Mathematical requirement for fractals? Implications for 1/f noise and climate.

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.

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2 Responses to Mathematical requirement for fractals? Implications for 1/f noise and climate.

  1. TinyCO2 says:

    Does it help to know this? I’m guessing that climate scientists assume the noise is just noise regardless of its nature and that there are some simple signals burried in the noise. This must in part ne true because we can clearly see regular patterns in the overall signal (eg ice ages).

    My pet thought is about the biggest signals of all, the solar trigger for those ice ages. Surely that should be the easiest to reconstruct but I’ve never seen a model output that mimics them. In fact, why don’t the ice ages look more like the insolation plot that they often show with the last 4 ice age temperature and CO2 plots? Why don’t the start when insolation is at its lowest and end when it reaches the peak? I’ve seen mixed reports about when the next ice age is due. Some say it’s overdue and we’re in line for a double interglacial. As that documentary pointed out, very small changes can create some very big effects (like the animal numbers). One simple equation can lead to infinite complexity where patterns an be seen but are hardly predictable without knowing the equation and the starting conditions. What about two or more equations. What if ice ages and bond events are like stripes an a zebra? They look regular but apart from the basic stripiness, they are completely unpredictable and every now and then the stripes significantly change width (Grevy’s zebra) or vanish or do something completely new.

    http://www.ispyanimals.com/2011/01/zebra-fun-black-zebras.html

    All this could mean that climate is impossible to model. The lack of success so far hints at that.

    • It was a sudden inspiration. When I looked at chaotic systems I couldn’t find any generalised way to determine what would and would not be a chaotic system.

      But looking at fractals, I read that they all involve feedback. And I hypothesised, it must be the feedback that makes a very simple system “obeying the laws of physcis” (like the climate) into one that is chaotic.

      Now, if I can understand how the feedbacks create a fractal – that may open the door to understanding what causes 1/f noise. And if I understand what causes 1/f noise and can prove it mathematically (some chance**), then I might be able to prove mathematically that the climate is 1/f noise and therefore what we see will have a mathematical proof that “it’s not man-made”.

      So, rather than saying “it looks like 1/f noise”, I suddenly realised that there might be a way to prove it’s 1/f noise by nature of the kind of feedbacks that operate in the climate.

      It’s a long shot – but whereas the catastrophists are able to argue black is white when interpreting the climate evidence (no warming = warming), they won’t have the same degree of freedom with a mathematical proof that the climate is chaotic fractal noise.

      **And by posting it – a mathematician might just read it and give me a helping nudge

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