Category Archives: Scientific ramblings

Pattern formation in coupled map lattices with the circle map, tanh map, and Chebyshev map

The coupled map lattices (CMLs), first defined by Kunihiko Kaneko around the same time Wolfram was beginning to explore cellular automata, combine features of cellular automata with chaotic maps. The simplest CMLs are defined on a one dimensional lattice with … Continue reading

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

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 , , , , , , , , ,

Triangles, Hexes and Cubes

One philosophical question which we have often ponder about is: Are numbers “real”? One way to approach this question is via figurate numbers, where numbers directly manifest as very tangible geometry. This idea has deep roots in our tradition: as … Continue reading

Posted in art, Heathen thought, History, Scientific ramblings | Tagged , , , , , , , , , , , , , ,

Godhūmo vijayate

As we have noted several times before, the Ṛgveda represents a very early stage of the evolution of Indo-Aryan. Its agricultural terms relate to a major puzzle in Indo-European history. There is an unmistakable agricultural vocabulary including words such as … Continue reading

Posted in Heathen thought, History, Scientific ramblings | Tagged , , , , , ,

A note on tales of fratricide, warfare, cannibalism and incest

The Osman conqueror of Constantinople, Mehmet-II, bothered by the civil wars his predecessors had to fight to take the throne, institutionalized the system of fratricide. In this system, the rival brothers of the sultan, who took the throne, were all … Continue reading

Posted in History, 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 , , , , , , , , , , ,