1. A method for generating an ordered pattern based on an existing image, comprising: providing a first image, the first image exhibiting an edgewise perimeter defining an isosceles right triangle including a first isosceles right triangle corner, a second isosceles right triangle corner, a third isosceles right triangle corner, a first isosceles right triangle leg extending between the first and second isosceles right triangle corners, a second isosceles right triangle leg joined to the first isosceles right triangle leg at the second isosceles right triangle corner and extending between the second isosceles right triangle corner and the third isosceles right triangle corner, and an isosceles right triangle hypotenuse joined to the second isosceles right triangle leg at the third isosceles right triangle corner, extending between the third isosceles right triangle corner and the first isosceles right triangle corner, and joined to the first isosceles right triangle leg at the first isosceles right triangle corner, including wherein each of the first and second isosceles right triangle legs exhibits a similar first length extent between the first and second isosceles right triangle corners, and the second and third isosceles right triangle corners, respectively, and the isosceles right triangle hypotenuse exhibits a second length extent between the third and first isosceles right triangle corners; and creating a second image based on the first image, the second image at least including a first portion formed in its entirety from a plurality of axially symmetrically mirrored or unmirrored, axially rotated or unrotated, and non-overlapping instances of the first image specifically arranged in the shape of a complete rectangle defining respective first and second pairs of parallel rectangle legs, each of the rectangle legs of the first pair of parallel rectangle legs exhibiting a similar third length extent between the rectangle legs of the second pair of parallel rectangle legs, and each of the rectangle legs of the second pair of parallel rectangle legs exhibiting a similar fourth length extent between the rectangle legs of the first pair of parallel rectangle legs; wherein each of the third and fourth length extents associated with the complete rectangle is at least as long as at least one of the first and second length extents associated with the isosceles right triangle; wherein a total area encompassed by the first portion of the second image is at least twice as large as a total area encompassed by the first image; and wherein the plurality of instances of the first image being specifically arranged in the shape of a complete rectangle includes wherein each instance of the first image of the plurality of instances of the first image is positioned adjacent to at least one other instance thereof, and further includes wherein adjacent instances of the first image of each pair of adjacent instances of the first image are one of: 1) joined at and aligned along their respective first isosceles right triangle leg, 2) joined at and aligned along their respective second isosceles right triangle leg, and 3) joined at and aligned along their respective isosceles right triangle hypotenuses, as well as two of: 4) joined at their respective first isosceles right triangle corners, 5) joined at their respective second isosceles right triangle corners, and 6) joined at their respective third isosceles right triangle corners.