Slanted Layers

Figure 18: Superposed folding of a layer inclined to the direction of the first fold, where the flow of the second folding is parallel to the axial plane of the first. The images show the initial orientation of the layer and its shape after each folding event.

Show[GraphicsArray[{FoldPlot[{x,y,-.5x},{x,-1.5,1.5},{y,-1,1}]
  , FoldPlot[{x,y,-.5x}//axiZY[1,1.6]
     ,{x,-1.5,1.5},{y,-1,1},PlotPoints -> {60,60}]
  , FoldPlot[{x,y,-.5x}//axiZY[1,1.6]//axiXZ[.5,1.3]
     ,{x,-1.5,1.5},{y,-1,1},PlotPoints -> {60,60}] }]]

Click on a frame for a larger-sized image.

Changing the orientation of the layer with respect to the first folding event is simply a matter of parametrising a different plane to be the initial layer, rather than that given by $z=0$. In Fig. 18 it is chosen to be the plane $2z+x=0$, whereas in Fig. 19 we show the effect on the plane $z+.4(x-y)=0$ of the type 3 refolding used for Fig. 17.

Figure 19: Effect of a type 3 superposed folding on a layer inclined to the direction of the first fold. The images show the initial orientation of the layer and its shape after each folding event.

Show[GraphicsArray[{FoldPlot[{x,y,-.4x+.4y},{x,-1,1},{y,-1.5,1.5}]
  , FoldPlot[{x,y,-.4x+.4y}//axiZY[1,1.5]
     ,{x,-1.5,1.5},{y,-1,1},PlotPoints -> {60,60}]
  , FoldPlot[{x,y,-.4x+.4y}//axiZY[1,1.5]//axiYZ[.4]
     ,{x,-1,1},{y,-1.5,1.5},PlotPoints -> {80,100}] }]]

Click on a frame for a larger-sized image.