Enabling fundamental understanding of Nature with novel binning methods for 2D histograms

Abstract

Context. Visualization of 2D distributions is an essential task, commonly done with a 2D histogram. The histogram is built by subdividing the sample space into regions and color-coding the number of samples in each region. Aims. We aim to solve long-standing problems with common 2D histogram methods: lack of thematic, visual, and conceptual unity with underlying data, and general stagnation in the field. Methods. We develop a new method for plotting 2D histograms with arbitrary bin shapes, including aperiodic tilings and geographic maps. We apply the method to several common plot types from the literature. Results. We find our method performs best across all tasks, solving the problems and propelling the scientific progress forward.

Figures (6)

• Figure 1: Hertzsprung-Russell diagram binned with Penrose P1 tiling. Data from HYG (Hipparcos, Yale, Gliese) Stellar database is used. Bottom left corner shows tile shapes.
• Figure 2: Posterior distribution of black hole masses from GW191109_010717 binned with Penrose P2 tiling.
• Figure 3: Total invariant mass of two heaviest jets $m_{JJ}$ versus the $\eta$-$\phi$ cylinder distance between them from the LHCO2020 BlackBox1 dataset, binned with Penrose P3 tiling.
• Figure 4: $P$ - $\dot P$ diagram for pulsars from ANTF Catalog Manchester2005 binned with aperiodic monotile "turtle". Lines of negative slope show constant characteristic lifetime $\tau \equiv \frac{P}{2 \dot P}$ and lines of positive slope show constant characteristic magnetic field $B \equiv \sqrt{\frac{P}{\text{sec}} \dot P} \; 3.2 \times 10^{19}~\text{G}$
• Figure 5: Raw $\gamma$-ray counts detected by Fermi LAT in the sky area around PSR J2032+4127, binned with aperiodic monotile "hat".