The boundary of the ℳ-set is of dimension 2

  • Benoit B. Mandelbrot


It is conjectured that the boundary of the ℳ-set of the complex map has a Hausdorff-Besicovich fractal dimension equal to 2.


Fractal Dimension Fractal Model Hausdorff Measure Small Branch Local Shape 
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Copyright information

© Benoit B. Mandelbrot 2004

Authors and Affiliations

  • Benoit B. Mandelbrot
    • 1
    • 2
  1. 1.Mathematics DepartmentYale UniversityNew HavenUSA
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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