Disclaimer: This post was an opportunity to explore computational mathematics, and it took a somewhat unconventional path away from the academic sphere. My goal was to enjoy the math (or art, depending on who you ask) and motivate readers to explore contour plots in their own way. I hope you enjoy it!
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equation=Sin[x^2]+Cos[y^2]+Exp[-x^2-y^2]Sin[xy];ContourPlot[equation,{x,-2Pi,2Pi},{y,-2Pi,2Pi},Contours->20,PlotRange->All,ColorFunction->"Rainbow",PlotLegends->Automatic]
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equation=Sin[x^2+y^2]+Cos[x*y]Exp[-x^2-y^2]+Sin[Sin[x]*Cos[y]]Log[Abs[1+x^2+y^2]];ContourPlot[equation,{x,-3,3},{y,-3,3},Contours->20,PlotRange->All,ColorFunction->"Rainbow",PlotLegends->Automatic]
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equation=Sin[Cos[Sin[x^2]]]+Exp[Cos[x+y]]-Log[Abs[1+Sin[x*y]]];ContourPlot[equation,{x,-4,4},{y,-4,4},Contours->30,PlotRange->All,ColorFunction->"Rainbow",PlotLegends->Automatic]
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equation=Sin[Cos[Sin[x^2]]]+Exp[Cos[x+y]]-Log[Abs[1+Sin[x*y]]]+Tan[Log[Abs[1+Sin[x^2+y^2]]]]-ArcSin[Cos[Sin[x*y]]];ContourPlot[equation,{x,-4,4},{y,-4,4},Contours->30,PlotRange->All,ColorFunction->"Rainbow",PlotLegends->Automatic]
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equation=Sin[Sin[Cos[x^2+y^2]]]+Log[Exp[Cos[Sin[x+y]]]]-ArcTan[Abs[Sin[Cos[x*y]]]]+Exp[Sin[Cos[ArcTan[Abs[Sin[x^2+y^2]]]]]];ContourPlot[equation,{x,-5,5},{y,-5,5},Contours->50,PlotRange->All,ColorFunction->"Rainbow",PlotLegends->Automatic]
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equation=Sin[Cos[Sin[x^2+y^2]]]+Log[Exp[Cos[Sin[x+y]]]]-ArcTan[Abs[Sin[Cos[x*y]]]]+Exp[Sin[Cos[ArcTan[Abs[Sin[x^2+y^2]]]]]]+ArcCos[Cos[Sin[ArcTan[Abs[Cos[Sin[x*y]]]]]]];ContourPlot[equation,{x,-6,6},{y,-6,6},Contours->50,PlotRange->All,ColorFunction->"Rainbow",PlotLegends->Automatic]
equation=Sin[Cos[Sin[x^2+y^2]]]+Log[Exp[Cos[Sin[x+y]]]]-ArcTan[Abs[Sin[Cos[x*y]]]]+Exp[Sin[Cos[ArcTan[Abs[Sin[x^2+y^2]]]]]]+ArcCos[Cos[Sin[ArcTan[Abs[Cos[Sin[x*y]]]]]]]+Cos[Sin[Cos[Exp[Sin[Cos[x^2+y^2]]]]]]-Log[Abs[Exp[Sin[Cos[ArcTan[Abs[Cos[Sin[x^2+y^2]]]]]]]]];ContourPlot[equation,{x,-7,7},{y,-7,7},Contours->100,PlotRange->All,ColorFunction->"Rainbow",PlotLegends->Automatic]