Figure 2 | Scientific Reports

Figure 2

From: Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems

Figure 2

Illustrations of the time evolution of a standard ECA (left) and of a Case I state-dependent CA (right). ECA evolve according to a fixed update rule (here Rule 30), with the same rule implemented at each time step. In an ECA rule table, the cell representation of all possible binary ordered triplets is shown in the top row, with the cell representation of the corresponding mapping arising from Rule 30 shown below. Rule 30 therefore has the binary representation 00011110. In a Case I CA (right), the environment subsystem e evolves exactly like an ECA with a fixed rule. The organism subsystem o, by contrast, updates its rule at each time-step depending on its rule at the previous time-step, its own state (green arrows) and the state of e (red arrows). The new rule for o is then implemented to update the state of o (blue arrows). The rules are therefore time-dependent in a manner that is a function of the states of o and e and the past history of o (through the dependence on the rule at the previous time-step).

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