dress waves ms mary byers choice bsg teapot
kapok picture frame community garden homelessness
If you draw a square, you create an infinite space in which every point has a defined location. For example, every point in this space is either within or not within the square you drew that defines the space.
It is now possible to display part of this space on a screen. We might maintain a record of images which are positioned in various locations in the space, and, if one of these images is positioned in the part of the space which is displayed on the screen, we can display that image. By this means we create the possibility of displaying any of a large number of images, and various groups of these images, by displaying various parts of the space. The problem this presents us with is this: how can we efficiently describe any location in this infinite space, for the purpose of including an image in that location, as well as for the purpose of displaying the images included in that location as desired?
For this purpose we could begin by surrounding the original square, which we could name 0, with a square that is three time as long on a side as 0, which we could name 1, such that 0 and 1 share the same center.
We can now identify the location of an image as being in either 0 or 1 by defining "in" as follows: all of the image in question is in 0, or not all of the the image is in 0 but all of it is in 1. The possibility also exists that not all of the image is in 1, but all of it is in a square called 2, which surrounds 1 using the same rules given for the relationship between 0 and 1.
For the purpose of efficiency let us call an infinite series of squares, each three times the length on a side of the square it encloses, and all sharing the same center, native squares. We can now place any image anywhere in this infinite space by specifying its native square, that is, the native square it is in, using the word in as defined above. (By implication an image is defined as being of finite width and height. There will exist, in such a system, a practical limit on the size of the space which can be so defined, because at some point the name of a native square will comprise a number so large that our system for recording numbers will no longer accommodate it. For example, if we were recording these numbers on a page, we might no longer be able to legibly write the number for some square on that page. With that said, even an elementary system for recording these native square names would be able to describe a very large space, even assuming square 0 is a very small square.)
cloud
