Figure 1.

Time series, attractor, bit image and example information calculation from bit-conditional PDFs of the x(t) in the Lorenz [17] model with initial condition uncertainty h=0.3. (a) A 25 time-unit sample of x(t) (black line) from the Lorenz attractor (b) together with perturbation x′(t) (grey line) resulting from a slight difference in the initial condition. (c) The floating point bits x_b(nΔt) that hold the numeric value of x at several time samples. (d) The information content of the sign bit for predicting the current state of x, I=1.00, is obtained from the difference in entropy H between the unconditional PDF p(x) and the weighted average of the PDFs conditioned on the true–false value of the sign bit p(x|x_b=1(τ=0)=1,0).