DEREK - dynamical systems exploring 

Attractive attractors

 

   Attractor is a set towards which the trajectory of the dynamical system ( i.e., the curve representing the evolution (change) of the system in space, the elements of which are the various states of the system)  tends (approaching, attracting). The simplest example of such set is a point of this space. If the system over time approaching to a fixed (stationary) state, its trajectory tends to a point. Another example of an attractor is a limit cycle, i.e., closed curve. The system, which attractor is a limit cycle over time begins to make periodic oscillations. 

 

    More complex attractors can be observed in systems described by a system of ordinary differential equations of at least third-order ( and, moreover, nonlinear). Such attractors are called "strange" and they are the subject of serious study by mathematicians and physicists. 

 

    Besides purely scientific, in the study of dynamical systems is another aspect - aesthetic. The fact is that the image of complex attractors can be very beautiful, attractive and mysterious. The site ChaoticAtmospheres contains many interesting examples of attractors created by the  4D Cinema software (it should be understood that all the images are not attractors themselves, attractor is a set of points to which the trajectory coming closer and closer with unlimited time increases ). Attractors images that created by DEREK are certainly not so beautiful, but, nevertheless, they can be used to visualize the structure of attractor. DEREK can even help you to detect new beautiful attractors!