Difference between revisions of "Pi calculator"
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The '''π calculator''' is a device constructed by [[Adam P. Goucher]] in February {{year|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 [[block]]s 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 '''π calculator''' is a device constructed by [[Adam P. Goucher]] in February {{year|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 [[block]]s 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 [https://en.wikipedia.org/wiki/Spigot_algorithm spigot algorithm] based on linear fractional transformations. The π calculator is made up of a 188-state [[computer]] connected to a printing device via period-8 [[regulator]]s and a binary-to-decimal conversion mechanism. The complete pattern can be found in [[Golly]]'s ''Very Large Patterns'' online archive,{{refn|group=note|Accessible in Golly via Help › Online Archives › Very Large Patterns › Pi calculator.}} 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.<ref name="post4110" /> | The actual calculation is done in binary, using a streaming [https://en.wikipedia.org/wiki/Spigot_algorithm spigot algorithm] based on linear fractional transformations. The π calculator is made up of a 188-state [[computer]] connected to a printing device via period-8 [[regulator]]s and a binary-to-decimal conversion mechanism. The complete pattern can be found in [[Golly]]'s ''Very Large Patterns'' online archive,{{refn|group=note|Accessible in Golly via Help › Online Archives › Very Large Patterns › Pi calculator.}} 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]].<ref name="post4110" /> | ||
[[File:Pidigits.png|center|frame|Detail of the π calculator after 63,850,210,955,854 generations, having calculated 13 digits of π, viewed at a scale of 2<sup>6</sup>:1.]] | [[File:Pidigits.png|center|frame|Detail of the π calculator after 63,850,210,955,854 generations, having calculated 13 digits of π, viewed at a scale of 2<sup>6</sup>:1.]] | ||
Revision as of 03:55, 19 March 2020
| π calculator | |||||
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| Pattern type | Miscellaneous | ||||
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| 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 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.[1]
Notes
- ↑ Accessible in Golly via Help › Online Archives › Very Large Patterns › Pi calculator.
References
- ↑ Adam P. Goucher (January 17, 2011). Re: Votes for Pattern of the Year 2010 (discussion thread) at the ConwayLife.com forums
External links
- Pi calculator at the Life Lexicon