SeedRandom[232];pattern=Image[ArrayPlot[Table[Evaluate[(∑_i^5)6 Boole[y>.25 Sin[RandomReal[{(1/5),3}] x+RandomReal[2 π]]+i]+(∑_i^5)Boole[x>.25 Sin[RandomReal[{(1/5),3}] y+RandomReal[2 π]]+i]],{x,0,6,1/50},{y,0,6,1/50}],ColorRules->MapIndexed[First[#2]->#1&,RandomChoice[ColorData[35,"ColorList"],36]],PixelConstrained->True,Frame->False,PlotRangePadding->None],ImageSize->Automatic]

Animate[Graphics[{Texture[ImageRotate[pattern,t,Floor[1/Sqrt[2] ImageDimensions[pattern]]]],GeometricTransformation[Polygon[{{0,0},{1,0},{1/2,Sqrt[3]/2}},VertexTextureCoordinates->{{1/2,Sqrt[3]/2},{0,0},{1,0}}],Join[Table[ReflectionTransform[{Cos[(2 π t)/3+π/2],Sin[(2 π t)/3+π/2]}],{t,0,2}],Table[RotationTransform[(2 π t)/3],{t,0,3}]]]},ImageSize->Medium],{t,0,2 π},AnimationRunning->False,SaveDefinitions->True]