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Thomas' Cyclically Symmetric Attractor
ẋ=sin(y)−bx · ẏ=sin(z)−by · ż=sin(x)−bz · drag to rotate
Parameters
Damping b:
0.208
Trail length:
3000
Num. particles:
5
Speed:
1.0×
Restart trajectories
Thomas' system
(René Thomas, 1999):
ẋ = sin(y) − b·x
ẏ = sin(z) − b·y
ż = sin(x) − b·z
Cyclic symmetry:
invariant under (x,y,z)→(y,z,x). Attractor looks the same rotated 120° around the (1,1,1) axis.
b≈0.208:
chaotic.
b≈0.32:
periodic.
b>0.4:
fixed point (origin).