Fractal PhysiologySpringer, 27.5.2013 - 384 sivua I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales. |
Sisältö
3 | |
11 | |
1 | 45 |
6 | 62 |
6 | 106 |
A Fractal Time Sequence | 177 |
Fractals in Nerve and Muscle | 210 |
Works Cited | 328 |
355 | |
Muita painoksia - Näytä kaikki
Fractal Physiology James B. Bassingthwaighte,Larry S. Liebovitch,Bruce J. West Rajoitettu esikatselu - 1994 |
Yleiset termit ja lausekkeet
action potentials algorithm analysis analyzed attractor average Bassingthwaighte behavior branching cells channel protein chaos coefficient complex correlation correlation dimension curve data set described determine deterministic diameter distribution dynamical effective kinetic rate embedding energy barriers equation estimates example exponent exponential Fano factor Figure flow fluctuations fractal dimension fractal model fractal relationship fractal scaling frequency growth heart heterogeneity histograms Hurst intervals inverse power law ion channel iteration Julia sets kinetic rate constant left panel length log-log logarithm Lyapunov exponents Mandelbrot Mandelbrot set mathematical mean measured membrane method neighbors neurons noise nonlinear observed open and closed parameters patterns phase plane phase space set physiological pieces pixels plot power law probability density function processes properties r₁ range recursion regions relative dispersion rescaled range Right panel self-similarity shown in Fig signal slope spatial statistical structure surface teff tissue two-dimensional values variables variance variation vascular versus