The Apollonian gasket is a well-known fractal identified more than 2000 years ago by Apollonius of Perga. The distribution of circle radii within the construct is governed by the Hausdorff dimension (roughly 1.3), however computing the exact dimension to a high degree of accuracy has eluded mathematicians until recently. Caroline Wormell (University of Sydney) and her collaborator Polina Vytnova (University of Surrey) published their method for calculating the Hausdorff dimension to 128 decimal places in Inventiones Mathematicae in January 2025. To celebrate its publication, we spoke to Caroline and asked her to break down the key concepts behind this paper.
Read the full preprint on ArXiv.