# A Few Animations (Using MATLAB):

**psd2.mp4:** Power spectrum of logistic map for alpha varying from 3.5 to 4 (1"05').

**psd1.mp4:** Power spectrum of logistic map for alpha varying from 3.35 to 3.575, lobes (1"56').

**medio.mp4:** Chaotic Dynamics resulting from Delay model & May eq. for alpha varying from 3 to 5 (see Medio). (1"39'):

**Ushape.mp4:** Natural measure of probability, u-shape convergence. (6').

**logmapDyn.mp4:** Basic dynamic of logistic map for alpha=3,...,4 (observe the revolution of points around a virtual axis). (1"06').

**genus1m.mp4:** Genus-1 (torus) whose radii change. The trajectory of point on the torus surface follows of course the radii changes. (4')

**fBM1.mp4:** Here are three histograms:

**(1)** Histogram of (pseudo) fract. Brownian motion,

**(2)** Histogram of its 1st-differences,

**(3)** Histogram of its 2nd-differences,

whose hurst exponent evolves H = 0.2,..., 1. (53').

**Walk2D.mp4:** Walk of a (pseudo) fractional Brownian motion for H=0.53 in a plane with 10000 steps. Observe the loops and the way in which the plane is
blackened by the walk of the fractional brownian motion.**11minutes** (11''06').

**Walk3D.mp4:** Walk of a (pseudo) fract. Brownian motion for H=0.5 in a 3-dimensional Euclidean space with 10000 steps. Observe the loops and the way in which the volume is
blackened by the fractional brownian motion walk.**11minutes** (11'')