(Page 1109h) Notes for: The Notion of Computation | The Phenomenon of Universality History of universality In Greek times it was noted as a philosophical matter that any ...

(Page 1186a) Notes for: The Principle of Computational Equivalence | Intelligence in the Universe Properties [of doubling rules] The number of steps increases irregularly but ...

(Page 0109) For when one deals with systems in nature it is normally impossible to set up or measure them with perfect precision -- and indeed it can be a challenge even to ...

(Page 0300) A crucial feature of these rules, however, is that they make the system behave in a way that depends sensitively on the details of its initial conditions. In the ...

(Page 0437) How can one now tell that such systems are reversible? It is no longer true that their evolution leads only to simple transformations of the initial conditions. ...

(Page 0782) In the early 1900s it was widely believed that this would effectively be the case in all reasonable mathematical axiom systems. For at the time there seemed to be ...

(Page 0206) But in both these cases it turns out to be not too long before these fluctuations essentially repeat. The picture below shows an example where a larger amount of ...

(Page 0325) [No text on this page] Captions on this page: The effects of various levels of external randomness on the behavior of continuous cellular automata with ...

(Page 0511) [No text on this page] Captions on this page: Examples of the evolution of networks in which a single cluster of nodes is replaced at each step according to the ...

(Page 0618) [No text on this page] Captions on this page: Minimal Boolean expression representations for the results of steps 1 through 5 in the evolution of three elementary ...