Lorenz Attractor: Multiple Particles (Segmented Trajectories)

This example visualizes how the Lorenz attractor generates complex motion in state space by evolving multiple particles in parallel. By connecting successive computed positions with many line segments, it reveals the characteristic folded, self-similar structure of an attractor and illustrates chaos via sensitivity to initial conditions (multiple nearby starts produce distinct but structured paths). The key mathematical ideas are differential equations (the Lorenz system), attractors/trajectory geometry (locus), and dynamical behavior under continuous-time evolution. Construction is based on repeatedly drawing segments using GeoGebra’s “Segment” command for many coordinate triples (objects such as a, b, c and sets like A1/B1/C1…K1, A2/B2/C2…F2, up through A6/B6/C6…F6), producing segmented 3D trajectories for each particle. Suitable for high school advanced study and undergraduate calculus/ODE classes, as well as for workshops on dynamical systems and scientific visualization.