Tag Archives: fractals

Some novel observations concerning quadratic roots and fractal sequences

Disclaimer: To our knowledge we have not found the material presented here laid out here presented in completeness elsewhere. However, we should state that we do not follow the mathematical literature as a professional and could have missed stuff. Introduction … Continue reading

Posted in Scientific ramblings | Tagged , , , , , , ,

The incredible beauty of certain Hamiltonian mappings

In our teens we studied Hamiltonian functions a little bit as part of our attempt to understand classical and quantum physics. A byproduct of it was a superficial interest in the geometry of some of the mappings arising from such … Continue reading

Posted in art, Scientific ramblings | Tagged , , , , , , , , ,

The Satija-Ketoja system

Satija and Ketoja discovered an interesting dynamical system in course of the study of the Schrödinger equation for one electron in a two dimensional periodic lattice on a uniform magnetic field. While this equation and its variants have several uses … Continue reading

Posted in art, Scientific ramblings | Tagged , , , , , , , , , , ,

Some simple maps specifying strange attractors

This note may be read a continuation of: Some reminiscences of our study of chaotic maps-2 While the story of the chaotic 2D attractors began with the simple-looking maps of Henon and Lozi, by the early 1990s the high-point was … Continue reading

Posted in art, Scientific ramblings | Tagged , , , , , ,

The Meru and Nārāyaṇa’s cows: Words and fractals

The fractals described herein are based on and inspired by the work of the mathematicians Rauzy, Mendes-France, Monnerot and Knuth. Some their works, especially the first of them, are dense with formalism. Here we present in simple terms the means … Continue reading

Posted in art, Scientific ramblings | Tagged , , , , , , , ,

Hofstadter and Nārāyaṇa: connections across space and time

The scientist-philosopher Douglas Hofstadter presents an interesting single-seeded sequence H in his book ‘Gödel, Escher, Bach: An Eternal Golden Braid’. It is generated by the recurrence relation, where …(1) Working it out one can see that it takes the form: … Continue reading

Posted in art, Scientific ramblings | Tagged , , , , , , , , , , ,

Wisdom from a tag system

The case of the mathematician Emil Post, like that of several others, indicates how the boundary between mania and mathematics can be a thin one. Nevertheless, Post discovered some rather interesting things that were to have fundamental implications the theory … Continue reading

Posted in art, Scientific ramblings | Tagged , , , , , ,