sample construct: the largest square that is entirely in the window.
alternatively, the smallest square that completely contains the window.
trying, here, to define a screen square whereby a view can be specified by naming the screen square and specifying its side length and its location relative to the screen.
we want a square that is about the same size as the window.
if each square is divided into four squares (possibly not the best arrangement), the window's longest dimension should be greater than 3/4 of the side length of the screen square and less than 1 1/2 times that dimension. this is a rational definition of the term "about the same size as".
if the squares change size they all do it together. if the size of the screen square changes, it's side length may now exceed the longest dimension of the screen, so it can no longer be the screen square. some smaller square must now be the screen square.
actually, let's consider the extreme example, where the screen square's size and location change by a very great amount.
we are now confronted with the problem of finding the native square which contains the window. we know the distance horizontally and vertically from the screen square to the widow's new location. finding the screen square's native square ought to be easy ... let's see ... when we specify a new window location we specify offsets horizontally and vertically, using some unit of measure, but what unit? the first option that jumps to mind is the side length of the screen square. One tenth of a side length, one one hundredth of a side length, and since the screen square is by definition about the same size as the window, these would then be small increments of motion ... which is probably what we want. it could be argued that a rational change in view is one that can be measured using quite small numbers.
the next problem, then, is this: when the view moves, squares that were previously not in the view may enter the view, and squares that were in the view may leave it.
we could approach this by trying to ascertain, based on a view and a change in view, what squares have newly entered the view and which ones have just left it, but there is possibly an alternative, which is just to ask, given a view, what squares are in that view.
it occurred to me to define the screen square as a square whose location - upper left corner - is in the window. advancing this as a hypothesis, if the screen square is about the same size as the window, there can only be one square of that size whose location is in the window. this seems to reveal a flaw - this is amazing - in my original definition of "about the same size as". a square is about the same size as the window if its side length is greater than the longest dimension of the screen and not greater than twice that length.
i haven't yet figured out how to draw a crisp line, represented by an equation, in this environment.
then there's this whole issue of tree care, yard care. throwing all that leafy and woody bounty in the garbage just doesn't make sense, yet it's fairly ubiquitous. it should all be made into products, of which there are several types: mulch, firewood, screens, timbers, and boards, plus what's called cane and maybe some other things. Oh, and fruits and veggies.
