Quote: Red John "Oooh, this is debateable. Fractals are difficult to define and understand - just like Super league squads beyond number 17 - but the common theme is self-replication. Do fractions of fractions exhibit self-replication? I don't believe they do. Self-replication implies infinite replication within a finite domain, while dividing a fraction by a fraction is the same as multiplying the top by the denominator of the bottom. As we are multiplying by a number greater than or equal to one, and doing it an infinite number of times, the result is infinite too.
Having achieved smug, I'm now aiming for ty.'"
There are some lovely fractal definitions of pi - with all sorts of intertwinings with e. The domain space for fractals can be considered as any field where multiplication is invertible - which is not necessarily infinite as you assumed! More a group whose binary operation is multiplication (which is a whole topic of algebraic topology - for this precise purpose) - and so long as the denominator is great than 1 (which can be assumed from the additive nature of denominators - that is the further into them you get, the closer to the limit of the fractal, yet the numbers are getting larger) were not multiplying numbers greater than one, limiting the co domain to a finite space ...
The maths might have gone a bit far agreed