Lorenz Attractor

thingiverse

A 3-D rendering of the Lorenz attractor, by taking the parametric path going a few times around each loop and "thickening" to form a solid. The design starts in Sage, export to X3D (resulting file included), edit X3D in Blender (to remove some artifacts Sage leaves behind, like a cube of lines around the figure) and export to STL, import STL into Cura, scale (because graph units in Sage become millimeters in Cura) and situate figure on print platform, then export STL again to form the STL thing file here. Here is the Sage code to generate the figure: x,y,z,t=var('x,y,z,t') sigma=10 rho=28 beta=8/3 lorenz=[sigma*(y-x),x*(rho-z)-y,x*y-beta*z] s=desolve_system_rk4(lorenz,[x,y,z],ics=[0,0,1,21.5],ivar=t,end_points=10, step=0.05) sol=[[q[1],q[2],q[3]] for q in s] p=Graphics() p+=line3d(sol, thickness=27, corner_cutoff=0.05) p.show() Since Sage is Python-based, be sure to check line breaks. Note this uses built-in Runge-Kutta version of desolve() method. The result is a list of points giving a parametric representation of the solution curve, plotted here using line3d() with "thickness" large enough to make the figure appear solid.