Rucklidge Attractor

thingiverse

Taylor Fountain MATH 401 - Math with 3D Printing George Mason University A strange attractor is an attractor of a dynamical system (ie. the set of values that a dynamical system tends towards) that takes on a fractal structure, which is usually indicative of the system being chaotic. A chaotic system is a dynamical system that exhibits sensitive dependance on initial conditions, and it's attractors can be subclassed as chaotic attractors: sets of values that towards which the system exhibits global stability, despite it's arbitrary pieces exhibiting instability. One such strange attractor is the Rucklidge model, which is the dynamical system described by the set of equations: dx/dt = -kx+ly-yz dy/dt = x dz/dt = -z+y^2 This system exhibits chaotic behavior where k=2 and l=6.7, with initial conditions (x0,y0,z0) = (1, 0, 4.5). To construct a 3D object of this system, I input the system into Mathematica (see attached file), evaluated the system with the initial conditions up to an a certain time timelenghta, re-evaluated with the initial conditions being the value of the system at t = timelengtha, and then plotted the interpolated functions in 3-space. After scaling, thickening, and creating the base, the file was then exported as the STL attached. This object was printed on the Makerbot Replicator 5th Generation. The first attempt at printing resulted in a size smaller than what was required, so the model was redesigned so that minimal rescaling would be needed in the slicer. The print required supports and rafts, and printed with no issues in 3hr and 35min. https://search-proquest-com.mutex.gmu.edu/docview/2259455417/B833C5AAF7724110PQ/ https://en.wikipedia.org/wiki/Attractor#Strange_attractor