The standard map

Drag K. While it is small, ivory invariant curves run right across the picture and the gold chaos is only thin bands between them. Click to release an orbit from that point; click somewhere else and the earlier ones (up to five) stay behind in ice-blue for comparison. The corner follows its momentum p step by step, without wrapping it round every 2π as the picture does: as long as some curve still runs across, the orbit is penned between two of them. Past K ≈ 0.9716 the last one breaks, and an orbit in the chaos can drift off, 2π after 2π. Just above that value the drift can be slow; at K = 2 it is plain to see.