The Variant-Rule Another Logically Universal Rule.
Cite as:
Gómez Soto José Manuel and Wuensche Andrew, The Variant-Rule Another Logically Universal Rule. To be published in Journal of Cellular Automata
Download paper from Arxiv: PDF
Variant rule in DDlab: vrule.rul
Variant rule in Golly: vrule.rule
Abstract
The Variant-rule derives from the Precursor-rule by interchanging two classes of its 28 isotropic mappings. Although this small mutation conserves most glider types and stable blocks, the glider-gun engine itself is changed, as are most large scale pattern behaviors, illustrating both the robustness and fragility of evolution. We demonstrate these newly dis- covered structures and dynamics, and build the logical gates required for universality in the logical sense.
1) Glider-gun 'a' of Period 22 .
The Variant-rule glider-gun GGa with Period 22. This is building from the interaction between two ocillators of period 22. DDlab file: [ggunp22.eed, (100 x 100 space size)] Golly file: [ggunp22.rle].
2) Glider-gun a of Period 15.
Two GG2a glider-guns at 90◦ create a Ga glider stream, stopped by an eater. Double Ga (G2a) gliders can be shot by a GG2a glider-gun constructed from two (same phase) P15 oscillators correctly juxtaposed at 90 grades. DDlab file: [ggunp15.eed (100 x 100 space size)], Golly File:[ggunp15.rle].
2) Glider-gun a of period 27.
Using the the Gc reflection property, double Ga (G2a) gliders, with a frequency of 27 time-steps, can be shot by a GG2aR glider-gun constructed from two Gc reflectors (same phase) correctly juxtaposed at 90 grades. In this way Two GG2a glider-guns at 90◦ create a Ga glider stream, stopped by an eater. DDlab file: [ggunrbo.eed (100 x 100 space size)], Golly file: [ggunrbo.rle].
Variant-rule is Powered by DDlab and Golly
and
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3) Gliders of Variant-rule have a high probability to emerge from a random initial condition.
DDlab file: [random.eed (100 x 100 space size)], Golly file: [random.rle].
4) Spirals in Variant-rule.
A glider stream (GS) circuit folds into a spiral, where a Gc-GS is transformed to double spaced Ga-GS by interaction with two P22 oscillators and three blocks. The circuit repeats steps 1) to 4), then 5) collision with a block, 6) transform to Ga-GS, 7) interaction with P22 oscillator, 8) transform to Gc-GS, 9) collision with a block, 10) transform to Ga-GS, stopped by an eater. DDlab file: [spiral.eed (120 x 120 space size)], Golly File: [spiral.rle].
5) In Variant-rule is possible build logical gates and therefore Logical Universality.
The dynamics making this OR gate first makes an intermediate NOT-A (NE 01110) which interacts with input B to make A-NOR-B (NE 01010) which interacts with the upper GGa shooting SE to make A-OR-B (SE 10101). A residual bi-product is A-AND-B (SE 10000). DDlab file: [or.eed (160 x 160 space size)], Golly file: [or.rle].
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