Tag Archives: fractal

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 , , , , , ,

Median and pedal triangles and derived fractals: an introductory account

It is rather easily seen that joining the midpoints of the sides of a triangle yields four congruent triangles that in turn are similar to the original triangle (Figure 1). This figure might be used to provided a self-evident geometric … Continue reading

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

Journeying through the fractal slopes of mount Meru with two-seeded recursive sequences

The Hindus have been fascinated by sequences and series from the beginning of their civilizational memory recorded in the Veda. This continues down to the medieval mathematician Nārāyaṇa paṇḍita, who discovered a general formula (sāmāsika paṅkti) that can be to obtain the … Continue reading

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