Q[z_,c_] = (z^2)+c;

CPts = {{0,0}};
For[cxval=-2, cxval≤1, cxval=cxval+0.01,
For[cyval=-1.5, cyval≤1.5, cyval=cyval+0.01,
cval = cxval + I cyval;
If[Abs[Q[NestWhile[Q[#,cval]&,  0., Abs[Q[#,cval]]< 2&,1,200],cval]]<2., 
CPts = Join[CPts,{{cxval,cyval}},1];
]
]
]

MandPlot1 = ListPlot[CPts,PlotStyle->{{Red}}, PlotRange->{{-2,2},{-2,2}}, AspectRatio->1]

ListPlot[CPts,PlotStyle->{{Red}}, PlotRange->{{-0.25,0.25},{-1.0,-0.6}}, AspectRatio->1]

cval=-0.18-0.75 I;

QJ[z_] = (z^2)+cval;

Pts = {{0.,0.}};

C2 = Max[Abs[cval],2];
For[x=-2,x≤ 2,x=x+0.01,
For[y=-2,y≤ 2,y=y+0.01,
v=x+I y;
StopVal=0;
For[k=1,k<50,k++;
If[Abs[v]>C2, {StopVal=1,Break;},v=N[QJ[v]]];
]
If[StopVal==0,Pts = Join[Pts,{{x,y}},1];]
]
]

ListPlot[Pts,PlotStyle->{{Red}}, PlotRange->{{-2,2},{-2,2}}, Axes->None]

ListPlot[CPts,PlotStyle->{{Red}}, PlotRange->{{-0.25,0.25},{0.6,1.0}}, AspectRatio->1]

cval=-0.2+0.8 I;

QJ[z_] = (z^2)+cval;

Pts = {{0.,0.}};

C2 = Max[Abs[cval],2];
For[x=-2,x≤ 2,x=x+0.01,
For[y=-2,y≤ 2,y=y+0.01,
v=x+I y;
StopVal=0;
For[k=1,k<50,k++;
If[Abs[v]>C2, {StopVal=1,Break;},v=N[QJ[v]]];
]
If[StopVal==0,Pts = Join[Pts,{{x,y}},1];]
]
]

ListPlot[Pts,PlotStyle->{{Red}}, PlotRange->{{-2,2},{-2,2}}, Axes->None]

CPts2 = {{0,0}};
For[cxval=-2, cxval≤-1, cxval=cxval+0.001,
For[cyval=-0.5, cyval≤0.5, cyval=cyval+0.001,
cval = cxval + I cyval;
If[Abs[Q[NestWhile[Q[#,cval]&,  0., Abs[Q[#,cval]]< 2&,1,200],cval]]<2., 
CPts2 = Join[CPts2,{{cxval,cyval}},1];
]
]
]

ListPlot[CPts2,PlotStyle->{{Red}}, PlotRange->{{-1.85,-1.7},{-0.05,0.05}}, AspectRatio->1]

cval=-1.76+0.005 I;

QJ[z_] = (z^2)+cval;

Pts = {{0.,0.}};

C2 = Max[Abs[cval],2];
For[x=-2,x≤ 2,x=x+0.005,
For[y=-0.5,y≤ 0.5,y=y+0.001,
v=x+I y;
StopVal=0;
For[k=1,k<50,k++;
If[Abs[v]>C2, {StopVal=1,Break;},v=N[QJ[v]]];
]
If[StopVal==0,Pts = Join[Pts,{{x,y}},1];]
]
]

ListPlot[Pts,PlotStyle->{{Red}}, PlotRange->{{-2,2},{-0.4,0.4}}, Axes->None]

ListPlot[CPts,PlotStyle->{{Red}}, PlotRange->{{-1.5,-0.75},{-0.1,0.1}}, AspectRatio->1]

cval=-1.3+0.03 I;

QJ[z_] = (z^2)+cval;

Pts = {{0.,0.}};

C2 = Max[Abs[cval],2];
For[x=-2,x≤ 2,x=x+0.01,
For[y=-2,y≤ 2,y=y+0.01,
v=x+I y;
StopVal=0;
For[k=1,k<50,k++;
If[Abs[v]>C2, {StopVal=1,Break;},v=N[QJ[v]]];
]
If[StopVal==0,Pts = Join[Pts,{{x,y}},1];]
]
]

ListPlot[Pts,PlotStyle->{{Red}}, PlotRange->{{-2,2},{-2,2}}, Axes->None]

ListPlot[CPts,PlotStyle->{{Red}}, PlotRange->{{0.2,0.4},{0.4,0.6}}, AspectRatio->1]

cval=0.3+0.51 I;

QJ[z_] = (z^2)+cval;

Pts = {{0.,0.}};

C2 = Max[Abs[cval],2];
For[x=-2,x≤ 2,x=x+0.01,
For[y=-2,y≤ 2,y=y+0.01,
v=x+I y;
StopVal=0;
For[k=1,k<50,k++;
If[Abs[v]>C2, {StopVal=1,Break;},v=N[QJ[v]]];
]
If[StopVal==0,Pts = Join[Pts,{{x,y}},1];]
]
]

ListPlot[Pts,PlotStyle->{{Red}}, PlotRange->{{-2,2},{-2,2}}, Axes->None]

cval=0.27+0.55 I;

QJ[z_] = (z^2)+cval;

Pts = {{0.,0.}};

C2 = Max[Abs[cval],2];
For[x=-2,x≤ 2,x=x+0.01,
For[y=-2,y≤ 2,y=y+0.01,
v=x+I y;
StopVal=0;
For[k=1,k<50,k++;
If[Abs[v]>C2, {StopVal=1,Break;},v=N[QJ[v]]];
]
If[StopVal==0,Pts = Join[Pts,{{x,y}},1];]
]
]

ListPlot[Pts,PlotStyle->{{Red}}, PlotRange->{{-2,2},{-2,2}}, Axes->None]