Pi calculator
| π calculator | |||||
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| View static image | |||||
| Pattern type | Miscellaneous | ||||
|---|---|---|---|---|---|
| Number of cells | 1189325 | ||||
| Bounding box | 117573 × 155887 | ||||
| Discovered by | Adam P. Goucher | ||||
| Year of discovery | 2010 | ||||
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The π calculator is a device constructed by Adam P. Goucher in February 2010, which calculates the decimal digits of π and displays them in the Life universe as 8×10 dot matrix characters formed by arrangements of blocks along a diagonal stripe at the top. A push reaction moves a ten-block diagonal cursor to the next position as part of the "printing" operation for each new digit.
The actual calculation is done in binary, using a streaming spigot algorithm[1] based on linear fractional transformations. The π calculator is made up of a 188-state computer connected to a printing device via period-8 regulators and a binary-to-decimal conversion mechanism. The complete pattern can be found in Golly's Very Large Patterns online archive,[note 1] along with the very similar 177-state phi calculator which uses a simpler algorithm to calculate and print the golden ratio, φ. The phi calculator ranked second place in the Pattern of the Year 2010 competition on the ConwayLife.com forums, behind Gemini.[2]
An updated version of the pi calculator pattern was made available with the Conway's Game of Life: Mathematics and Construction textbook.[3] Some but not all of the calculator's components were reduced in size, using smaller mechanisms such as the Snark and syringe that were discovered after 2010. The new pi calculator's bounding box is 38343 by 34603; it could easily be made considerably smaller by replacing the remaining 2010-era components.
See also
Notes
- ↑ Accessible in Golly via Help › Online Archives › Very Large Patterns › Pi calculator.
References
- ↑ Spigot algorithm at Wikipedia
- ↑ Adam P. Goucher (January 17, 2011). Re: Votes for Pattern of the Year 2010 (discussion thread) at the ConwayLife.com forums
- ↑ Life textbook website, Modernized pi calculator
External links
- Pi calculator at the Life Lexicon
- Smaller Pi Calculator Challenge (discussion thread) at the ConwayLife.com forums
- Phi and pi calculators at Game of Life News. Posted by Dave Greene on January 09, 2011.