This is a community where INTJs can meet others with similar personalities and discuss a wide variety of both serious and casual topics. If you aren't an INTJ, you're welcome to join anyway if you would like to learn more about this personality type or participate in our discussions. Registration is free and will allow you to post messages, customize your account and use other features only available to our members.
Continued fractions have amazing properties. Every real number has a continued fraction expansion (many, actually), and they usually converge very rapidly. The theory is wonderful, and provides lots of opportunities for creating fascinating expressions.
I was thinking about that formula you posted that created sequential fractions, and I think Im starting to get what you said about it being like art. It really is. It occurred to me that your formula may be applicable in game coding in order to remove a number of constants that have to be coded manually.