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Jacob Gröning: Cantormängders dimensioner

Time: Thu 2021-06-03 11.00 - 12.00

Location: Meeting ID: 621 0069 4618

Respondent: Jacob Gröning

Abstract

Fractals are objects which traditional geometry often fails to describe and instead they are often described using the concept of dimension. In this report we discuss how the Cantor set, von Koch curve and the Sierpiński triangle are constructed and three notions of dimension namely the similarity dimension, the box dimension and the Hausdorff dimension. We also find the similarity dimension of all the above mentioned fractals and the box dimension and Hausdorff dimension of the Cantor set. Using the method for calculating the different dimensions of the Cantor set we show that we can generalise the Cantor set in order to find a fractal whose similarity dimension, box dimension and Hausdorff dimension is any number between 0 and 1.

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Belongs to: Department of Mathematics
Last changed: May 27, 2021