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The webcam + monitor loop demonstrates a recursive "Droste effect" http://en.wikipedia.org/wiki/Droste_effect#mediaviewer/File:Droste.jpg which the Wikipedia article describes as a visual example of a "strange loop", a self-referential system of geometry instancing. The resulting still image has self-similarity http://en.wikipedia.org/wiki/Self_similarity ...


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How far ahead can we predict solar and lunar eclipses? NASA has uncertainty calculations that show how certain we are about when eclipses happen. From a back of the envelope, the eclipses will likely vary by a full day 35 thousand years from now. That said, we have eclipse seasons, so we know eclipses will continue to happen, and at roughly which time of ...


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On predicting planetary orbits A number of studies have shown that the inner solar system is chaotic, with a Lyapunov time scale of about 5 million years. This 5 million year time scale means that while one can somewhat reasonably create a planetary ephemeris (a time-based catalog of where the planets were / will be) that spans from 10 million years into ...


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Look I know link only answers are terrible, but I don't want to ruin the surprise. Check out this link. That's on Wikipedia! It's safe to say that if wikipedia knows something, the experts know quite a bit more. We know the dynamics of the Sun-Earth-Moon system really well including the perturbations and the most likely sources of future upsets, so barring ...


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Given that we exist at all, we can confidently back-track the positions of the planets (and our moon) for a couple billion years. I see no reason, barring rather massive exo-system-sourced objects showing up unexpectedly, that the positions will go chaotic enough to be unpredictable any time in the next couple billion years. I suppose it might depend a bit ...


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Classical physics is developed based on this idea that understanding of a phenomenon will help in predicting the future and the past of a system. It actually works on the prejudice that quantities which are measurable can be measured with utmost accuracy by developing better methodology for experiments. So, the based on classical physics i.e.ignoring the ...


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The answer to your question is yes, the logistic map definitely has an attractor. To show this for general maps/dynamical systems, we can use a direct numerical study, delve into analytical arguments which might not be entirely complete, or a combination of both. An attractor is a set in the phase space of the dynamical system or map which attracts a ...


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While I am not familiar with signal processing, the question of the 1-to-1 mapping may be easy to answer - assuming your alphabet of symbols is finite. Suppose your symbol alphabet is $A = \{ a_0, a_1, \dots , a_{n-1} \} $. First define a mapping $$ f : A \rightarrow \mathbb \{ 0, 1, \dots (n-1) \} : f(a_i) \mapsto i.$$ Then for a sequence of symbols $$b = ...


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It has been shown by Eichhorn, Linz and Hänggi in 2000 that the numerical values of Lyapunov exponents are invariant under any invertible variable transform. This is just a reformulation of the fact that they are metric invariant, because the authors presume the norm $|\cdot|$ to be an arbitrary norm in the given coordinates - just it's basic properties such ...



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