Bravais mark BRAVAIS
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Kleinian Pearl Necklace
Kleinian & Apollonian

Kleinian Pearl Necklace

Kleinian Limit Set

The limit set of a quasi-Fuchsian group built by Grandma's recipe from tr(a) = 1.91 + 0.05i and tr(b) = 2, which gives tr(ab) = 1.91 - 1.95i and a parabolic commutator of trace exactly -2. That puncture pinches the quasicircle into four cusps at the compass points. Reduced words in the two generators are enumerated depth first, each branch stopping once the four commutator fixed points accumulate below one pixel. Luminance is log density and hue tilts with mean word depth.