Figure 3

Graphical comparison of proposed CGR generalization (right, Equation 2) with previously proposed generalization in reference (left, Equation 1). The points in each image represent a 10,000-long uniformly distributed random sequence of n units. The gray circles involve the corresponding polygons, dark gray for 1^st order Markov transition and light gray for 2^nd order. In the proposed generalization (right), the polygons do not overlap but the evolving circles may. On the contrary, in the reference generalization in reference (left), the circles do not ever overlap. The desired bijective property of the iterative function is satisfied by both solutions.