EDIT: The synthesis itself:
This could most likely be improved.
Congratulations on the Fore and Back synthesis! I had been expecting it to come from a symmetrical predecessor, so I was surprised at the immediate predecessor shown here. I tried to create another way to synthesize that predecessor directly and more cheaply, but it was ultimately unrewarding. Basically, starting from a 3-part still-life (that would likely take 10-12 gliders to create), and then activating it with 12 additional gliders - and that only made everything except the top block (which was impossible to add), which would have cost than the original synthesis itself, so it wasn't worth it.
However, 15 generations after this (2 generations before the Fore and Back actually forms), the predessor resembles a round object whose two sides are mutilated in different ways. It turns out that either kind of mutilation can be done on both sides simultaneously, i.e. from a symmetrical predecessor. The top one can be accomplished by adding a simple domino spark. The central symmetrical object itself seems fairly common, and turns into a tub. There just happens to be a 4-glider tub synthesis (i.e. from two adjacent boats) that makes it using this very predecessor, which makes a good starting point. Unfortunately, adding the required spark takes some work (8 glider per side), so it takes 20 gliders to put it all together, only a slight improvment on the original:
Code: Select all
x = 103, y = 37, rule=B3/S23
This should be reducible further, probably to 16 gliders. They key catalyst occurs at generation 14. Ideally, a domino spark with a bit-spark form the required domino in one step. Here, the bit-spark is replaced by another domino, making a blinker instead. This affects the predecessor in a slightly different way, but ends up with the same result. It should theoretically be possible to make the outside domino from 3 gliders rather than 5, but I couldn't find it.