where a$_{i}$ is the i th bit of string A , b$_{i}$ is the i th bit of string B , and | A | represents the length of both strings. In other words, d measures the fraction of bits that are different between A and B . For the Boolean case, d = 0 ⇐⇒ A = B and d = 1 ⇐⇒ A = ¬ B , while A and B are uncorrelated ⇐⇒ d ≈ 0 . 5. The normalized Hamming distance d can be used to measure homeostasis. If we focus on the information change produced by a process, d ( I$_{in}$, I$_{out}$ ) will measure how much change took place. Homeostasis H can be defined as the opposite: H = 1 − d ( I$_{in}$, I$_{out}$ ) . (9) A high H implies that there is no change, i.e. information is maintained. This occurs naturally in highly ordered systems (with a high S ), but is also desirable in complex systems (with a high C ). d and thus H are unitless measures. Homeostasis is closely related to sensitivity to initial conditions. A high sensitivity to initial conditions (uncorrelated H ) is a signature of chaotic dynamics, and can be formally measured with Lyapunov exponents (Gershenson, 2004a). A high H indicates stability. 3.1 Multi-scale measures To measure emergence, self-organization, complexity, and homeostasis at multiple scales, binary strings can be converted to different bases. If we take two bits, then we will have strings in base 4. If we take three bits, strings will have base 8. Taking b bits will give strings of base 2 $^{b}$. The information of strings can be normalized to [0 , 1] by dividing Shannon’s information by the number b of bits considered: I$_{b}$ = I/b. (10) Table 1 shows an example of a 32-bit string converted to different bases, each row repre- senting an order of magnitude difference (Salthe, In Press). Notice that I$_{b}$ seems to decrease 11