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Description
We explore the possibility that the underlying flavour structure of the Standard Model may originate from mass chains defined on a fractal geometry. As an explicit example, we consider a theory space constructed on a Sierpinski-like geometry. The fermion mass chains on such a geometry with three iterations naturally give rise to three zero modes, which can be identified with the three generations of the Standard Model. This framework successfully reproduces the observed charged and neutral lepton masses and mixing angles with naturally ordered parameters. Possible extensions to the quark sector and how this approach addresses some of the limitations of alternative mechanisms will also be briefly discussed.
