- Life Objects
- P2 Oscillator Rotors
Every cell has an influence over the next generation of surrounding cells. The sum of all these cells is called the zone of influence of a cell. For multiple generations, this influence is felt in every cell which has at least the same number of paths between it and the active cell. This has the effect of clipping the corners of the expanding set of cells. The sample image shows the zone of influence for a single cell for one, two and three generations.
Rotor cells are shown in one of three colors. Cells active in generation 0 which are going to die due to underpopulation (they have 0 or 1 neighbor) are colored blue. Those which are going to die due to overpopulation (they have 4 or more neighbors) are colored red. Birth cells, which will become active in generation 1, are shown in green.
The set of cells which fall into the zone of influence of at least one cell of a rotor, and are not themselves part of the rotor, constitute the casing of a rotor. Casing cells are shown in black.
The remaining cells of the an object which play no other part are the frame. Their arrangement doesn't matter, but often they consist of an inductor which supresses births that might be caused by the outside of the casing. These cells are either not shown, or shown in gray.
To the left are shown the rotors of all oscillators with a population of 13 or fewer bits. The blinker [3P2.1] has a four bit rotor supported by a single central casing cell. The toad [6P2.1] has an eight bit rotor with each hafl supported by a single cell. The beacon [6P2.2] has a two bit rotor supported by a pair of pre-blocks as the casing. The clock [6P2.3] has an eight bit rotor, and like the blinker, has an internal casing.
The bipole [8P2.1] has a rotor identical to that of the blinker, but in this case the casing is external. As the next objects, the tripole [9P2.1] and quadpole [10P2.1] show, this type of rotor can be extended indefinitely. A rotor consisting of two parallel and alternating rotor cells has the generic name of barberpole. In a later section, it will be shown how barberpoles can be used as the basis for a whole host of rotors and objects.
Objects [12P2] and [12P2.4] show how a frame can be added to the basic beacon oscillator by trivally attaching a table inductor. The phoenix [12P2.6] demonstrates that an object does not require a casing. Finally, object [13P2.2] is simply a bipole [8P2.1] with the addition of a contiguous frame section.
The number of Period 2 objects for each bit size is show in this table. A complete census has only been done for objects up to 20 bits, for which there are 4652. For larger objects, the results are based on a partial result based on all objects that fit into a 10x10 rectangle, some attempts to enumerate 21 bit objects, along with other objects created by hand.
The zones of influence of a rotor must be contiguous. If they can be partioned into two or more disconnected sets, then that object has a composite rotor. In the illustration, [16P2.58] in an object that consists of a pair of touching bipoles [8P2.1]. It contains a pair of four bit rotors whose zones of influence have a common border, but do not overlap. [19P2.973] is two beacons [6P2.1] are separated a common inductor. In the third object, the zones of influence of the two rotor halves have a cell in common, so this is a disjoint four bit rotor, where the rotors don't exert a direct influence over each other.