Layout
This section deals with the positioning of elements within any layout or design. Have you ever walked into a room and felt immediately uncomfortable for no apparant reason? It could be sparkling clean, you could be with all of your closest friends, it could be beautiful weather outside... but for some reason you just can't find your center? Likely, the room was laid out poorly, and your design sense took over.
Symmetry
Symmetry is something that is easily learned and recognized. It is something most people feel comfortable with. Symmetry is when identical things are positioned an equal distance from the center. For example: if your house has a door in the center, with two windows on either side of it, that house is laid out using symmetry. American money, with the president's face in the center and equal-sized objects to his left and right, is designed symmetrically.
Asymetry
Asymetry means, literally, "without symmetry". This is the exact opposite of the above concept, and something that takes some people a little while to grasp. Asymetry is having things of contrasting "weight" away from the center. In the example pictured here, the small star is balanced against the three large stars because of all the "white" (empty) space around it. Balance, a somewhat abstract concept, is something that is understood more with practice.
Quadrant
"Quad" means "one of four", and the meaning is consistent with its usage in design. This type of design is most often used in advertising - billboards, magazine ads, etc. It is when the design space (usually, a page) is broken up into four, equal-sized spaces in which to hold different information or designs. In the example pictured, each quadrant has a different shape element: three large stars, one small star, one small circle, and three larger circles.
Sequential
Mathematically, a sequence is an ordered list, such as "1, 2, 3, 4, 5" or even "1, 2, 4, 8, 16". This is also used most commonly with advertising. It is when the page is broken up into several spaces that grow sequentially different. My example pictured here is almost a symmetrical sequential design, with the circles breaking up the space between the stars, but each "sequence" in the image is progressively different from the other.

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