Pi calculator

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π calculator
π calculator image
Pattern type Miscellaneous
Number of cells 1189325
Bounding box 117573×155887
Discovered by Adam P. Goucher
Year of discovery 2010

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]

Detail after 63,850,210,955,854 generations, having calculated 13 digits of π, viewed at a scale of 26:1.

See also


  1. Accessible in Golly via Help › Online Archives › Very Large Patterns › Pi calculator.


  1. Wikipedia, Spigot algorithm
  2. Adam P. Goucher (January 17, 2011). Re: Votes for Pattern of the Year 2010 (discussion thread) at the ConwayLife.com forums

External links