All animations and still images here bellow were generated with help of VRA .


SOFTWARE : original software "VRA", v.4.2

AUTHOR: Eugene Kononov, W.Springfield, MA 01089, USA,



   "Vasarely look" of Lorenz Attractor
Visual Recurrence Analysis (VRA) for Windows 95, 98 and NT is a software package for topological analysis, qualitative and quantitative assessment, and nonparametric prediction of nonlinear/chaotic time series. It can detect hidden patterns and determinism in time series using a graphical device known as the recurrence plot. VRA first expands a given one-dimensional time series into a higher-dimensional space, in which the dynamics of the underlying generator takes place. VRA then constructs a recurrence plot, which is essentially a graphical representation of the correlation integral in such a way so that the time dependence in the system under study is preserved.

Examples: Lorenz Attractor

   "Vasarely look" of Lorenz Attractor
Sine Wave

Sine With Noise

Human Electrocardiogram

Sound Balrina.wav

Dow Jones

   Sine Data      
The following data examples are also included with VRA:

Far-Infrared-Laser in a chaotic state (5000 data points);
Sun spots activity, annually 1700-1979, (280 data points);
A fragment from Beethoven’s 5th symphony (381624 data points);
Logistic difference equation, chaotic region (1000 data points);
Ikeda attractor;
Brownian motion, integrated white noise process, (1000 data points);
DNA code for Human Immunodeficiency Virus (HIV)
(1=A, 2=C, 3=G, 4=T) (9770 points);


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