I agree with @James Camacho, at least intuitively, that stickiness in the space of observations is equivalent to switchiness in the space of their prefix XORs and vice versa. Also, I tried to replicate, and didn’t observe the mentioned effect, so maybe one of us has a bug in the simulation.
Mathematica notebook is here! Link in the full paper.
How did you define Switchy and Sticky? It needs to be >= 2-steps, i.e. the following matrices won’t exhibit the effect. So it won’t appear if they are eg
Switchy = (0.4, 0.6; 0.6, 0.4)
Sticky = (0.6,0.4; 0.4,0.6)
But it WILL appear if they build up to (say) 60%-shiftiness over two steps. Eg:
I agree with @James Camacho, at least intuitively, that stickiness in the space of observations is equivalent to switchiness in the space of their prefix XORs and vice versa. Also, I tried to replicate, and didn’t observe the mentioned effect, so maybe one of us has a bug in the simulation.
Mathematica notebook is here! Link in the full paper.
How did you define Switchy and Sticky? It needs to be >= 2-steps, i.e. the following matrices won’t exhibit the effect. So it won’t appear if they are eg
Switchy = (0.4, 0.6; 0.6, 0.4)
Sticky = (0.6,0.4; 0.4,0.6)
But it WILL appear if they build up to (say) 60%-shiftiness over two steps. Eg:
Switchy = (0.4, 0 ,0.6, 0; 0.45, 0, 0.55, 0; 0, 0.55, 0, 0.45, 0, 0.6, 0, 0.4)
Sticky = (0.6, 0 ,0.4, 0; 0.55, 0, 0.45, 0; 0, 0.45, 0, 0.55, 0, 0.4, 0, 0.6)