Category Archives: art

Packing constants for polygonal fractal maps

Among the very first programs which we wrote in our childhood was one to generate the famous Sierpinski triangle as an attractor using the “Chaos Game” algorithm of Barnsley. A couple of years later we returned to it generalize it … Continue reading

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Creating patterns through matrix expansion

People who are seriously interested in emergent complexity and pattern formation might at some point discover matrix expansion for themselves. It is a version of string rewriting that allows one to create complex patterns. For me, the inspiration came from … Continue reading

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A dinnertime conversation

A complete version of this apolog will currently not be visible to the public. Things had cooled off a bit on the political front after the assassination of the Prime Minister Pratap Simha by a massed drone attack. On the … Continue reading

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The second strike

PDF version Childhood Thrice a week, starting Fridays, Lootika’s mother taught her daughters mantra-siddhānta after dinner. She had covered the praxis of the secret mantra-s of the Vīṇāśikhā and had moved on to relevant sections of the Jayadratha-yāmala and the … Continue reading

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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

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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

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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

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