Crystallization of space: Space-time fractals from fractal arithmetic
General Relativity and Quantum Cosmology
2016-01-20 v3 Mathematical Physics
math.MP
Quantum Physics
Abstract
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated with appropriate Lie groups. The construction is illustrated by explicit examples.
Keywords
Cite
@article{arxiv.1506.00487,
title = {Crystallization of space: Space-time fractals from fractal arithmetic},
author = {Diederik Aerts and Marek Czachor and Maciej Kuna},
journal= {arXiv preprint arXiv:1506.00487},
year = {2016}
}
Comments
version accepted in Chaos, Solitons & Fractals