Fractal forms

B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York, 1982 Fractals Form, Chance, arul Dimension, Freeman, New York, 1977. 

Mandlebroot, B.B., 1977. Fractals form, chance and dimension. San Francisco Freeman. 

Mandelbrot BB (1977) Fractals - form, chance, and determination. Freeman, San Francisco, CA... 

B. Mandelbrot, Fractals, Form, Chance and Dimension. W. H. Freeman, San Fransisco, 1977. 

Mandelbrot, B., Fractals Form, Chance, and Dimension, W.H. Freeman, San Francisco, 1977. 

Mandelbrot BB (1977) Fractals Form, chance and dimensions, Freeman WH, New York (1982) The fractal Geometry of Nature, Freeman WH, New York... 

Mandelbrot B B (1975) Les Objets Fractals Forme, Hasard et Dimension, Flammanon, Pans... 

C. E.Zair and E.Tosan Unified IFS-based model to Generate Smooth or Fractal Forms. pp345-354 in Surface Fitting and Multiresolution Methods (eds Le Mehaute, Rabut and Schumaker) Vanderbilt University Press 1997 ISBN 0-8265-1294-1... 

The success of fractal models applied to the physics of disordered media may be explained first of all by the fact that fractal forms are characteristic of a huge number of processes and structures because many diverse models of the formation and growth of disordered objects of disparate nature may ultimately be reduced to a transition model—namely a connected set and an unconnected set—and to a limited diffusive aggregation [1-6]. In the first case a fractal percolation cluster is formed in the second case a fractal aggregate is formed. 

Rogers, C.A. (1970). Hausdorff measures. Cambridge University Press, Cambridge. See also Mandelbrot, B.B. (1977). Fractals, form, chance and dimension. Freeman, San Francisco. 

Stapleton HI, Allen JP, Flynn CP, Stinson DG, Kurtz SR. 1980. Fractal form of proteins. Phys. Rev. Lett. 45 1456-1459. 

Data on the fractal forms of macromolecules, the existence of which is predetermined by thermodynamic nonequilibrium and by the presence of deterministic order, are considered. The limitations of the concept of polymer fractal (macromolecular coil), of the Vilgis concept and of the possibility of modelling in terms of the percolation theory and diffusion-limited irreversible aggregation are discussed. It is noted that not only macromolecular coils but also the segments of macromolecules between topological fixing points (crosslinks, entanglements) are stochastic fractals this is confirmed by the model of structure formation in a network polymer. 

The Eq. (182) at the condition /g=const=0.270 nm and C =const=10 is reduced to a purely fractal form, that is, to the Eq. (8) with 5=0.349. Let us note essential distinctions of the Eqs. (180) and (8). Firstly, if the first from the indicated equations takes into accoimt object mass only, then the second one uses elements number N of macromolecule, that is, takes into account dynamics of molecular structure change. Secondly, the Eq. (8) takes into account real structural state of macromolecule with the aid of its fractal dimension The indicated above factors appreciation defines correct description by the equation (8) the dependence of macromolecular coil gyration radius R on molecular weight MIT of polynner [235]. 

Kozlov, G. V. Dolbin, I. V. Zaikov, G. E. A fractal form of Mark-Kuhn-Houwink equation. In book New Perspectives in Chemistry and Biochemistry. Ed. Zaikov, G. New York, Nova Science Publishers, Inc. 2002, 41 7. 

Kozlov, G. V Dolbin, I. V. A fractal form of the Maik-Kuhn-Houwink equation. 

Mai NK, Fujiwara M, Tanaka Y, Taguchi T, Matsukata M (2003a) Chem Mater 15 3385-3394 Mai NK, Fujiwara M, Tanaka Y (2003b) Nature 421 350-353 Mandelbrot BB (1977) Fractals, form, and chance. Freeman, San Francisco Mandelbrot B (1982) The fractal geometry of nature. W.H.Freeman Co, New York Manzanoa M, Aina V, Arean CO, Balas F, Cauda V, Colilla M, Delgado MR, Vallet-Regi M (2008) Chem Eng J 137 30-37... 

Mandelbrot, B.B. (1975). Les Objets Fractals Forme, HasardetDimension. Flammarion, Paris. 

---