The two wings are independent, and the amount they are separated by is determined by the length of the string underneath holding them together. The elastic cords pull the wings apart, so that the string is always taut, and the separation is maintained. To change the spacing, the string's length is adjusted.
Succinctly stated, Rob.
By accident I discovered what happened with the spacing when the book was open at one of the ends vs. when it was open near the center. Because the string runs underneath the wings which have a thickness, the distance that remains constant is the distance between the edges of the bottom of the wings. Measured from the top planes of the wings, that distance changes depending on which part of the book is open. The greatest distance between the top planes of the wings is when the front or back page is open. The shortest distance between the planes of the top surfaces of the wings is when the book is open to the middle. In practice this means that if you set the gap so that there is no arch under the spine when the book is open to the first page, there will be an arch when the book is open to the middle.