Abstract：In order to study the problem of harmonic analysis on fractal interpolation curve, its self-similar structure was considered according to the characteristics from creating curve. A sequence of resistance networks on a self-affine fractal interpolation curve was established by the construction of similar Laplacian on boundary points, and through limiting the Laplacian of network the corresponding harmonic structure was given. The results indicate that scale factor qualified some conditions and a symmetrical matrix form the fractal harmonic structure. At the same time, from the electrical point of view, the concept of effective resistance associated with the Laplacian between any two points was defined. This effective resistance is a metric on boundary points thus there′s a new metric space on this interpolation curve.
2011, Vol. 32 
