How to plot a graph similar to this figure in Mathematica?

Question

I am trying to plot a graph similar to

I have tried using ContourPlot with GridLines as

ContourPlot[x^2 + y^2 == 400, {x, -40, 40}, {y, -40, 40}, 
 LabelStyle -> Directive[Black, FontSize -> 18], 
 GridLines -> Automatic]

However this only plots a circle with a transparent interior. But I want the inside to be dark just like in the figure. Also GridLines only shows the dark lines around -40,-20,0,20,24 without the grey lines inbetween. Is there a better way to do it?

Answer 1

You can alternatively use Graphics with the primitive Disk.

Definitions.

disk = {Darker[Gray, 0.5], Disk[{0, 0}, 20]};
frame = {{Automatic, None}, {Automatic, None}};
plotrange = {{-50, 50}, {-50, 50}};

gridlines = ConstantArray[
   Join[
        (* all lines *)
        {#, Directive[LightGray, Thin]} & /@ Range[-50, 50, 2], 
        (* main lines *)
        {#, Directive[Lighter[Black, 0.5]]} & /@ Range[-40, 40, 20]], 
   2
];

labelstyle = Directive[Black, FontSize -> 18];

Graphics.

Graphics[disk, 
         Frame -> frame, PlotRange -> plotrange, GridLines -> gridlines, 
         LabelStyle -> labelstyle
]

Comments.

The symbol gridlines could be instead defined with a DownValues, as shown by anderstood in his answer. This would read here:

Clear[gridlines];
gridlines[min_, max_] := Table[
     If[Divisible[i, 20], 
         (* main lines *)
         {i, Directive[Lighter[Black, 0.5]]}, 
         (* other lines *)
         {i, Directive[LightGray, Thin]}
     ], 
     {i, Ceiling[min], Floor[max], 2}
];

---

Update

To get outward ticks, as in the graphics of the question, you can define:

myticks[min_, max_] := Table[
    If[Divisible[i, 20],
         (* ticks for main lines *)
         {i, i, {0, 0.005}},
         (* ticks for other lines *)
         {i, "", {0, 0.005}}
    ],
    {i, Ceiling[min], Floor[max], 2}
];

frameticks = {{myticks[##] &, None}, {myticks[##] &, None}};

which gives

Graphics[disk, 
     Frame -> frame, FrameTicks -> frameticks, 
     PlotRange -> plotrange, GridLines -> gridlines, 
     LabelStyle -> labelstyle
]

Answer 2

Using your approach:

grids[min_, max_] := 
 Table[If[Mod[i, 20] == 0, {i, Black}, {i, Gray}], {i, Ceiling[min], 
   Floor[max], 1}]
RegionPlot[x^2 + y^2 < 400, {x, -40, 40}, {y, -40, 40}, GridLines -> grids]

Slight variation: increase grid spacing, change blue to gray, increase ticks label size and reduce disk diameter with:

grids[min_, max_] := 
     Table[If[Mod[i, 20] == 0, {i, Black}, {i, Gray}], {i, -40, 40, 2}]
RegionPlot[x^2 + y^2 < 300, {x, -40, 40}, {y, -40, 40}, 
     GridLines -> grids, PlotStyle -> Directive[Lighter[Black, 0.4]], 
     BoundaryStyle -> Gray, LabelStyle -> Directive[Black, FontSize -> 18]]