measured in bits, the units of C are also bits. C can be interpreted as how much information is reduced ( S ) multiplied by the information production ratio (E). Considering the previous simplification of I$_{in}$ = 1, we can represent complexity in terms of I$_{out}$ : C = a · I$_{out}$ (1 − I$_{out}$ ) , (7) where a is a normalizing constant. For the Boolean case, since I ∈ [0 , 1], a = 4 will bound C ∈ [0 , 1]. An illustration of the simplified versions of E , S , and C (equations 3, 5, and 7) can be seen in Figure 2. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 P(x) I(X) E S C Figure 2: Emergence E , self-organization S , and complexity C of a binary string X for different probabilities P ( x ), considering random inputs ( I$_{in}$ = 1). The Hamming distance d measures the percentage of different bits or symbols in two strings, say A and B , of the same length ( | A | = | B | ). For binary strings, it can be calculated with the XOR function ( ⊕ ). Its normalization bounds the Hamming distance to the interval [0 , 1]: d ( A, B ) = ∑ i ∈ [0 .. | A | $_{]}$a$_{i}$ ⊕ b$_{i}$ | A | , (8) 10