Pythagorean Triplets, Integral Apollonians and The Hofstadter Butterfly

Indubala Satija

Hierarchical sets such as the Pythagorean triplets ($\mathcal{P}\mathcal{T}$) and the integral Apollonian gaskets ($\mathcal{I}\mathcal{A}\mathcal{G}$) are iconic mathematical sets made up of integers that resonate wit…