150,000 particles trace paths through Thomas' cyclically symmetric attractor, a chaotic system defined by three coupled differential equations involving sine functions. The system has cyclic symmetry: each variable's equation has the same form, rotated through the triple (x, y, z). This symmetry gives the attractor its characteristic three-lobed structure. Each particle integrates the ODE via fourth-order Runge-Kutta, producing smooth trajectories that never repeat.
The damping parameter b controls how "tight" the orbits are. At higher b values, the system settles into a simple limit cycle. As b decreases toward zero, the attractor transitions through increasingly complex chaotic behavior: orbits wander further before folding back, loops multiply, and the structure fills more of phase space. The value used here sits in the chaotic regime where trajectories are bounded but aperiodic.
Fourth-order Runge-Kutta is essential because cheaper integrators (Euler, midpoint) accumulate error fast enough to push particles off the attractor entirely. RK4 evaluates the derivative four times per step and combines them with specific weights, keeping trajectories faithful to the true dynamics over thousands of frames.
Particles are born near the attractor's center and die after a few seconds, fading in and out to create ghostly trails. A slow background fade preserves recent history. The 3D structure is projected through a rotating camera you control with your mouse. Additive blending reveals density where orbits converge, making the attractor's invariant measure visible as brightness.
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