I had some problems with this as well so here's my understanding.

> 1. what are the differences between "basis-size" and
> "size" in lattice properties ('cause I do not think
> they are redundant...)? Is there any difference in
> using these 2 options and the actual shapes of the
> objects defined in ctl files??

basis-size defines the length of the basis vectors, while basis defines 
only the direction of those basis vectors. Size on the other hand 
determines the size of the computational cell that you are using in 
units of basis-size.

For example in your case

> (set! geometry-lattice (make lattice (size 1 1
> no-size) 
> (basis1 (vector3 1 0 0)) (basis2 (vector3 0 1 0))
> (basis-size 0.5 1 1)))

your basis vectors are a1 = (0.5 0 0) and a2 = (0 1 0). This means that 
(size 1 1 no-size) creates a computation sell which is a1 by a2, hence 
0.5 in the x direction and 1 in the y direction.

> 2. if I plot the epsilon directly with h5topng I get
> an ellips and a rectangle, whereas if I use map-data
> (with but also) WITHOUT the "-r" option, I get a
> circle and a square. Which is the real simulated
> structure?

In this case you don't actually need to use the -r option in mpb-data, 
because your unit cell is already rectangular. The problem is that the 
variable resolution is the number of points per basis vector. Since the 
x basis vector is half the size of the y basis vector, effectively the 
resolution in x is twice as large. Hence what you need to use is -n 32 
with mpb-data (or whatever resolution you want) and that will fix the image.

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