Minimal Glider-Gun in a 2D Cellular Automata.
Cite as:
Gómez Soto José Manuel and Wuensche Andrew: Minimal Glider-Gun in a 2D Cellular Automata. Published in Complex System Journal.
Download paper from Complex System Journal: PDF
Download paper from Arxiv: PDF
Sayab Rule in DDlab: sayab.rul
Sayab Rule in Golly: sayab.rule
Abstract
To understand the underlying principles of self-organisation and compu- tation in cellular automata it would be helpfull to find the simplest form of the essential ingredients, glider-guns and eaters, because then the dy- namics would be easier to interpret. Such minimal components emerge spontaneously in the newly discovered Sayab-rule, a binary 2D cellular au- tomaton with a Moore neighborhood and isotropic dynamics. The Sayab- rule has the smallest glider-gun reported to date, consisting of just four live cells at its minimal phases. We show that the Sayab-rule can imple- ment complex dynamical interactions and the gates required for logical universality.
1) Searching for gliders
The first step was to search CA rules for emergent gliders and stable structure. In order to do that we fixed the parameter to be similar to the game-of-Life, and use the variability of inputentropy, see bellow figure . Like Sapin the search was restricted to isotropic rules only (equal outputs for any neighborhood rotation, reflection, or vertical flip) where rule-space is reduced to 2102. The result was a very large rule sample, from we take a shortlist of about 70 rules in the ordered sector of figure with both gliders and stable structures. Five rules, with gliders travelling both orthogonally and diagonally, were selected for further study.
1) Sayab-rule have a minimal Glider-gun of 4 live cells.
A minimal glider-gun of 4 live cells. The glider-gun in action shooting two diagonal glider streams with a frequency of 20 time-steps and glider spacing of 5 cells. Each glider streams is stopped by an eater. Because the system is isotropic, any orientation of the glider-gun is equally valid. DDlab file: [ggaH.eed, (100 x 100 space size)] Golly file: [ggaH.rle].
2) Glider-gun's Sayab-rule can emerge from a simple collision between two gliders or a glider vs periodic structure.
Sayab-rule's glider-gun emerge from a simple collision. Here we ilustrate a glider-gun from collision between two gliders. DDlab file: [pregg.eed (100 x 100 space size)], Golly File:[Golly file (.rle)].
Sayab-rule's glider-gun emerge from a simple collision between glider and a periodic pattern. DDlab file: [pre3h.eed (100 x 100 space size)], Golly file: [pre3h.rle].
3) Glider-gun's Sayab-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) Sayab-rule have structures like oscillators, spaceships, etc.
Sayab-rule have Spaceships, here we show a Six large space-ships moving North with speed c/2. Periods, from left to right, are 2, 2, 2, 4, 4, 4. DDlab file: [spacetod.eed (200 x 50 space size)], Golly File: [spacetod.rle].
5) In Sayab-rule is possible build logical gates and therefore Logical Universality.
Is possible build logical gates in Sayab Rule. Here we show An example of the OR gate which makes a disjuntion between two stream of data represented by two streams of gliders and gaps. The 5-bit input strings A (1101) and B (1110) both moving SE interact with two glider-streams, the lower Glider-gun shooting NE, and subsequently with an upper glider-gun shooting SE, finally resulting in the A-OR-B string (1111) moving SE shown after 333 time-steps. DDlab file: [sayabor.eed (200 x 200 space size)], Golly file: [sayabor.rle].
Video about Game of Life.
Sayab-rule is Powered by DDlab and Golly
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