Art by Zakir Gowani

hp[r_: 1] := Polygon[{

   {-r, 0},

   {-r/2, r Sqrt[3]/2}, {r/2, r Sqrt[3]/2}, {r, 0},

   {r/2, -r Sqrt[3]/2}, {-r/2, -r Sqrt[3]/2}

   }];

hexSwirl[thickness_: .8, depth_: 20, color_: Blue,

 edgeColor_: Black, scalingRate_: .2, xtranslationRate_: .2,

 ytranslationRate_: .2, background_: White, rotationRate_: 1,

 pt_: {1, 1}, rotModifier_: 5] :=

Graphics[{EdgeForm[

   Directive[{AbsoluteThickness[thickness], edgeColor}]], color,

  GeometricTransformation[

   hp[],

   Table[

    ScalingTransform[{\[Alpha]/(depth - \[Alpha])^

         scalingRate, \[Alpha]/(depth - \[Alpha])^

         scalingRate}].TranslationTransform[{-\[Alpha]^

         xtranslationRate, \[Alpha]^

        ytranslationRate}].RotationTransform[\[Pi]/(depth - \

\[Alpha])^rotationRate, pt + rotModifier/\[Alpha]],

    {\[Alpha], (depth - 1), 1, -1}]

   ],

  ImageSize -> 500

  }, Background -> background

 ]

(*

An example of some good values for the inputs:

thickness = .2,

depth = 900,

color = LightPink,

edgeColor = Lighter@Purple,

scalingRate = .001,

xtranslationRate = -1,

ytranslationRate = -1,

background = LightPurple,

rotationRate = -.2,

pt = {0, 5},

rotModifier = 50

amoeba[a_, b_, c_, d_, size_, color1_: Darker[Darker[Green]],  color2_: Orange, color3_: Red, color4_: Green] := PolarPlot[{   5,   Nest[Sin, c \[Theta] + \[Pi]/c*d, 3]^(a - .5) + 4,   Nest[Sin, c \[Theta] + \[Pi]/c*(d + 1), 3]^a + 3,   Nest[Sin, c \[Theta] + \[Pi]/6*c, 3]^3 + 1.7,   Nest[Sin, a \[Theta] + b*(\[Pi]/6), 2]^2}, {\[Theta], 0, 2 \[Pi]},  Axes -> False,  ImageSize -> size,  PlotStyle -> {{color1, Thickness[.01]}, {color2,     Thickness[.01]}, {color3, Thickness[.01]}, {color4,     Thickness[.005]}}]

amoebaPattern[size_] := GraphicsGrid@Partition[   RandomSample[    Flatten[Table[      amoeba[       RandomInteger[{1, 4}],        RandomInteger[{3, 5}],       RandomInteger[{2, 9}],       RandomInteger[{4, 5}],       RandomReal[{400/(size), (500)/(size)}],       Black,       Darker[Darker[Blue]],       Pink,       Pink       ]      , {\[Alpha], 1, size*size}]],    size*size],   size]

flowerEqn = {  (a - 2)*(Cos[b \[Theta]])^c + d (Cos[e \[Theta]])^f +   g (Sin[h \[Theta]])^(i - 2) + j - 2,  Sin[k \[Theta]] + .5,  a (Cos[b \[Theta]])^c + d (Cos[e \[Theta]])^f +   g (Sin[h \[Theta] ])^i + j };

flowerEqn2 = {  (a - 2)*(Cos[b \[Theta]])^c + d (Cos[e \[Theta]])^f +   g (Sin[h \[Theta]])^(i - 2) + j - 2,  Sin[k \[Theta]] + .5,  (a - 1)*(Cos[b \[Theta]])^c + d (Cos[e \[Theta]])^f +   g (Sin[h \[Theta]])^(i) + j - 1, ,  a (Cos[b \[Theta]])^c + d (Cos[e \[Theta]])^f +   g (Sin[h \[Theta] ])^i + j };

flowerParameters[dev1_: 0, dev2_: 0,  dev3_: 0] := {{a, 8 + dev1}, {b, 3}, {c,   If[dev2 != 0, RandomChoice[{2, 4}], 4]}, {d, 2 + dev2}, {e,   9}, {f, 20}, {g, 2.84 + dev2}, {h, 6}, {i, 4}, {j,   2.5 + 2*dev3}, {k, 6}};

getFlowerParam[var_, dev1_: 0, dev2_: 0, dev3_: 0] := Select[flowerParameters[dev1, dev2, dev3],  ToString[#[[1]]] == ToString[var] &][[1, 2]]

FlowerRules[dev1_: 0, dev2_: 0, dev3_: 0] := Flatten@Table[{ToExpression[      FromCharacterCode[\[Alpha]]] -> (getFlowerParam[       ToExpression[FromCharacterCode[\[Alpha]]], dev1,       dev2])}, {\[Alpha], 97, 107}];

colorSets = {  {{Thickness[.005], Pink}, {Thickness[.005],    Darker[Green]}, {Thickness[.005], Darker[Pink]}},  {{Thickness[.005], Darker[Red]}, {Thickness[.005],    Pink}, {Thickness[.005], Darker[Green]}},  {{Thickness[.005], Darker@LightBlue}, {Thickness[.005],    Black}, {Thickness[.005], Red}}};

mkFlower[dev1_: 0, dev2_: 0, dev3_: 0, rotation_: 0, imagesize_: 120] := Rotate[PolarPlot[  Evaluate[   RandomChoice[{flowerEqn, flowerEqn2}] /.    FlowerRules[dev1, dev2, dev3]], {\[Theta], 0, 2 \[Pi]},  PlotRange -> All, Axes -> False,  PlotStyle -> RandomChoice[colorSets], ImageSize -> imagesize], rotation]

object1 = PolarPlot[ Evaluate[flowerEqn /. FlowerRules[1]], {\[Theta], 0, 2 \[Pi]}, ImageSize -> 300, PlotRange -> All, PlotLabel ->  ToString[Evaluate[flowerEqn /. FlowerRules[1]][[1]],   TraditionalForm], PlotStyle -> {{Thin, Black}, {Thin, Black}, {Thin, Black}}];

object2 = Rotate[PolarPlot[  Evaluate[flowerEqn /. FlowerRules[0]], {\[Theta], 0, 2 \[Pi]},  PlotRange -> All, Axes -> False,  PlotStyle -> {Pink, Green, {Darker[Pink]}}, ImageSize -> 350], 20 Degree];

object3 = GraphicsGrid[ Partition[  RandomSample[   Flatten[Table[     mkFlower[\[Alpha], \[Beta], \[Gamma], rot, 120], {\[Alpha], 1,      6, 3}, {\[Beta], 0, 1, .5}, {\[Gamma], 0, 4, 2}, {rot, 0, 60,      10}]], 9], 3], Frame -> All];

   ImageSize -> 500, ViewPoint -> {α, 0, 180}, Axes -> False,     PlotStyle -> Transparent,     MeshFunctions -> {Sin@Sin[#]^2 - Sin@Cos[3 #] + Cos@Sin@Sin@Cos@# &},     Background -> Lighter@Pink];

time = ParallelTable[    n, {α, Flatten[{Table[α, {α, 1, 30, 1.3}], Table[α, {α, 30, 1, -1.3}]}]}];