% Digital simulation of the walk in a plane (or in three-dimensional space) % of a (pseudo) fractional brownian motion by using the % function fBr = makebrownian(n,H,par) with: % % Inputs % n signal length % H base of digits in expansion % par optional, degree of extension in algorithm, default =8. % Outputs % fBr (pseudo) Fractional Brownian signal % % Description % Uses a Frequency Domain algorithm to get a pseudo Brownian Motion % The law is NOT normalized to give unit variance to unit increments t=10000; H=0.5; fBr1 = makebrownian(t,H); fBr2 = makebrownian(t,H); %fBr3 = makebrownian(t,H); for tn=1:1:t; a1=fBr1(1:tn); b2=fBr2(1:tn); %c3=fBr3(1:tn); Mi1=min(fBr1); Mi2=min(fBr2); %Mi3=min(fBr3); Mx1=max(fBr1); Mx2=max(fBr2); %Mx3=max(fBr3); pause(0.00000001) l1=plot(a1,b2,'b'); %l1=plot3(a1,b2,c3,'b'); title('Brownian Motion for a Hurst exponent h=0.5'); axis([Mi1 Mx1 Mi2 Mx2]); axis('off'); %axis([Mi1 Mx1 Mi2 Mx2 Mi3 Mx3]);box; end % "Complex and Chaotic Nonlinear Dynamics. % Advances in Economics and Finance, % Mathematics and Statistics" % T.Vialar, Springer 2009. % Copyright(c).