hexwrench

A Clojure library for manipulating hex-grids, with a focus on Generalized Balanced Ternary.

Generalized Balanced Ternary

There should be lots of great diagrams here as soon as the diagram generator is working.

A library for manipulating Generalized Balanced Ternary values in two dimensions.

Balanced Ternary is a base 3 number system where instead of using the digits 0,1,2 the digits are balanced around 0, hence -1,0,1. Donald Knuth proclaims it the most beautiful number system. Spatially it can be represented as a one dimensional number line.

GBT2 is a base 7 number system. Spatially a hexagonal tiling of a 2d plane, so each hexagon gets its own unique address.

(For reference, GBT3 is a base 15 number system. Spatially is is a tiling of 3d space using truncated octahedrons. GBTn is base 2^(n + 1) - 1 number system and is a tiling of a space of dimension n.)

References:

• "The Art of Computer Programming Vol2 Seminumerical Algorithms" by Donald Knuth (for Balanced Ternary)
• Laurie Gibson and Dean Lucas's 1982 paper defining GBT (I've never obtained this)
• "An isomorphism between Generalized Balanced Ternary and the p-adic integers" by Wei Zeng Kitto
• "Image Algebra" by G. Ritter (Kitto's advisor)