Rule of Thirds- As you’re taking an image you would have done this in your mind through your viewfinder or on the LCD display that you use to frame your shot. With this grid in mind the ‘rule of thirds’ now identifies four important parts of the image that you should consider placing points of interest in as you frame your image.
Not only this – but it also gives you four ‘lines’ that are also useful positions for elements in your photo.
Golden Rule (Rule of Thirds on Steroids)- It was made famous by Leonardo Fibonacci circa 1200 AD where he noticed there was an ‘absolute’ ratio in all appearances to nature. “Almost a sort of design that is universally effective in living things and pleasing to the human eye.” (https://digital-photography-school.com/divine-composition-with-fibonaccis-ratio-the-rule-of-thirds-on-steroids/) This theory could be brought down into a ratio, 1:1.618. It can be seen in famous works such as the Pantheon and the world-renowned painting of Mona Lisa. When applied to photography, this ratio can produce aesthetically pleasing compositions that can be magnets for the human sub-conscious.
Golden Rectangle otherwise known as The Phi Grid is like Rule of Thirds, but with greater outward squares and a tighter central square, as seen here:
Space- Space is the unused area around the subject. But sometimes the more space you give to an image the more the subject can breathe, and the easier it is so set a location, time and maybe even storyline to an image.
Frame within a frame- This is seen when there is a frame within the frame of the lens. As if as a lense you are looking into another mirror.