OTCA metapixel

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OTCA metapixel
OTCA metapixel image
Pattern type Unit cell
Number of cells 64691
Bounding box 2058 × 2058
Cell size 2048 × 2048
Period 35328
Discovered by Brice Due
Year of discovery 2006

The OTCA metapixel[note 1], is a 2048 × 2048 period-35328 unit cell that was constructed by Brice Due between the autumn of 2005 and the spring of 2006. It has many advantages over the previously known unit cells such as the p5760 unit Life cell and deep cell, including the ability to emulate any Life-like cellular automaton[note 2] and the fact that, when zoomed out, the ON and OFF cells are easy to distinguish (the ON version of the cell is shown to the right and the OFF version of the cell is shown below).

It is designed to run quickly under the Hashlife algorithm, and thus Golly is generally used to view and/or manipulate meta-patterns made up of OTCA metapixels, some of which even come packaged with Golly under Patterns/HashLife/Metacell folder.

To tile these unit cells manually to emulate other patterns, place them so that the cornermost blocks overlap; the unit cells will physically overlap by 5 cells in every direction. The overlap will place tubs inside cross-corner neighbours. Alternatively, select a pattern under the desired two-state outer-totalistic rule, and run either of the following scripts: Scripts/Lua/metafier.lua or Scripts/Python/metafier.py.

Details

Also see: Illustrated diagrams of OTCA metapixel

Period-46 and 184 (= 46 × 4) technologies based on twin bees shuttle and period-184 glider gun are used extensively throughout the metacell. A period-184 tractor beam acts as a clock, which pulls a block downwards by eight cells per impact, releasing a glider in the process. Some of the gliders are utilised; the rest are eaten. A new block is created from the third impact to be used when the timer restarts.

The rule is encoded in two columns, each of nine eater 1s, where one column corresponds to the 'Birth' rule and the other corresponds to 'Survival'. The nine eaters correspond to the nine different quantities of on cells (0 through 8). The presence or absence of the eater indicates whether the cell should be on in the next meta-generation. The state of the eater is read by the collision of two antiparallel LWSSes, which radiates two antiparallel gliders (not unlike an electron-positron reaction in a PET scanner). These gliders then collide into beehives, which are restored by a passing LWSS in Brice's elegant honeybit reaction. If the eater is present, the beehive would remain in its original state, thereby allowing the LWSS to pass unaffected; if the eater is absent, the beehive would be restored, consuming the LWSS in the process. Equivalently, the state of the eater is mapped onto the state of the LWSS.

ON metacells send a MWSS counterclockwise around the cell, which reacts with twin bees to send gliders to neighboring cells' beehives in honeybit reactions. A 9-LWSS stream then goes clockwise around the cell, losing a LWSS for each adjacent ON cell that triggered a honeybit reaction. The number of missing LWSSes is counted by detecting the position of the front LWSS by crashing another LWSS into it from the opposite direction. This collision releases gliders, which triggers another one or two honeybit reactions if the eaters that indicate that birth/survival condition are absent.

When the display is ON, two perpendicular waves of LWSSes collide, mutually annihilating each other. These streams of LWSSes are generated from an out of the blue reaction, triggered by passing HWSSes.

Meta-metapixels

It is possible to use the OTCA metapixel to emulate itself, and emulate other patterns on the resulting meta-metapixel. Adam P. Goucher presented a meta-meta-blinker in December 2016, with a period of 2,496,135,168 (=2·35,3282), noting that Golly can successfully run the entire period over the course of a day at a step size of 85.[3]

Gallery

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The OFF version of the OTCA metapixel (click above to open LifeViewer)
RLE: here Plaintext: here
OTCA metapixel used to simulate Kok's galaxy
The metapixel by itself turning from ON to OFF in 35,328 generations
The OTCA metapixel being used to emulate Kok's galaxy

See also

Notes

  1. Also sometimes "OTCAMP" (for "Outer Totalistic Cellular Automaton Meta-Pixel").[1][2]
  2. A specific case of outer-totalistic cellular automaton (abbreviated OTCA).

References

  1. Dave Greene (September 9, 2006). "Brice Due's Game-of-Life Metapixel -- Sample Patterns". Conway's Life: Work in Progress.
  2. Brice Due. "OTCAmetapixel".
  3. Adam P. Goucher (December 15, 2016). Meta-meta-blinker (discussion thread) at the ConwayLife.com forums

External links