2 Added discussion of 1D behavior edited Feb 13 '15 at 21:25 bbgodfrey 46.1k1010 gold badges6363 silver badges115115 bronze badges It appears that PlotRange must be specified to assure that the Full range of data is displayed in the second DensityPlot. Also, specifying PlotPoints improves the appearance of the first DensityPlot. DensityPlot[Max[0, 0.1 - Abs[1. - Sqrt[x^2 + y^2]]], {x, -1.1, 1.1}, {y, -1.1, 1.1}, ColorFunction -> (Opacity[#, Blue] &), PlotPoints -> 100, Frame -> False, PlotRange -> Full]  DensityPlot[Max[0, 0.1 - Abs[1. - Sqrt[x^2 + y^2]]], {x, -1.2, 1.2}, {y, -1.2, 1.2}, ColorFunction -> (Opacity[#, Blue] &), PlotPoints -> 100, Frame -> False, PlotRange -> Full]  Update - Corresponding 1-D behavior Plot exhibits similar behavior Plot[Max[0, 0.1 - Abs[1. - Sqrt[x^2]]], {x, -1.2, 1.2}]  omits part of the curve unless PlotPoints is set to 100 or more. And, Plot[Max[0, 0.1 - Abs[1. - Sqrt[x^2]]], {x, -1.1, 1.1}]  has far too small a PlotRange, unless it is set explicitly to All or Full. This same behavior persists for ranges as large as about {x, -1.14, 1.14}, and as small as about {x, -1.09, 1.09}. It is not uncommon that Mathematica plotting routines have difficulty with functions that are zero except in narrow ranges. It appears that PlotRange must be specified to assure that the Full range of data is displayed in the second DensityPlot. Also, specifying PlotPoints improves the appearance of the first DensityPlot. DensityPlot[Max[0, 0.1 - Abs[1. - Sqrt[x^2 + y^2]]], {x, -1.1, 1.1}, {y, -1.1, 1.1}, ColorFunction -> (Opacity[#, Blue] &), PlotPoints -> 100, Frame -> False, PlotRange -> Full]  DensityPlot[Max[0, 0.1 - Abs[1. - Sqrt[x^2 + y^2]]], {x, -1.2, 1.2}, {y, -1.2, 1.2}, ColorFunction -> (Opacity[#, Blue] &), PlotPoints -> 100, Frame -> False, PlotRange -> Full]  It appears that PlotRange must be specified to assure that the Full range of data is displayed in the second DensityPlot. Also, specifying PlotPoints improves the appearance of the first DensityPlot. DensityPlot[Max[0, 0.1 - Abs[1. - Sqrt[x^2 + y^2]]], {x, -1.1, 1.1}, {y, -1.1, 1.1}, ColorFunction -> (Opacity[#, Blue] &), PlotPoints -> 100, Frame -> False, PlotRange -> Full]  DensityPlot[Max[0, 0.1 - Abs[1. - Sqrt[x^2 + y^2]]], {x, -1.2, 1.2}, {y, -1.2, 1.2}, ColorFunction -> (Opacity[#, Blue] &), PlotPoints -> 100, Frame -> False, PlotRange -> Full]  Update - Corresponding 1-D behavior Plot exhibits similar behavior Plot[Max[0, 0.1 - Abs[1. - Sqrt[x^2]]], {x, -1.2, 1.2}]  omits part of the curve unless PlotPoints is set to 100 or more. And, Plot[Max[0, 0.1 - Abs[1. - Sqrt[x^2]]], {x, -1.1, 1.1}]  has far too small a PlotRange, unless it is set explicitly to All or Full. This same behavior persists for ranges as large as about {x, -1.14, 1.14}, and as small as about {x, -1.09, 1.09}. It is not uncommon that Mathematica plotting routines have difficulty with functions that are zero except in narrow ranges. 1 answered Feb 12 '15 at 12:52 bbgodfrey 46.1k1010 gold badges6363 silver badges115115 bronze badges It appears that PlotRange must be specified to assure that the Full range of data is displayed in the second DensityPlot. Also, specifying PlotPoints improves the appearance of the first DensityPlot. DensityPlot[Max[0, 0.1 - Abs[1. - Sqrt[x^2 + y^2]]], {x, -1.1, 1.1}, {y, -1.1, 1.1}, ColorFunction -> (Opacity[#, Blue] &), PlotPoints -> 100, Frame -> False, PlotRange -> Full]  DensityPlot[Max[0, 0.1 - Abs[1. - Sqrt[x^2 + y^2]]], {x, -1.2, 1.2}, {y, -1.2, 1.2}, ColorFunction -> (Opacity[#, Blue] &), PlotPoints -> 100, Frame -> False, PlotRange -> Full]