Top panels: fractional differences ﹩{\rm{\Delta }}{({W}_{2}^{1,1})}_{11}﹩, ﹩{\rm{\Delta }}{({W}_{2}^{1,1})}_{22}﹩ defined in Equation (17). We exhibit these quantities as a function of ﹩{\nu }_{{\rm{A}}}﹩, which is related to the area fraction of the field. The dependence of ﹩{\rm{\Delta }}{({W}_{2}^{1,1})}_{11}﹩, ﹩{\rm{\Delta }}{({W}_{2}^{1,1})}_{22}﹩ on Δ and ﹩{R}_{{\rm{G}}}﹩ is negligible. Middle panels: off-diagonal component ﹩{({W}_{2}^{1,1})}_{12}﹩ divided by the average of the two diagonal components ﹩\langle {W}_{2}^{1,1}\rangle ﹩. This quantity is consistent with zero for all ﹩{R}_{{\rm{G}}}﹩ and Δ values. Bottom panels: ﹩{\beta }_{\mathrm{tot}}﹩ calculated using all connected regions and holes at each ﹩{\nu }_{{\rm{A}}}﹩ threshold. Left panels: ﹩{\rm{\Delta }}=30\,{h}^{-1}\,\mathrm{Mpc}﹩, ﹩{R}_{{\rm{G}}}=20,15,10\,{h}^{-1}\,\mathrm{Mpc}﹩ (green, yellow, and blue). Right panels: ﹩{R}_{{\rm{G}}}=15\,{h}^{-1}\,\mathrm{Mpc}﹩, ﹩{\rm{\Delta }}=40,30,20\,{h}^{-1}\,\mathrm{Mpc}﹩ (cyan, yellow, and red). Error bars denote the error on the mean from ﹩{N}_{\mathrm{slice}}=75﹩ fields.