Period 2 Oscillators

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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Joined: June 20th, 2009, 11:40 am

Period 2 Oscillators

Post by hkoenig » April 9th, 2022, 8:54 pm

Every so often someone posts the assertion that "period 2 oscillators are not interesting". I respectfully disagree, as it all depends on the definition of "interesting."

Years ago I started a project of cataloging all the parts which can be combined to make Period-2 oscillaters. Have worked on it when I've found some time available, but I seem to not have done much this past few years. Don't see much opportunity in the coming months, either. So decided I'll toss out what I have for now, to see if anyone is interested in this.

This is similar to, yet different from, Beluchenko's rotor chemistry. I got a few ideas from what he published, but he seemed to be more interested in long, repeating chains and how they could be combined. I'm more interested in the atomic parts which can make up those chains.

To make this process easier, I adapted my Life editor program to support the placement and validation of these links. The app contains a catalog of links which can be added to a worksheet. The worksheet validates the current bitarray, showing where cells need to be added or suppressed in order to produce a valid Life object. Finally, it produces the descriptors for the object.

Attached here are some PDF files with a series of pages showing much of my work so far. (These are based on text editor files, but I don't want to distribute those as they probably aren't cross-platform compatible.)

The "RotorLinks" file is the most useful one. I've called the basic components which make up these oscillators "links". For each entry I present an image, a recipe for my editor to use in building the entry, the wCode of the link, and the RLE code for one of the phases. A cell active in the current phase is shown in red, while a cell active in the alternate phase is shown in green. Sometimes the immediate casing cells are in purple with non-critical support cells in gray, or stable cells in black. (I need to go back and update the earlier images which use black.)

First are the types of link connections between components I've found. The connections can be thought of as the places where two links overlap and snap together.

Next are the links themselves. A link has one or more link connections, along with other cells needed to make an object. These extra cells constitute the casing if they are stable.

The next section are various terminators for chains. Each terminator shows the basic state, along with several other links attached to demonstrate how the terminator can be used.

The next few sections continue the theme, showing how single chains can be build using various links, or double chains where the links alternate. I've also cataloged "bends" where chains can change direction, and "joins", where various links can be brought together.

Included as separate files are a directory of Period 2 Oscillators broken down by the links from which they are made, and a file with the various Type M links. The latter are parallel two bit sparks where I've found several dozen (so far) links that can be joined to create various chains. I've also figured out, in some cases, how to shift those chains, or bend then 90 degrees.

I'd be interested in hearing from anyone who wants to dig deeper into this, or would like better documentation of some of the coding.
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