Physical review. B, Condensed matter · 1986 · 153 citations · 5 references
Natural SciencesMathematicsPhysicsGeometryOpticsPattern FormationDiffractionFourier AnalysisFourier OpticsFractal GeometryPhysical OpticsWave DiffractionDiffraction AnalysisFourier TransformFractal AnalysisHausdorff Distance
Diffraction experiments are performed on two-dimensional deterministic fractals such as Cantor bars or Vicsek fractals. We show that the intensity I(q) which is scattered at a wave vector q by a fractal grating is simply its optical Fourier transform. This allows a direct determination of the Hausdorff dimension D and of other geometrical characteristics of fractals. Applications of this analog method to experimentally obtained aggregates are discussed.
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Thomas A. Witten, Leonard M. Sander · Physical review. B, Condensed matter · 1983 · 1.9K citations
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