Labyrinth chaos: Revisiting the elegant, chaotic, and hyperchaotic walks.

Labyrinth chaos was discovered by Otto Rössler and René Thomas in their endeavor to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we celebrate their discovery by considering a single labyrinth walk system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behavior, reminiscent of chimera-like states, a peculiar synchronization phenomenon. We discuss the properties of the single labyrinth walk system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, which amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walk system by showing that even though it is volume-preserving, it is not force-conservative.