Rucklidge Attractor

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Taylor Fountain MATH 401 - Math with 3D Printing George Mason University A dynamical system's attractor is a set of values that it tends towards, and a strange attractor exhibits a fractal structure, often indicating chaotic behavior. Chaotic systems are characterized by sensitive dependence on initial conditions, and their attractors can be subclassified as chaotic attractors - sets of values towards which the system exhibits global stability despite exhibiting instability in its individual parts. One such strange attractor is the Rucklidge model, described by the set of equations: dx/dt = -kx + ly - yz dy/dt = x dz/dt = -z + y^2 This system exhibits chaotic behavior when k=2 and l=6.7, with initial conditions (x0,y0,z0) = (1, 0, 4.5). To create a 3D object of this system, I input the system into Mathematica, evaluated it up to a certain time length, re-evaluated with the initial conditions being the value of the system at t = timelength, and plotted the interpolated functions in 3-space. After scaling, thickening, and creating the base, the file was then exported as STL. This object was printed on the Makerbot Replicator 5th Generation. The first attempt at printing resulted in a size smaller than required, so the model was redesigned for minimal rescaling in the slicer. The print required supports and rafts, and it printed without issues in 3 hours and 35 minutes. https://search-proquest-com.mutex.gmu.edu/docview/2259455417/B833C5AAF7724110PQ/ https://en.wikipedia.org/wiki/Attractor#Strange_attractor