Reflectorless rotating oscillator

A reflectorless rotating oscillator (or looping spaceship; abbreviated as RRO) is a hypothetical pattern, which rotates itself after a certain number of generations. There is the additional constraint that two non-interacting copies of the pattern could be combined into an oscillator with a period equal to exactly half of that of the component oscillators. This is like the pi orbital, but without the stabilisation.

Such patterns can be proven to exist (see universal constructor), but none have been explicitly constructed in Life. A universal constructor-based RRO has no limit on the number of independent patterns that can orbit a single point.

Alternatively, the term may refer to any statorless oscillator that rotates itself after a certain number of generations. The term "statorless rotating oscillator" is sometimes used to refer to these, as opposed to "classical" RROs.

Examples

There is only one known reflectorless rotating oscillator in an outer-totalistic Life-like cellular automaton. It exists in B02348/S0123, and has a period of 272. It is technically not a classical RRO, because two copies combined into a half-period oscillator interact but do not interfere with each other.

In other classes of CAs:

• Dean Hickerson discovered a reflectorless rotating oscillator in a Larger than Life cellular automaton, which has a period of 552. He placed eight copies in a circle, yielding a period-69 oscillator. Dave Greene noticed that twelve copies can orbit a central point with period 46.
• Aidan F. Pierce discovered a period-420 reflectorless rotating oscillator in the non-totalistic rule B2i34ik7/S23-a4ikn5j7 in November 2016.
• Daniel R. Collazo discovered a period-184 reflectorless rotating oscillator in the non-totalistic rule B3/S23-a4i5i6ci in July 2017.
• Rhombic discovered a period-72 reflectorless rotating oscillator in the non-totalistic rule B2e3-a4a/S1c23-aky in August 2017.
• Saka discovered a period-68 reflectorless rotating oscillator in the non-totalistic rule B3-n4rtw5i/S23-n4q5i in August 2017.

Gallery

• 
  Reflectorless rotating oscillator in B02348/S0123.
  Catagolue: here
• 
  Dean Hickerson's period-552 reflectorless rotating oscillator in the Larger than Life rule R7,C0,M1,S65..114,B65..95,NM.
• 
  Dave Greene's 12-fold, period-46 version of Dean Hickerson's period-552 RRO.
• 
  Reflectorless rotating oscillator in B2i34ik7/S23-a4ikn5j7.
  Catagolue: here

External links

• Rotary oscillators? (discussion thread) at the ConwayLife.com forums