Symmetrica / Rakes

Tugboat rakes are classified according to two properties:

  • Spacing: How many cells apart the tugboats are.

  • Sign: Either “up” or “down.” Up means that the long sides of the tugboats are oriented in the rake’s direction of motion; down means that the long sides are oriented away from the rake’s direction of motion.

A rake with spacing X is called an X up rake or an X down rake depending on its sign. All rakes known so far have a front end that produces tugboats along with additional debris, and a back end that cleans up the debris.

16 down rake

16 up rake

32 up rake

  • Front end consists of two byzantines

32 down rake

  • Consists of a 32 up rake, a victory puffer, and a Varangian guard

40 up rake

  • First rake discovered
  • Front end consists of two sea urchins and an SBS

80 down rake

  • Front end consists of two byzantines

Schooner rakes

Any tugboat rake with spacing greater than ~20 can be used to construct a schooner rake with the same spacing and opposite sign by positioning three copies of the rake so as to produce the following reaction:

A single SBS can clean up the debris:

Alternatively, one can replace two of the rakes with a victory puffer of the same period. For example, here is the smallest known schooner rake, a 32 down schooner rake constructed from a 32 up tugboat rake and a victory puffer:

Mason breeder

  • Grows quadratically
  • Consists of two victory puffers, a 16 up rake, a 32 down rake, and three 32 up rakes