Colour palette for periodic z-axis

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You can try creating your own colour palette, ensuring that the last point on the scale is the same colour as the first one. See the CreateGradientColorTable example in the “Color palettes” section on the page you linked. Based on the example there, you could have:

{
   TCanvas *c2  = new TCanvas("c2","c2",0,0,600,400);
   TF2 *f2 = new TF2("f2","0.1+(1-(x-2)*(x-2))*(1-(y-2)*(y-2))",1,3,1,3);
   const Int_t Number = 4;
   Double_t Red[Number]    = { 1.00, 0.00, 0.00, 1.00};
   Double_t Green[Number]  = { 0.00, 1.00, 0.00, 0.00};
   Double_t Blue[Number]   = { 0.00, 0.00, 1.00, 0.00};
   Double_t Length[Number] = { 0.00, 0.33, 0.66, 1.00};

   Int_t nb=50;
   TColor::CreateGradientColorTable(Number,Length,Red,Green,Blue,nb);
   f2->SetContour(nb);
   f2->SetLineWidth(1);
   f2->SetLineColor(kBlack);
   f2->Draw("surf1z");
   return c2;
}

which starts and ends on red.