FracTran: A Turing-Complete Programming Language Based on Fractions
2025-04-10
This essay commemorates mathematician John Horton Conway and explores his creation, the FRACTRAN programming language. FRACTRAN uses a sequence of fractions as a program, achieving Turing completeness through simple multiplication and division. The article details FRACTRAN's operation, implementing a FRACTRAN program for the Fibonacci sequence in JavaScript. Furthermore, it examines the relationship between FRACTRAN and Minsky machines, showing how to transform multi-state Minsky machines into single-state ones. Finally, it highlights FRACTRAN's potential applications in tackling problems like the Collatz conjecture.
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