spiral glider-gun rule

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The -rule: universal computation in a non-isotropic Life-like Cellular Automaton Journal of Cellular Automata, Vol 10. No.3-4, 261-294, arXiv preprint pdf -- 1.8M

José Manuel Gómez Soto
Universidad Autónoma de Zacatecas, Unidad Académica de Matemáticas. Zacatecas, Zac. México, jmgomezuam@gmail.com, http://matematicas.reduaz.mx/~jmgomez
Andrew Wuensche
Discrete Dynamics Lab, London, UK, andy@ddlab.org, http://www.ddlab.org

We present a new Life-like cellular automaton capable of logic universality -- the X-rule. The CA is 2D, binary, with a Moore neighborhood and λ parameter similar to the game-of-Life, but is not based on birth/survival and is non-isotropic. We outline the search method. Several glider types and stable structures emerge spontaneously within X-rule dynamics. We construct glider-guns based on periodic oscillations between stable barriers, and interactions to create logical gates.

The site is still under construction, but some details from the paper are shown below:

The X-rule presents small stable configurations behaving as eaters, reflectors, destroyers, and in other ways.
There are 6 basic types

There are two basic glider-guns for gliders Ga and Gb click to enlarge

GGa shooting gliders Ga NW and SW,
gap=24, period=38. Increasing the gap by +4 increases the period by +8 thus reduces glider frequency.
GGb shooting gliders Gb North and South,
gap=23, period=110 consisting of 2 sub-periods of 55. Increasing the gap by +4 increases the period by +16 thus reduces glider frequency.

Ga gliders, period 4, speed=c/4
Gb gliders, period 4, speed=c/2

Gc glider-guns are compound, made by combining Ga glider-guns and eaters, click to enlarge

Gc gliders, period 4, speed=c/2

Gc glider-gun North

Gc glider-gun South then East
Gc glider-gun West

More compound glider-guns made fron Ga and Gc glider-guns, and eaters click to enlarge

Gc glider-gun South then Ga NE
Gc glider-gun West

Logical gates NOT, AND OR and NAND, with output towards the WEST click to enlarge

NOT logical gate
AND logical gate

OR logical gate
NAND logical gate

Logical gates NOT, AND OR and NAND, with output towards the East click to enlarge

NOT logical gate
AND logical gate

OR logical gate
NAND logical gate

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July 2015

The X-rule presents small stable configurations behaving as eaters, reflectors, destroyers, and in other ways. There are 6 basic types
There are two basic glider-guns for gliders Ga and Gb click to enlarge
GGa shooting gliders Ga NW and SW, gap=24, period=38. Increasing the gap by +4 increases the period by +8 thus reduces glider frequency.	GGb shooting gliders Gb North and South, gap=23, period=110 consisting of 2 sub-periods of 55. Increasing the gap by +4 increases the period by +16 thus reduces glider frequency.
Ga gliders, period 4, speed=c/4	Gb gliders, period 4, speed=c/2

Gc glider-guns are compound, made by combining Ga glider-guns and eaters, click to enlarge Gc gliders, period 4, speed=c/2
Gc glider-gun North	Gc glider-gun South then East	Gc glider-gun West

More compound glider-guns made fron Ga and Gc glider-guns, and eaters click to enlarge
Gc glider-gun South then Ga NE	Gc glider-gun West

Logical gates NOT, AND OR and NAND, with output towards the WEST click to enlarge
NOT logical gate	AND logical gate	OR logical gate	NAND logical gate