Can you explain the notation [0,1)^2 unit square, does the 2 represent the spatial dimensionality? So,[0,1)^3 is the unit cube? Why is 0 inclusive, but the 1 is exclusive?
"The first is that this mapping is area-preserving, not distance-preserving." Which area is being preserved?
Is there a volume preserving choice function?
What are points t0 and t3, are those the location of the singularity points? What is the definition of those "singularity points"? Is it that seeming void in the center of the fibonacci spiral? And that void doesn't exist within the unit square case?
So[0,1)^1 is a line interval, [0,1)^2 is a unit square and [0,1)^3 is the unit cube, and [0,1]^d is a d-dimensional cube.
2.Only one boundary can be included
It includes 0 but not 1 because it can only the context is usually that practitioners want a region where one edge will wrap to the opposite edge.
Thus they treat [0,1)^2 as if it is actually a 2-dimensional torus.
thus the the 2 boundaries acutally map to the same point, so you can only include one of them.
In our case as we are using x %1 = fractional part of x, the fractional part could be 0, if x=3.0, but it could never be exactly 1.
"The first is that this mapping is area-preserving, not distance-preserving." Which area is being preserved?
Is there a volume preserving choice function?
What are points t0 and t3, are those the location of the singularity points? What is the definition of those "singularity points"? Is it that seeming void in the center of the fibonacci spiral? And that void doesn't exist within the unit square case?
I especially enjoyed footnote #1.