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; 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; wherein the step of providing the first image further includes: selecting an existing image; defining a pictorial reference based on the existing image, wherein the pictorial reference exhibits an edgewise perimeter defining a regular rectangle, the regular rectangle including a first leg, a second leg adjacent the first leg, a third leg adjacent the second leg, an fourth leg adjacent both the first leg and the third leg, a first corner joining the fourth leg and the first leg, a second corner joining the first leg and the second leg, a third corner joining the second leg and the third leg, and an fourth corner joining the third leg and the fourth leg; and selecting a first portion of the pictorial reference in the shape of an isosceles right triangle; and creating the first image by selecting and cropping from the pictorial reference a first portion thereof in the shape of an isosceles right triangle, the first portion of the pictorial reference being a half-portion of the pictorial reference associated with a first one of the first, second, third, and fourth corners of the regular rectangle such that the legs of the isosceles right triangle associated with the first portion of the pictorial reference are defined by a corresponding first unique pairing of the first, second, third, and fourth legs of the regular rectangle joined by the first one of the first, second, third, and fourth corners thereof, and the hypotenuse of the isosceles right triangle associated with the first portion of the pictorial reference extends diagonally across the regular rectangle between the regular rectangle legs of the first unique pairing; and wherein the method further comprises: creating a third image by selecting and cropping from the pictorial reference a second portion thereof in the shape of an isosceles right triangle, the first and second portions of the pictorial reference overlapping each other to an extent of half the total area of each such portion, the second portion being a half-portion of the pictorial reference associated with a second one of the first, second, third, and fourth corners of the regular rectangle adjacent the first one thereof such that the legs of the isosceles right triangle associated with the second portion of the pictorial reference are defined by a corresponding second unique pairing of the first, second, third, and fourth legs of the regular rectangle joined by the second one of the first, second, third, and fourth corners thereof, and the hypotenuse of the isosceles right triangle associated with the second portion of the pictorial reference extends diagonally across the regular rectangle between the regular rectangle legs of the second unique pairing; creating a second portion of the second image based on the third image, the second portion of the second image being formed in its entirety from a similar plurality of axially symmetrically mirrored or unmirrored, axially rotated or unrotated, and non-overlapping instances of the third image specifically arranged in the shape of a similar, complete rectangle defining respective third and fourth pairs of parallel rectangle legs, each of the rectangle legs of the third pair of parallel rectangle legs exhibiting a similar third length extent between the rectangle legs of the fourth pair of parallel rectangle legs, and each of the rectangle legs of the fourth pair of parallel rectangle legs exhibiting a similar fourth length extent between the rectangle legs of the third pair of parallel rectangle legs; assembling the rectangle-shaped first portion of the second image and the rectangle-shaped second portion of the second image together, including wherein the first and second portions of the second image are joined at and aligned along respective corresponding instances of one of their respective first and second isosceles right triangle legs, and as well as each of: 1) joined at respective corresponding instances of one of their respective first isosceles right triangle corners positioned between the isosceles right triangle hypotenuse thereof and a first one of the isosceles right triangle legs thereof, and 2) joined at respective corresponding instances of another one of their respective second isosceles right triangle corners positioned between the first one of the isosceles right triangle legs thereof and the second one of the isosceles right triangle legs thereof; creating a fourth image by selecting and cropping from the pictorial reference a third portion thereof in the shape of an isosceles right triangle, the second and third portions of the pictorial reference overlapping each other to an extent of half the total area of each such portion, the third portion being a half-portion of the pictorial reference associated with a third one of the first, second, third, and fourth corners of the regular rectangle adjacent the second one thereof such that the legs of the isosceles right triangle associated with the third portion of the pictorial reference are defined by a corresponding third unique pairing of the first, second, third, and fourth legs of the regular rectangle joined by the third one of the first, second, third, and fourth corners thereof, and the hypotenuse of the isosceles right triangle associated with the third portion of the pictorial reference being aligned with and coextensive with the hypotenuse of the isosceles right triangle associated with the first portion of the pictorial reference; creating a third portion of the second image based on the fourth image, the third portion of the second image being formed in its entirety from a similar plurality of axially symmetrically mirrored or unmirrored, axially rotated or unrotated, and non-overlapping instances of the fourth image specifically arranged in the shape of a similar, complete rectangle defining respective fifth and sixth pairs of parallel rectangle legs, each of the rectangle legs of the fifth pair of parallel rectangle legs exhibiting a similar third length extent between the rectangle legs of the sixth pair of parallel rectangle legs, and each of the rectangle legs of the sixth pair of parallel rectangle legs exhibiting a similar fourth length extent between the rectangle legs of the fifth pair of parallel rectangle legs; assembling the rectangle-shaped second portion of the second image and the rectangle-shaped third portion of the second image together, including wherein the second and third portions of the second image are joined at and aligned along respective corresponding instances of one of their respective first and second isosceles right triangle legs, and as well as each of: 1) joined at respective corresponding instances of one of their respective first isosceles right triangle corners positioned between the isosceles right triangle hypotenuse thereof and a first one of the isosceles right triangle legs thereof, and 2) joined at respective corresponding instances of another one of their respective second isosceles right triangle corners positioned between the first one of the isosceles right triangle legs thereof and the second one of the isosceles right triangle legs thereof; creating a fifth image by selecting and cropping from the pictorial reference a fourth portion thereof in the shape of an isosceles right triangle, the third and fourth portions of the pictorial reference overlapping each other to an extent of half the total area of each such portion, and the fourth and first portions of the pictorial reference overlapping each other to an extent of half the total area of each such portion, the fourth portion being a half-portion of the pictorial reference associated with a fourth one of the first, second, third, and fourth corners of the regular rectangle adjacent each of the third and first ones thereof such that the legs of the isosceles right triangle associated with the fourth portion of the pictorial reference are defined by a corresponding fourth unique pairing of the first, second, third, and fourth legs of the regular rectangle joined by the fourth one of the first, second, third, and fourth corners thereof, and the hypotenuse of the isosceles right triangle associated with the fourth portion of the pictorial reference being aligned with and coextensive with the hypotenuse of the isosceles right triangle associated with the second portion of the pictorial reference; creating a fourth portion of the second image based on the fifth image, the fourth portion of the second image being formed in its entirety from a similar plurality of axially symmetrically mirrored or unmirrored, axially rotated or unrotated, and non-overlapping instances of the fifth image specifically arranged in the shape of a similar, complete rectangle defining respective seventh and eighth pairs of parallel rectangle legs, each of the rectangle legs of the seventh pair of parallel rectangle legs exhibiting a similar third length extent between the rectangle legs of the eighth pair of parallel rectangle legs, and each of the rectangle legs of the eighth pair of parallel rectangle legs exhibiting a similar fourth length extent between the rectangle legs of the seventh pair of parallel rectangle legs; and assembling the rectangle-shaped third portion of the second image and the rectangle-shaped fourth portion of the second image together, including wherein the third and fourth portions of the second image are joined at and aligned along respective corresponding instances of one of their respective first and second isosceles right triangle legs, and as well as each of: 1) joined at respective corresponding instances of one of their respective first isosceles right triangle corners positioned between the isosceles right triangle hypotenuse thereof and a first one of the isosceles right triangle legs thereof, and 2) joined at respective corresponding instances of another one of their respective second isosceles right triangle corners positioned between the first one of the isosceles right triangle legs thereof and the second one of the isosceles right triangle legs thereof.