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I nest the right turns with # + Normalize@Cross[#] &. Since 2012rcampion2012rcampion has rather solved the coloring, here's a version using a close match from one of Mathematica's gradients.

cf = Lighter[ColorData["AvocadoColors", 1. - #], (1. - #)^8] &;
With[{npts = 87},
 Graphics[
  GraphicsComplex[
   NestList[# + Normalize@Cross[#] &, {1., 0.}, npts - 1] ~Append~ {0., 0.},
   {EdgeForm[Thin],
    Table[{cf[i/npts], Polygon[{i, i + 1, npts + 1}]}, {i, npts - 1, 1, -1}], 
    Table[{White, Disk[i, 1/3], Black, Text[HoldForm[Sqrt[#]] &@i, i]}, {i, npts}]}
   ],
  BaseStyle -> {FontSize -> Scaled[0.1/Sqrt[npts]]}
  ]
 ]

Mathematica graphics

I nest the right turns with # + Normalize@Cross[#] &. Since 2012rcampion has rather solved the coloring, here's a version using a close match from one of Mathematica's gradients.

cf = Lighter[ColorData["AvocadoColors", 1. - #], (1. - #)^8] &;
With[{npts = 87},
 Graphics[
  GraphicsComplex[
   NestList[# + Normalize@Cross[#] &, {1., 0.}, npts - 1] ~Append~ {0., 0.},
   {EdgeForm[Thin],
    Table[{cf[i/npts], Polygon[{i, i + 1, npts + 1}]}, {i, npts - 1, 1, -1}], 
    Table[{White, Disk[i, 1/3], Black, Text[HoldForm[Sqrt[#]] &@i, i]}, {i, npts}]}
   ],
  BaseStyle -> {FontSize -> Scaled[0.1/Sqrt[npts]]}
  ]
 ]

Mathematica graphics

I nest the right turns with # + Normalize@Cross[#] &. Since 2012rcampion has rather solved the coloring, here's a version using a close match from one of Mathematica's gradients.

cf = Lighter[ColorData["AvocadoColors", 1. - #], (1. - #)^8] &;
With[{npts = 87},
 Graphics[
  GraphicsComplex[
   NestList[# + Normalize@Cross[#] &, {1., 0.}, npts - 1] ~Append~ {0., 0.},
   {EdgeForm[Thin],
    Table[{cf[i/npts], Polygon[{i, i + 1, npts + 1}]}, {i, npts - 1, 1, -1}], 
    Table[{White, Disk[i, 1/3], Black, Text[HoldForm[Sqrt[#]] &@i, i]}, {i, npts}]}
   ],
  BaseStyle -> {FontSize -> Scaled[0.1/Sqrt[npts]]}
  ]
 ]

Mathematica graphics

1
source | link

I nest the right turns with # + Normalize@Cross[#] &. Since 2012rcampion has rather solved the coloring, here's a version using a close match from one of Mathematica's gradients.

cf = Lighter[ColorData["AvocadoColors", 1. - #], (1. - #)^8] &;
With[{npts = 87},
 Graphics[
  GraphicsComplex[
   NestList[# + Normalize@Cross[#] &, {1., 0.}, npts - 1] ~Append~ {0., 0.},
   {EdgeForm[Thin],
    Table[{cf[i/npts], Polygon[{i, i + 1, npts + 1}]}, {i, npts - 1, 1, -1}], 
    Table[{White, Disk[i, 1/3], Black, Text[HoldForm[Sqrt[#]] &@i, i]}, {i, npts}]}
   ],
  BaseStyle -> {FontSize -> Scaled[0.1/Sqrt[npts]]}
  ]
 ]

Mathematica graphics