polygonSwirls.txt

hexagon[] := Polygon[
   {
    {-1, 0},
    {-1/2, Sqrt[3]/2}, {1/2, 1 Sqrt[3]/2}, {1, 0},
    {1/2, - Sqrt[3]/2}, {-1/2, -1 Sqrt[3]/2}
    }
   ];

equilateralTriangle[] := Triangle[
  {
   {0, Sqrt[.75]/2}, {-.5, -Sqrt[.75]/2}, {.5, -Sqrt[.75]/2}
   }
  ]

square[] :=
  Polygon[{{-.5, -.5}, {-.5, .5}, {.5, .5}, {.5, -.5}}];

polygonSwirl[
   polygon_: Disk[],
   thickness_: .8,
   depth_: 20,(* The number of polygons that will be generated. 
   Good range: 100 - 2000 *)
   color_: Blue,
   edgeColor_: Black,
   scalingRate_: .2, (* Values between 0 and 1 change scale speed *)
   xtranslationRate_: .2,(* Making this smaller (e.g., .01) translates in the x-direction *)
   ytranslationRate_: .2,(* Making this smaller (e.g., .01) translates in the y-direction *)
   background_: White,
   rotationRate_: 1, (* Values between 0 and 1 change rotation speed*)
   rotPoint_: {1, 1},(* The point about which rotation occurs. {0, 0} and {0,1} are good starting values. *)
   rotModifier_: 5
   ] := Graphics[{EdgeForm[
     Directive[{AbsoluteThickness[thickness], edgeColor}]], color,
    GeometricTransformation[
     polygon,
     Table[
      ScalingTransform[{\[Alpha]/(depth - \[Alpha])^
           scalingRate, \[Alpha]/(depth - \[Alpha])^
           scalingRate}].TranslationTransform[{-\[Alpha]^
           xtranslationRate, \[Alpha]^
          ytranslationRate}].RotationTransform[\[Pi]/(depth - \\[Alpha])^rotationRate, rotPoint + rotModifier/\[Alpha]],
      {\[Alpha], (depth - 1), 1, -1}]
     ],
    ImageSize -> 500
    }, Background -> background
   ];


(* Some examples: *)

polygonSwirl[
 polygon = hexagon[],
 thickness = .4,
 depth = 900,
 color = Pink,
 edgeColor = Lighter@Purple,
 scalingRate = -.0001,
 xtranslationRate = -1,
 ytranslationRate = -1,
 background = LightPink,
 rotationRate = -.9999,
 rotPoint = {0, 0},
 rotModifier = 5
 ]


polygonSwirl[
 polygon = square[],
 thickness = .2,
 depth = 2000,
 color = Brown,
 edgeColor = White,
 scalingRate = -1,
 xtranslationRate = -.01,
 ytranslationRate = -.0001,
 background = LightGray,
 rotationRate = -.4,
 rotPoint = {1, 1},
 rotModifier = 5
 ]


polygonSwirl[
 polygon = equilateralTriangle[],
 thickness = .3,
 depth = 100,
 color = Pink,
 edgeColor = White,
 scalingRate = -.0001,
 xtranslationRate = -1,
 ytranslationRate = -1,
 background = Pink,
 rotationRate = 1,
 rotPoint = {0, 0},
 rotModifier = 0
 ]