nc = 8;

ineqs = Table[(x - 2/3 Cos[i 2 Pi/nc])^2 + (y -

2/3 Sin[i 2 Pi/nc])^2 < 1, {i, 0, nc - 1}];

Show[Table[

RegionPlot[ineqs[[k]], {x, -2, 2}, {y, -2, 2}, PlotPoints -> 35,

PlotStyle -> Opacity[.2]], {k, 1, nc}]]

What if we want to color overlapping regions according to how many overlaps they had?

We can use "BooleanCountingFunction" as follows

plots = Table[

RegionPlot[

BooleanCountingFunction[{k}, ineqs], {x, -2, 2}, {y, -2, 2},

PlotPoints -> 100, Frame -> None,

PlotStyle -> ColorData["Pastel"][k/nc]], {k, 0, nc}];

GraphicsGrid@Partition[plots, 3]

Show[Rest[plots]]

Its a great posting. Thank you for sharing with us.

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