FRACLAB Functions |
![]() ![]() |
Generates a pre-multifractal stochastic 2D measure related to Multinomial Measure
MES = multinomstoc2d(BASE,S)
MES = multinomstoc2d(...,'Method')
MES = multinomstoc2d(BASE,S) Generates the pre-multifractal stochastic 2D measure, MES, using a base of the multinomial, BASE, and a number of scales, S. The parameters BASE and S are positive integers not smaller than 2 and BASE must be a (X,Y) vector
The matrix size, [N1,N2], of the generated signal is defined by the base value and the number of scales : [N1 N2] = (BASE(X)*BASE(Y)).^S |
MES = multinomstoc2d(...,'Method') Generates the pre-multifractal stochastic 2D measure, MES, using a specific method. The supported Methods can be choosen from the list below :
Specifier | Method Type | |
---|---|---|
'unifmeas' | Synthesize a multinomial 2D measure with uniformly distributed weights (default) | |
'pertmeas' | Synthesize a multinomial 2D measure with log normaly distributed weights and using a standard deviation, s. | |
'shufmeas' | Synthesize a shuffled multinomial 2D measure using a vector VP containing the weight coefficients.
| |
'pertmeas' | Synthesize a perturbated multinomial 2D measure using a vector VP containing the weight coefficients and a perturbation parameter, e.
The paramater e is a positive real lower than the smallest weigth coefficient |
B = [2,2]; S = 8;
x = multinomstoc2d(B,S);
figure; imagesc(x);
title('Pre-multifractal 2D measure with uniform law');
B = [2,2]; S = 8;
x = multinomstoc2d(B,S,'pertmeas',{[0.1 0.2;0.3 0.4] 0.05});
figure; imagesc(x);
title('Perturbated pre-multifractal 2D measure');
[1] Carl J. G. Evertsz and Benoit B. MandelBrot, "Multifractal Measures", Chaos and Fractals, New Frontiers of Science, Appendix B,
Peitgen, Juergens and Saupe, Springer Verlag, Springer Verlag (1992) 921-953.
[2] Benoit B. MandelBrot, "A class of Multinomial Multifractal Measures with negative (latent) values for the 'Dimension' f(alpha)",
Fractals' Physical Origins and Properties, Proceeding of the Eric Meeting, 1988, L. Pietronero, Plenum Press, New York (1989) 3-29.
[3] Benoit B. MandelBrot, "Limit Lognormal Multifractal Measures", Frontiers of Physics, Landau Memorial Conference, Proceeding of Tel-Aviv Meeting, 1988
Errol Asher Gotsman, Yuval Ne'eman and Alexander Voronoi, New York Pergamon (1990) 309-340.
![]() |
multinomstoc | normalize_list | ![]() |