Chaotic Attractors

thingiverse

Fernanda Garcia CamargoMATH 401 - GMU Mathematics Through 3D Printing Chaotic attractors are sets of states that a system can be in, but the exact state that the system will be in is unpredictable, even if we know the system's current state and the equations that govern it. This is because any small change in the initial state of the system can lead to a large difference in the system's state over time. Chaotic attractors are found in many different systems, including the weather, the stock market, and even the human heart. They are a fascinating example of how complex behavior can emerge from simple deterministic systems. This week assignment is about The Lorenz Chaotic Attractor. It is a set of differential equations originally studied by Edward Lorenz in 1963. The Lorenz Attractor is a three-dimensional object whose body plan resembles a butterfly. The equations that describe the Lorenz system are:dx/dt =σ(y−x)dy/dt=x(ρ−z)−ydz/dt=xy−βz The most common used values for these parameters are: σ=10, ρ=28, β=8/3. I decided to use for my project: σ=13, ρ=30, β=2. I wanted one side to be smaller than the other side. The code was made using Mathematica. My 3D print of the Lorenz Chaotic Attractor took approximately two hours and was done at a temperature of 215°C. Although I used supports, I later realized the design should have been thicker. Unfortunately, the model broke when I attempted to remove the supports. I plan on revisiting the print with a thicker design, then I will share the outcome here.