By Sergio Albeverio (auth.), Prof. Dr. Gabriele A. Losa, Prof. Dr. Danilo Merlini, Prof. Dr. Theo F. Nonnenmacher, Prof. Dr. Ewald R. Weibel (eds.)
"Fractals in Biology and drugs, quantity 2" explores the potential for the fractal geometry in knowing the right way to examine common shapes. the quantity devotes distinct emphasis to the complicated box of human tumours.
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Additional info for Fractals in Biology and Medicine
Here we consider error-free deterministic systems where the state of the dynamical system at time t is entirely predetermined by the initial state (Xl (0), X2(0), ... ,xn(O)). A trajectory is obtained by connecting the points in phase space according to their sequence in time. Every trajectory represents another realization of the dynamical system. The concept of deterministic chaos denotes dynamical systems with sensitive dependence on initial conditions, 52 T. Mattfeldt due to exponential divergence of nearby trajectories.
C & F. 24, respectively. expectation, namely that structures of low variability have low L, while those with high structural variation have high Ls. It should be apparent, however, that holes or gaps do not appear to be an important feature related to lacunarity examined here, since images of low (Fig. 10 C and D) and high (Fig. 10 I and J) lacunarity can have large holes. Thus, «lacunarity» would appear to be a misnomer, but we are probably stuck with the term because of historical precedence.
Biological Cellular Morphometry-Fractal Dimensions, ... Nonuniform niform B 45 : ~III )loll III ,. ,. i c " ,. I)hUMt~r D Fig. 14 A. 9, uniformly (uniform) and nonuniformly (nonuniform). B. Log pixel counts vs. log diameter for two images. C. Log partition fUllction vs. log diameter for two images. D. Generalized fractal dimension D(q)s vs. q plots . Vertical lines in 0 indicate error bars (95% confidence level). See text. The generalized sandbox method is the one we have followed with our data.