Dependence of the T₂ − T₃ relationship on different physical properties. Top row: Individual data points. Bottom row: Corresponding hexagonal binning. The colour-coding indicates the three selected physical properties, computed as median values within each bin in the bottom panels: the [O III]/[O II] line ratio (left), the electron density n_e (centre), and the softness parameter η (right). In the top panels, MARTA objects are shown as hexagons and low-redshift galaxies as circles. The plots also include the Pilyugin et al. (2009) relation, the Garnett (1992) relation, the 1:1 relation, and our best-fit model. The direction of maximum variation in the colour-coded quantity, determined by the gradient angle, is indicated by navy arrows, with the associated uncertainty shown for reference as light blue arrows. This provides a visual representation of how each parameter varies across the T₂ − T₃ plane.