HBK caterpillar

HBK caterpillar
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Pattern type	Spaceship
Family	Half-baked knightship
Number of cells	346912
Bounding box	123938 × 112538
Direction	Oblique
Period	1024 (mod: 1024)
Speed	(6,3)c/1024 | (6,3)c/1024
Heat	Unknown
Kinetic symmetry	Unspecified
Discovered by	FWKnightship
Year of discovery	2023
Rules Outer-totalistic rules B3/S23 only # of rules 20 = 1 Isotropic rules B3/S23 only
Pattern files Macrocell hbkcaterpillar.mc

The HBK caterpillar, knightship caterpillar, or knightpillar is a period-1024 oblique spaceship completed by FWKnightship on December 2, 2023. On the same day, Dave Greene reduced the bounding box to 110025x105406 and the minimum population to 341572 alive cells.

In the HBK caterpillar, chains of half-bakery pairs are used to generate "over-unity" perpendicular gliders, as shown in half-bakery. In the Parallel HBK, each half-bakery pair is activated to produce a glider every 245,912 ticks -- but the HBK caterpillar manages to do this much faster, every 1024 ticks. This kind of massive period reduction by "caterpillar-izing" an HBK design has been talked about several times, starting before the HBKs were even finished, but no specific designs were completed until now.

The HBK caterpillar's main spine is made up of a long chain of identical constellations of twenty half-bakeries. A flotilla of twenty southwest-traveling gliders goes through each half-bakery constellation every 1024 ticks. At any given time, many twenty-glider flotillas are traveling along the spaceship's spine, activating each half-bakery constellation in turn, and finally being suppressed cleanly at the tail of the spaceship.

The main idea is that gliders travel in a set of nested diagonal rectangular loops, mediated by target objects at three of the four corners of the loops. Collisions with these objects every 1024 ticks are carefully designed so that the objects all move (+6,+3) southeastward on each cycle. The half-bakeries in the west corners of the nested rectangles move this distance naturally whenever a single glider collides with them. But the half-blockades in the south corners of the rectangles, and the blocks in the east corners, need specially designed synchronized salvos to get them to move the correct distance while releasing output gliders at 90 degrees to the input salvos.

Details

Each half-bakery constellation produces ten southeast-traveling gliders. Eight of those gliders make up a very narrow synchronized salvo of gliders aimed at a half-blockade target some distance to the southeast. The salvo is designed to be narrow, just four lanes wide, because the trailing gliders have to fit through the four-lane-wide gap in the half-bakery pair that generates the leading glider.

The half-blockade is moved (+6,+3) every 1024 ticks by the collision, which also generates two output gliders. The remaining two southeast-traveling gliders are offset a good distance to either side of the eight-glider stream, to participate in kickback reactions with those output gliders. One output glider is initially sent northeast, then kicked back to collide with the last two salvo gliders to make a new half-blockade in the right (+6,+3) offset location. The other output glider is initially sent southwest, then kicked back to be added to a new northeast-traveling synchronized salvo.

Each northeast-traveling salvo is a three-glider group aimed at a block, which moves the block (+6,+3) and sends out a single glider heading northwest. There are twenty blocks in all, producing twenty singleton northwest-traveling gliders.

There are also twenty singleton northeast-traveling gliders. These are created in the same exact way as the other NE-traveling gliders, in a tight group of half-bakery constellations at the very top of the HBK caterpillar's spine.

The twenty individual northeast-traveling gliders hit the twenty individual northwest-traveling gliders and are kicked back. They form a flotilla of twenty SW-traveling gliders, which is exactly what is needed to close the loop and activate each half-bakery constellation in the spine -- one glider for each half-bakery in the ten half-bakery pairs.

Cleanup in the Southeast

Without the triangular tail at the end of the spine, this whole structure would spew 20-glider flotillas southwestward every 1024 ticks. The triangular structure cleanly stops the southwest-traveling flotillas.

The northeast edge of the triangular tail is made up of two non-standard half-bakery constellations. The first of these constellations creates only nine gliders instead of the usual ten. Those nine southeast-traveling gliders are aimed at a half-bakery as usual, but the resulting southwest-traveling output glider just keeps traveling southwest instead of getting kicked back. The second constellation creates only one southeast-traveling glider instead of the usual ten. The southeastward glider and the southwestward glider collaborate with a final half-bakery to make a new block at the end of the chain of blocks on the southwest edge of the triangular tail.