Some Structures arising from the Farey Fractal

Shai Haran

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arXiv · 2509.10959

Some Structures arising from the Farey Fractal

Shai Haran

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Abstract

This work explores new arithmetic and combinatorial structures arising from the interplay between Farey-type graphs, Fibonacci expansions, and operadic constructions. We introduce Fibonadic numbers, defined as an inverse limit under the Zeckendorf shift, equipped with a metric, order, and commutative rig structure.

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Shai Haran. 2025-09-13. Some Structures arising from the Farey Fractal. https://arxiv.org/abs/2509.10959

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