Basically, for this specific structure, they had to develop their own "sub structures" on the 1d line. These sub structures are known to create one little thing going diagonally (and then leave a bunch of debris behind, but that doesn't matter too much for that first step, they called this custom part "the fuse"). Then, there is a known technique where taking "diagonal moving objects" created on the same y-coordinate and placing them at the "right x position" makes the collide in a way where you can "program" where to create diagonal moving objects but at arbitrary positions on the screen (this is called a "binary construction arm"). And then, once you can create these anywhere on the screen, then you've basically won ; there's another technique to turn arbitrary positions into arbitrary shapes ("extreme compression construction arm", or ECCA), and it's "just" a matter of making the ECCA clean up all of the debris and build a new fuse but moved over.

Of course, the "just" here does the heavy lifting and represents over two years of exploration, writing algorithms for how to clean up everything, and so on.

I believe this one is a deliberate construction, they knew the evolution of the pieces and gradually put it together.

There’s search programs too, for smaller patterns. This construction is just too big and with such a long period. The search space would be enormous.

I got involved in this stuff years ago when I modified a search program for Life to search any CA rule. That’s how we found the HighLife rule and others like Day and Night.

Right. Interesting small patterns can be found using clever search algorithms. There's also the approach of running trillions of random 'soups' and scanning the results for interesting patterns. These small patterns are then pieced together to build the larger structures.