Could anyone explain what an equiangular spiral is? How does that grid affect focus or view of subject?
An "equiangular spiral" is another name for a logarithmic spiral. A spiral grid can be made by drawing squares enclosing arcs of this spiral. I expect that in photography, the particular equiangular spiral you've heard about is a golden spiral — a logarithmic spiral where the growth factor is equal to the golden ratio. It looks like this, with subdivided squares:
A rule might involve putting objects of interest within the squares of this pattern, or putting things at the intersections, or along the curve. How does this affect focus or view of the subject? Well.... I highly encourage you to read my answer about the golden ratio itself here:
What is the 'Golden Ratio' and why is it better than the 'Rule of Thirds?'
as well as this about the "rule of thirds":
In each of these, while there's plenty of sense in the idea that symmetrically-balanced compositions can be static and boring while unequal or off-center balance is more lively, there is no strong argument for any particular number. Likewise, there's no strong argument for this particular spiral or associated grid.
For centuries, and especially since the enlightenment and the dawning of the Age of Reason, people have looked for a mathematical underpinning for aesthetics and beauty. This is an idea which has a lot of appeal, to the point where once people are told that there might be a simple number or shape which has natural resonant beauty, they really, really cling to it despite lack of evidence. Especially for those of us who tend to think about art rather than just feel it, or feel that we have no natural talent for composition, the idea that there's simply a formula to learn is very comforting.
You've probably heard dozens of stories about how the ancients or renaissance artists used the golden ratio with this or similar "rules", or how it occurs in nature. There is no actual evidence for any of this. If you look at enough paintings or enough shells, you certainly can find some which line up, but if you've had to discard 999 to find that 1, that's just selection bias.
All that is not to say that it can't be fun or useful to compose using rules like this. There's nothing inherently more beautiful about ABAB CDCD EFEF GG in iambic pentameter, but there's still a lot of value in writing Shakespearean sonnets. Likewise, it can be an interesting exercise to choose a particular form for photographic composition. I'd just be inclined to call it the "Game of the Equiangular Spiral" rather than the rule.
+1 for "There is no actual evidence for any of this." So many people misled by these ideas! Really nice way to sum it all up. Aug 27, 2017 at 2:51
Many attempts have been made to explain the appeal of oil on canvas art created by the Grand Masters. Many ponder that the charm is due in part to its distinctive composition and layout. Because of this, many photographers attempt to duplicate by copying their arrangements.
Many see this composition paralleling design found in nature such as the spirals seen in pine cones and shape of sea and snail shells. Looking about we can see many such natural spiral shapes in flowers and tree branches etc. Studied at length by mathematicians, they attempt to explain using number sequences, the appeal. Also some associate mystical qualities that add to the charm. Many say, there are no rules in art, you are free to follow your heart.