a4mula

I am currently reading a paper about complexity.  The author starts with a brief introduction to chaos.  In the paper it's stated that chaos is defined by stretching and folding.  The paper goes on to equate a baker crafting a croissant. The visualization of how two starting initial conditions can quickly diverge is clear in the example.  I'm curious if this analogy goes further than just baking however.  Can we equate the stretching of the dough to time and the folding of the dough to space?  

I appreciate any thoughts, and I apologize if direct links and quotes such as this are any type of misstep.  

Quoted Source: https://necsi.edu/chaos-complexity-and-entropy

Quote

And how does nonlinearity manufacture fractals and chaos? There is one and only one answer: stretching and folding. All flows and all maps that manufacture fractals do it by stretching and folding. Let’s look at a simple example. Think of a pastry chef making a croissant. She puts down the dough and stretches it with a rolling-pin. Then she puts a layer of butter on it and folds it. She rolls and stretches it again, puts another layer of butter, and folds it again. And so on ad infinitum, or almost. What you get is an object, a delicious croissant, which is a fractal in the direction perpendicular to the table, with a very large (quasi-infinite) number of layers. This is the way all dynamical chaos works! It is easy to see how the sensitivity to initialconditions comes about. Consider two points close to each other in the initial dough. When the chef rolls the dough the first time, they get farther apart, unless they happen to be on the same vertical, which is very unlikely. Next time she rolls the dough, they get farther apart again. Eventually it is bound to happen that, in one of the folding operations, our two points end up in different layers. After that, they have completely different histories, and if they come close again it will be pure accident. All this is pretty simple and pretty obvious! But for physicists in the 1970’s it was new. And it turns out to be very, very useful. And where is the nonlinearity in this? It is in the folding. Linear equations of motion have solutions whose behavior does not change with amplitude. If they start stretching, they stretch forever; they never fold. It is the nonlinearity that folds.