ローレンツ・アトラクタ：100万分の1の差で分かれる2本の軌道

Build an interactive browser visualization of the Lorenz system that shows sensitive dependence on initial conditions. Simulate two trajectories with identical equations, one starting at (1, 1, 1) and one with the x value nudged by one millionth, integrated with a fourth-order Runge-Kutta method and a small time step. Draw the x-z projection on a dark navy background as a butterfly-shaped attractor: faint full paths and bright recent segments, one trail in cyan and the other in coral, with glowing head dots. Add a headline reading that the starts are one millionth apart, labels for both starting points, a simulation-time readout and a large live counter of the three-dimensional separation. Let the viewer change the starting difference and scrub through time. Accelerate time and include a short caption saying these are numerical trajectories, not a forecast. Done means the two trails overlap at first, then visibly split, with the counter growing from tiny values to double digits.