Fractal mountains and binary random loops
Chaotic Dynamics
2021-05-28 v1 Classical Analysis and ODEs
Combinatorics
Functional Analysis
Abstract
We discuss a variation of Takagi curves based, however, more on algebraic than geometric principles. Namely, we construct functions of loops in a special binary representation. The graph of these functions usually has chaotic and fractal forms, sometimes recall mountain landscapes. Nevertheless, the values in a dense set of points and even the integral of these functions can be calculated explicitly.
Cite
@article{arxiv.2105.13292,
title = {Fractal mountains and binary random loops},
author = {Anton A. Kutsenko},
journal= {arXiv preprint arXiv:2105.13292},
year = {2021}
}