Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

Noncommutative geometry provides a framework, via the construction of spectral triples, for study certain classes fractals. Many fractals are constructed as natural limits sets with simpler structure: instance, Sierpiński gasket is limit finite graphs consisting various affine images an equilateral triangle. It thus to ask whether on class called piecewise C 1 -fractal curves, indeed limits, in appropriate sense, triples approximating sets. We answer this question affirmatively paper, where we use propinquity metric order formalize sought-after convergence triples. Our results and methods relevant analysis have potential physical applications.