Arithmetic Properties of Fractal Estimates - Department of ...
Arithmetic Properties of Fractal Estimates - Department of ...
Arithmetic Properties of Fractal Estimates - Department of ...
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<strong>Fractal</strong> geometry – What is a fractal?<br />
<strong>Arithmetic</strong><br />
<strong>Properties</strong> <strong>of</strong><br />
<strong>Fractal</strong><br />
<strong>Estimates</strong><br />
Tommy<br />
Löfstedt<br />
Outline<br />
Problem<br />
description<br />
<strong>Fractal</strong><br />
geometry<br />
Multifractal<br />
geometry<br />
<strong>Arithmetic</strong>s <strong>of</strong><br />
fractals<br />
Projections <strong>of</strong><br />
fractal<br />
measures<br />
Results<br />
Conclusions<br />
Roughly, the dimension <strong>of</strong> a set describes how much space the<br />
set fills<br />
Definition:<br />
The set has fine structure, it has details on arbitrary scales.<br />
The set is too irregular to be described with classical<br />
euclidean geometry, both locally and globally.<br />
The set has some form <strong>of</strong> self-similarity, this could be<br />
approximate or statistical self-similarity.<br />
The Hausdorff dimension <strong>of</strong> the set is strictly greater than<br />
its Topological dimension.<br />
The set has a very simple definition, i.e. it can be defined<br />
recursively.
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