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mrn16

Pi Spiral

Jan 22nd, 2014
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  1. colors = {{0.0588235, 0.258824, 0.352941}, {0.196078, 0.643137, 0.905882}, {0.301961, 0.466667, 0.0980392}, {0.27451, 0.811765, 0.392157}, {0.411765, 0.0156863, 0.0156863}, {0.905882, 0.0588235, 0.0980392}, {0.580392, 0.321569, 0.}, {0.890196, 0.411765, 0.0117647}, {0.247059, 0.117647, 0.305882}, {0.54902, 0.317647, 0.764706}};
  2.  
  3. f[t_] := {((Pi + t) Cos[t])/(2 Pi), ((Pi + t) Sin[t])/(2 Pi)}
  4.  
  5. fun[x_] := x + FindRoot[(d^2 + 2 d (Pi + t) + 2 (Pi + t)^2 - 2 (Pi + t) (d + Pi + t) Cos[d])/(4 Pi^2) == 1 /. {t -> x}, {d, 0.0000001}][[1, 2]]
  6.  
  7. val = 10000;
  8. tab = Table[{n, First[RealDigits[Pi, 10, 1, -(n - 1)]][[1]], Count[RealDigits[Pi, 10, n][[1]], First[RealDigits[Pi, 10, 1, -(n - 1)]][[1]]], If[n == 1, {}, {First[RealDigits[Pi, 10, 1, -(n - 2)]][[1]], First[RealDigits[Pi, 10, 1, -(n)]][[1]]}]}, {n, 1, val + 1}];
  9. maximus = Table[{n, tab[[Last[Flatten[Position[tab[[All, 2]], n]]], 3]]}, {n, 0, 9}];
  10. ta = {{Pi/2, fun[Pi/2], f[Pi/2]}};
  11. Quiet[Do[AppendTo[ta, {Last[ta][[2]], fun[Last[ta][[2]]], f[Last[ta][[2]]]}], {n, 1, val}]];
  12. h = Graphics[Table[{RGBColor[colors[[tab[[val + 1 - n, 2]] + 1]]], Disk[ta[[n, 3]], .5]}, {n, 1, Length[ta] - 1}]]
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