The Rossler Attractor

Jonathan Tarr

The Rossler Attractor

The point of this project was to study both attractors, a concept in dynamical systems that looks at points in space that “pull” all other points towards themselves within a given system, and the chaotic behavior of said systems, despite it being deterministic, i.e. the initial conditions determine all future conditions. In these cases, the system does not exhibit an orbit, a repeated pattern, but does not diverge to infinity, i.e. continually grow larger (or smaller) and is called chaotic.

I chose to look specifically at the Rossler Attractor for my system. This system exhibiting chaotic behavior was created in 1976 by Otto Rossler in order to simplistically model another famous attractor, the Lorenz Attractor. It consists of two fixed point attractors, one on the x, y plane, creating a spiral with orbit-like behavior, and another in the z-dimension, causing a twist and uplift of the system towards it.

Figure1: The Rossler System    

The Rossler Attractor is generated by the system shown in figure one, with the most famous systems being: a=0.2, b=0.2, c = 5.7    having been studied by Rossler himself, and a=0.1, b=0.1, c = 14 , which is Figure1: The Rossler System   used for the modern modeling of the system.

The Rossler Attractor I chose to model was created using the above system by assigning the following values to the following variables: a=0.1, b=0.1, c = 10
 ; see Figure 2 for the Mathematica code. After plotting the system, I exported the file and rendered it in Makerbot Desktop, using a Makerbot 5^th generation 3-D printer, Figure 3, to print out my 3-D model. Figure 4 is the printed model after cleaning; it took just under four hours to print.

Figure 2: My Mathematica code for generating a Rossler Attractor.