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.

The rotating part must be moving. Or else the blinker or clock can be considered reflectorless rotating because it turns 90 degrees every 1 generation.

Examples

Outer-totalistic rules

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.

• 
  Reflectorless rotating oscillator in B02348/S0123.
  Catagolue: here
  Twofold: Catagolue: here

Non-totalistic rules

Multiple reflecterless rotating oscillators have been found in non-totalistic rules, especially recently:

• dmqwerty425 discovered a period-420 reflectorless rotating oscillator in B2i34ik7/S23-a4ikn5j7 on Catagolue in November 2016.
• Daniel R. Collazo discovered a period-184 reflectorless rotating oscillator in B3/S23-a4i5i6ci in July 2017.
• Rhombic discovered a period-72 reflectorless rotating oscillator in B2e3-a4a/S1c23-aky in August 2017.
• Saka discovered a period-68 reflectorless rotating oscillator in B3-n4rtw5i/S23-n4q5i in August 2017.
• 2718281828 discovered a number of loopable RROs, with 2-, 3-, 4-, 5-, and even 6-fold loopability, in July 2018.

• 
  Reflectorless rotating oscillator in B2i34ik7/S23-a4ikn5j7.
  Catagolue: here

Larger than Life

One reflectorless rotating oscillator has been found in a Larger than Life rule, discovered by Dean Hickerson with 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.

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

Classification

A method for classifying RROs by the amount of times they can fit into a single loop in a way that evenly divides the period has been discussed; by this logic, patterns such as the p160 oscillator in tlife, the p88 in B36ce7c/S23-y, and the natural gun in Pedestrian Life could be classed as reflectorless rotating oscillators with a loopability of 1.

External links

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