pieces pointing up and turning pieces?