Fractal systems all have feedbacks. They all have infinite self-similar states at different scale. As such it seems the fractal nature is caused by the feedback. Therefore I suggest that if P is the probability function of a system describing all these self-similarities. For a fractal system, the feedback must be such that the in general the probability function itself is in some sense fractal with the result that the feedback causes the number of self-similar states to increase whilst the probability of each self-similarity state. The result is that the feedback, tends to increase the information content (proportional to -ln(p)) so that it tends to infinity.
Applying this to 1/f type noise as is often seen in the climate ( see Global Warming disproved: Bad posts, CET, Antarctic Ice and Fractal Noise), As 1/f noise appears in general to be fractal, then it appears only necessary to show that the complexity of the system and self-similarity increases due to feedbacks to show that they are fractal noise.
Or conversely, it may be that 1/f type noise (which no one seems to know how it originates) is a system where the feedback increases the number of self-similar states or put another way, each feedback increases the complexity and information of the system.
This is in contrast to white noise which is seen to be due to physical processes such as the discrete nature of electrons or nuclear decay. So 1/f type noise, may not be the result of physical properties as such, but the result of certain types of feedback mechanisms which create chaos of this form.