Sixty Years of Fractal Projections

TL;DR

This paper reviews the historical development and significance of Marstrand's projection theorems in fractal geometry, highlighting their impact over the past 30 years and numerous applications.

Contribution

It provides a comprehensive overview of six decades of research on fractal projections, emphasizing the theorems' foundational role and recent advancements.

Findings

Marstrand's theorems are central to fractal geometry.

Theorems have inspired numerous variants and applications.

The importance of these results has grown over 30 years.

Abstract

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.