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 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 5th 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.
; see Figure 2 for the Mathematica code. After plotting the system, I exported the file and rendered it in Makerbot Desktop, using a Makerbot 5th 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.
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